【劳特里奇哲学导读】维特根斯坦的《逻辑哲学论》

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\nRoutledgePhilosophyGuideBooktoWittgensteinandtheTractatusLudwigWittgensteinisthemostinfluentialphilosopherofthetwentiethcentury.TheTractatusLogicoPhilosophicusisarguablyhismostwidelyreadworkyetremainsoneofthemostcrypticandcontroversialphilosophybookseverwritten.Withitsprofoundinsightsintothenatureoflanguage,realityandrepresentationithasinspirednotonlyphilosophersbutalsowritersandmusicians.WittgensteinandtheTractatusintroducesandassesses:•Wittgenstein’slifeandthebackgroundtotheTractatus•theideasandtextoftheTractatus•thecontinuingimportanceofWittgenstein’sworktophilosophytoday.Amuch-neededguidetoawidelystudiedtext,TheRoutledgePhilosophyGuideBooktoWittgensteinandtheTractatusisessentialreadingforallstudentsofWittgenstein,philosophyoflanguageandmetaphysics.MichaelMorrisisProfessorofPhilosophyattheUniversityofSussex.\n\nRoutledgePhilosophyGuideBooktoWittgensteinandtheTractatusLogico-PhilosophicusMichaelMorris\nFirstpublished2008byRoutledge2ParkSquare,MiltonPark,Abingdon,Oxon,OX144RNSimultaneouslypublishedintheUSAandCanadabyRoutledge270MadisonAve,NewYork,NY10016ThiseditionpublishedintheTaylor&Francise-Library,2008.“TopurchaseyourowncopyofthisoranyofTaylor&FrancisorRoutledge’scollectionofthousandsofeBookspleasegotowww.eBookstore.tandf.co.uk.”RoutledgeisanimprintoftheTaylor&FrancisGroup,aninformabusiness©2008MichaelMorrisAllrightsreserved.Nopartofthisbookmaybereprintedorreproducedorutilisedinanyformorbyanyelectronic,mechanical,orothermeans,nowknownorhereafterinvented,includingphotocopyingandrecording,orinanyinformationstorageorretrievalsystem,withoutpermissioninwritingfromthepublishers.BritishLibraryCataloguinginPublicationDataAcataloguerecordforthisbookisavailablefromtheBritishLibraryLibraryofCongressCataloginginPublicationDataAcatalogrecordforthisbookhasbeenrequestedISBN0-203-00309-8Mastere-bookISBNISBN13:978-0-415-35721-0(hbk)ISBN13:978-0-415-35722-7(pbk)ISBN13:978-0-203-00309-1(ebk)\nCONTENTSPrefaceviIntroduction11Thenatureoftheworld212ThelegacyofFregeandRussell593Thegeneraltheoryofrepresentation1144Sentencesasmodels1435Logicandcompoundsentences2036Solipsism,idealism,andrealism2637Metaphysics,ethics,andthelimitsofphilosophy309Appendix:Thesubstanceargument355Notes364Bibliography385IndexofpassagesinTheTractatus393Generalindex398\nPREFACEThisbookderivesultimatelyfromsomelecturehandoutswhichIproducedwhenIﬁrsttaughttheTractatusinanundergraduatecourse.MyfriendJulianDoddandIhadtheideaofputtingthesehandoutstogetherwithsomethingshewasinterestedin—aboutthenotionoftruth,andaboutrecentinterpretationsoftheTractatus—toformabook.Withthisinmind,weworkedtogetheronapaperontheapparentparadoxoftheTractatus(MorrisandDodd2008),whosemainpointsappearintheﬁnalchapterofthisbook.Intheend,however,otherphilosophicalcommitmentstookJulianawayfromthisproject,andthatpaperwastheonlythingwewrotetogether.Thatmeansthateverythinginthisbook,apartfromthosepartsoftheﬁnalchapterwhichderivefromourjointpaper,issolelymyresponsibility.Iam,however,extremelygratefultoJulianforhisencouragementinthewritingofthisbook,aswellasforhispartinprodu-cingthatjointpaper.Largethanksarealsoduetoanumberofpeopleforthingstheyhavesaidinconversation,bymeansofwhichtheyhavehelpedmemorethanthey,perhaps,everrealized.AmongtheseIwouldliketomentionthefollowingpeopleinparti-cular:LeoCheung,RichardGaskin,AndreasGeorgallides,WarrenGoldfarb,ColinJohnston,MarieMcGinn,AdrianMoore,MichaelPotter,ThomasRicketts,TanjaStaehler,RogerWhite,andJoséZalabardo.PeterSullivanreadthepenultimatedraftofthewholebook,andmadealargenumberofveryhelpfulcommentsandsuggestionswhichsavedmefromseveralerrorsandledmetounderstandtheTractatusbetter:Iamenormouslygratefultohim.Finally,IwouldliketothankGemmaDunnatRoutledge,forhertoleranceandhelpinseeingtheprojectthrough.\nINTRODUCTION1THEWORKANDITSHISTORYWittgenstein’sTractatusLogico-Philosophicusisoneofthegreatphilosophicalworksofthetwentiethcentury.Fortherangeofitsconcernsandthedepthofitsthoughtitsclosestcompanionsaretwounﬁnishedworks:Heidegger’sBeingandTime,andWittgenstein’sownPhilosophicalInvestigations.ButeveninthiscompanytheTractatuslookseccentric.Itisveryshort,andwritteninastylewhichisatleastepigram-matic.Thecharacteroftheworkisareﬂectionofthenatureofthemanwhowroteit,andofhiscastofmindwhenhewroteit.LudwigWittgensteinwasborninAustriain1889,intooneofthewealthiestfamiliesinEurope.Hisupbringingwasoneofenormousprivilege,butalsodeeplycultured,anditbroughtwithitanintensityofexpectationwhichwasnoteasytolivewith(twoofhisbrotherscommittedsuicidewhileWittgensteinwasstillaboy).Afterschool,hebegantostudyengineering,ﬁrstinBerlinandtheninManchester.WhileinManchesterhedevelopedaninterestinmathematics,\n2INTRODUCTIONandtheninthefoundationsofmathematics.Hereadtwoground-breakingworksinthefoundationsofmathematics,whichhadthenonlyrecentlybeenpublished:BertrandRussell’searlywork,ThePrinciplesofMathematics,andGottlobFrege’smore-or-lesscontemporaryGrundgesetzederArithmetik(BasicLawsofArithmetic),whichattemptstoshowthatarithmeticrestsonnothingmorethanlogic.In1911hevisitedFregeinJena,whorecommendedthathestudyunderRussellinCambridge.BythistimeRussell’sviewshaddevelopedandchanged.Hehadjustpublished,withAlfredNorthWhitehead,themonumentalPrincipiaMathematica,whichdevelopsthegeneralviewofFrege’sGrundgesetzeinenormousdetailandwithgreattechnicalsophistication—muchofwhichwasneededtocircumventacontradictionwhichRussellhadfoundinFrege’ssystem.Russellwasatthistimethegreatﬁgureincontemporarylogic,but,byhisownaccount,wornoutfromhisworkonPrincipia.Wittgensteinattachedhim-selftohim,andwassomethingofapest,pursuingRussellbacktohisroom,andbadgeringhimwithquestions,evenwhileRussellwasdressing.Buthewasnotjustanuisance:helearnedextraordinarilyfast,andbeforelongRussellfeltthatWittgensteinwouldbethepersontocarryonthetech-nicallogicalworkwhichhefeltthathehimselfwasnolongerupto.By1913WittgensteinwasshapingtheviewsonlogicwhichwouldlaterbecomethebackboneoftheTractatus.TheﬁrstrecordoftheseviewsistheNotesonLogicofthatyear:thiswork(nowpublishedasanappendixtothelaterNotebooks)isanimportantresourceforthosetryingtounderstandtheTractatus.Bytheendof1913,however,WittgensteinfeltthathecouldnolongerdotheworkhewascapableofwhilestayinginCambridge,sohedecidedtogoandlivealoneinNorwayandworkthere.Inthespringof1914hewasvisitedtherebyG.E.Moore,anotherCambridgephilosopher,andoneoftheleaders(Russellwasanother)oftherevoltagainstHegelianismwhichinauguratedanalyticphilosophyintheEnglish-speakingworld.Despite\nINTRODUCTION3hisseniority,Moorewasnotevenanequalpartnerintheirdiscussions:infact,Wittgensteinusedhimtotakedownnoteswhichhedictated.TheseNotesDictatedtoG.E.MooreinNorwayarealsopublishedasanappendixtotheNotebooks.Inthesummerof1914,however,theFirstWorldWarbegan,andWittgensteinimmediatelyjoinedupontheAustrianside.Wittgensteindidnotshirkhismilitarydutiesbyanymeans—indeed,hewaskeentobepostedtothefrontandshowedextraordinarycouragewhenhewassentthere—buthedidnotstopdoingphilosophyeither.Heworkedinnotebooks,someofwhichsurviveandarepub-lishedasNotebooks1914–16(thoughthelastentryisdatedJanuary1917).Thesebeginwithquestionsinthefoundationsoflogic.Theveryﬁrstentry,indeed,reads:Logicmusttakecareofitself.AndformostoftheﬁrsttwoyearsWittgenstein’sconcernsarechieﬂydirectedtodifﬁcultieswhichariseoutofhisworriesabouttheworkofRussellandFrege.ButinJune1916Wittgenstein’sunitwasinthemidstofextremelyheavyﬁghting,inwhichterriblecasualtiesweresuffered.Atthispointthenoteslurchovertoquestionsaboutthemeaningoflife—back,infact,toquestionswhichhadpre-occupiedhimandhisownolderbrothers,aswellasmuchofacertainclassinVienna,intheﬁrstyearsofthecentury.Fromnowon,theworkhewaswritingbegantobeauni-ﬁcationofhisapproachtothefoundationsoflogicwithacertainattitudetoproblemsofthemeaningoflife.TheTractatusitselfwasputtogetherfromWittgenstein’swartimenotebooksoverthenexttwoyears.Therewasanintermediateﬁrstdraft,nowknownasthePrototractatus,andtheﬁnalversionwastypedupinthesummerof1918.Wittgensteindidnotﬁnditeasytogetitpublished,however,andintheenditwasonlyundertheauspicesofRussell’sname,andaccompaniedbyRussell’sownexplanatoryintro-duction—whichWittgensteinhimselfdisliked—thattheworkﬁnallycameoutin1922.ItwaswritteninGerman,but\n4INTRODUCTIONappearedinaparalleltext,alongsideatranslationwhichispresentedasbeingbyC.K.Ogden,butwhichseemslargelytohavebeentheworkofFrankRamsey,abrilliantmathe-maticianandphilosopheratCambridge,whowasnoteventwentyatthetime.AftertheappearanceoftheTractatus,Wittgensteinwith-drewfromacademiclife—indeedfromtheordinaryintel-lectuallifewhichwouldhavebeennaturalforamanofhisbackground.Hegaveawayhismoney,andbecameateacherinavillageschoolinAustria.Ramseyvisitedhimthere,andhegraduallybecameengagedinphilosophyagain,boththroughRamsey’squestionsabouttheTractatus,andthroughtheinterestofagroupofyoungphilosophersinViennawhowerestronglyinﬂuencedbytheTractatus,andformedthe‘ViennaCircle’oflogicalpositivistsaroundit.(RudolfCarnapwasthememberofthisgrouptohavethegreatestinﬂuenceinhisownright.)WittgensteineventuallyreturnedtoCambridgein1929,andbeganare-examinationoftheissuesoftheTractatuswhichgraduallybroughtaboutatransformationinhisviewsduringthe1930s,untilhereachedthepositionofthegreatworkofhislaterlife,thePhilosophicalInvestigations(thebulkofwhichwaswrittenby1945,thoughitwasnotpublisheduntil1953,afterWittgenstein’sdeath).2THEPROBLEMSFORINTERPRETERSTwothingsabouttheTractatusmakeitpeculiarlyhardforinterpreters—bothprofessionalscholarsandstudents.Theﬁrstisitsstyle,andtheseconditscontent.Wittgenstein’sstylisticintentionsaredeclaredinthePreface.Hereistheopeningparagraph:Thisbookwillperhapsonlybeunderstoodbythosewhohavethem-selvesalreadythoughtthethoughtswhichareexpressedinit—orsimilarthoughts.Itisthereforenotatextbook.Itsobjectwouldbeattainedifitaffordedpleasuretoonewhoreaditwithunderstanding.(TLP,p.27)\nINTRODUCTION5Heisnotgoingtomakethingseasyforthereader.ThethoughthereisechoedinthePrefaceofhislaterwork,thePhilosophicalInvestigations:Ishouldnotlikemywritingtospareotherpeoplethetroubleofthink-ing.But,ifpossible,tostimulatesomeonetothoughtsofhisown.(PI:x)ThereisatleastthatmuchcommonalitybetweentheearlyandthelateWittgenstein.Infact,theTractatusismuchhardertogetagriponthanthePhilosophicalInvestigations:therearetimesintheTractatuswhenWittgensteinseemstoabbreviatehisexpressionofpointsinordertomakethemharder,ratherthaneasier,tounderstand.Thereisastrongcontrastoftoneherebetweentheearlierandthelaterwriting:thePhilosophicalInvestigationsisaworkofgreat—sometimesevenpatronizing—patience;theTractatusis,ifanything,impatient.Thepointcanbeillustratedwithanexample.MuchofthetechnicalityofWhiteheadandRussell’smonumentalPrincipiaMathematicaisdesignedtodealwiththeparadoxRussellfoundinFrege’ssystem.WittgensteindevotesjustﬁveparagraphstothisintheTractatus(3.331–3.333),beforeconcluding:HerewithRussell’sparadoxvanishes.(3.333)Theworkseemstobedeliberatelydifﬁcult,madedifﬁcultinordertoforcethereadertothinkforherself.Sadly,thisseemstohavefrustratedoneofthebook’sambitions.ItistemptingtothinkthatWittgensteinhopedthatFrege,inparticular,wouldbe‘onewhoreaditwithunderstanding’,andhesentFregeacopyofthetypescriptbeforeitwaspublished.Unfortunately,Fregecouldmakenothingofit.(Wittgenstein’shopewasnotaltogetherfrustrated,however:hecertainlyfoundonepersonwhoreadthebookwithunderstanding—andderivedgreatpleasurefromit—inFrankRamsey.)\n6INTRODUCTIONThedifﬁcultiescreatedbythecompressionofstylearesevere.Thosewhobegintospeakaforeignlanguagearefamiliarwiththedangersof‘falsefriends’—wordswhichseemlikewordsofourownlanguage,andwhichwearethereforeinclinedtoassumehaveasimilarmeaning,butwhichinfactmeansomethingquitedifferent.TherearemanyfalsefriendsintheTractatus,even—perhapsespe-cially—forprofessionalscholars.Therearephrasesandsnatchesofargumentwhicharereminiscentofthingswehavecomeacrosselsewhereinotherauthors,andwhenwereadthem,weclutchatthem,thinkingthatWittgensteinmusthaveinmindsomethingsimilartowhatthoseotherauthorshadinmind;butoftenhedoesnot.ItisnotmereperversitywhichdictatesWittgenstein’sstyle,however.Hiswritingisguidedbyacertainausterepoeticsense.LaterinthePrefaceWittgensteinwrites:Ifthisworkhasavalueitconsistsintwothings.Firstthatinitthoughtsareexpressed,andthisvaluewillbethegreaterthebetterthethoughtsareexpressed.Themorethenailhasbeenhitonthehead.(TLP,p.29)(Wewillreturntothesecondthinginamoment.)HereweseeWittgensteinattendingabovealltothewayinwhichthethoughtsofthebookareexpressed—infact,thiscomesbeforetheissueofwhetherthosethoughtsaretrue(whichWittgensteinaddressesinthenextparagraph).Hisconcernhereistheconcernofapoet(eveniftheimageheusesisratherhumdrum),andtheTractatusismeanttoworkpoe-tically.Thereis,Ithink,aparticularreasonforthat,apartfromsimpleconsiderationsoftaste,aswewillseeinamoment.UnfortunatelyforsomeonetryingtomakesenseoftheTractatus,thispoeticstyleisitselfsomethingofafalsefriend:theverycadenceofsomeofthebook’sremarksseducesusintothinkingthatweknowwhatisbeingsaid,whenreallywedonot.Theveryﬁrstremarkofthebook—‘Theworldiseverythingthatisthecase’—isanexampleofthis.\nINTRODUCTION7Theotherthingwhichisdifﬁcultaboutthebookisitscontent—or,rather,oneparticularfeatureofitscontent.Thebookiscertainlytechnicalattimes,andWittgenstein’simpatienceinexpositiondoesnothelphere,butthisisnotthedeepestproblem.Therealproblemisthatthebookseems,onthefaceofit,tobeparadoxical:itseemstoundermineitself.Thebook’spenultimatesectionbegins:Mypropositionsareelucidatoryinthisway:hewhounderstandsmefinallyrecognizesthemassenseless,whenhehasclimbedoutthroughthem,onthem,overthem.(6.54)Wewillnote,ofcourse,thatWittgensteincannotresistputtingthispoetically.Butthekeyproblemisthatthisremarkseemstodeclarethesentencesofthebook(‘mypropositions’)tobewithoutanymeaningatall.Toseetheproblemthiscausesforaninterpreter,weneedtoreﬂectalittleonthepracticeofinterpretation.Interpretationisguidedbywhatisknownasa‘principleofcharity’.Theideawhichthislabelenshrinesisthatwedonotinterpretsomeonewellifourinterpretationrepresentsherasanidiot.Butthereisasimpleranddeeperpointhere.Itisthatinterpretingatextisamatterofmakingsenseofit.Andtomakesenseofatextistorepresentitasmakingsense.Inthegeneralcase,representingatextasmakingsenseisrepresentingitassayingsomethingwhichis,inthecontext,areasonablethingtosay.Butitisatleastaminimalconditionondoingthatthatonerepresentsthetextas,lit-erally,makingsense—thatistosay,asnotbeingmean-ingless.ThepenultimatesectionoftheTractatusnowseemstoputanimpossibleburdenonaninterpreter:inordertorepresentitassayingsomethingwhichitisreasonable,inthecontext,tosay,weseemtohavetorepresentitasnotsayinganythingatall.Thisgeneralproblemalsohasparticularapplications.Usually,ifweareinterpretingawork,wehavereasontothinkthattheauthorisnotsayingsomethingifwehave\n8INTRODUCTIONclearevidencethathedeniesthatverything.Unfortunately,ifaworkdeclaresitselftobeparadoxical,thatrulecannotbeusedwithoutextremecaution.Wehavetomakequitedeli-catejudgementsindecidingwhichdenialsindicatethattheauthordoesnotmeansomething,andwhichdonot.InthecaseoftheTractatus,oneinterpretercantakeWittgensteintobesayingsomething,whileanothercanpointtoapieceoftextandsay,‘Butlook:hedeniesthathere’.Theﬁrstinter-pretercanstillrespond,‘Yes,indeedhedoes’,andfeelnopressuretoreviseherinterpretation.Myownviewisthattheparadoxicalityoftheworkisoneofthereasonsfortheimportanceofitsmodeofexpression—fortheimportanceofthepoeticinthewayitiswritten.Becausetheworkisparadoxical—becauseitismeaninglessbyitsownlights—itcannotreallybetakentobetryingtosayanything.Andherethepoetryofthelanguagecanbeusedtoworkinadifferentway,toachieveadifferentkindofpurposefromthestatementoftruths.(Butthisisamatterfortheﬁnalchapter.)ThisconnectswiththesecondthingwhichWittgensteinsaysgivesvaluetothework.Wittgensteindoesindeedclaimthatinitalltheproblemsofphilosophy‘haveinessentialsbeenﬁnallysolved’(TLP,p.29).Butitisnotthiswhichmakestheworkworthwhile.Rather,Wittgensteincontinues:AndifIamnotmistakeninthis,thenthevalueofthisworksecondlyconsistsinthefactthatitshowshowlittlehasbeendonewhentheseproblemshavebeensolved.(TLP,p.29)AndthislinkswithsomethingwhichhehadatonepointthoughtofwritinginthePreface.Ashetoldapublisher,LudwigvonFicker:WhatImeanttowritethenwasthis:myworkconsistsoftwoparts:theonepresentedhereplusallIhavenotwritten.Anditispreciselythissecondpartthatistheimportantone.(WSP,94–95)\nINTRODUCTION9Thisliesbehindthecrypticandepigrammatic,poeticstyleofwriting:theaimistogiveasensealwaysofwhathasnotbeensaid,whichisthemostimportantthing.3TRACTATUSSCHOLARSHIPWearecurrentlyinanexcitingperiodinTractatusscholar-ship—indeedinthescholarshipoftheearlyperiodofanalyticphilosophyingeneral.Inpartthisisbecausetheanalytictraditionhasjustwokenuptothefactthatitsownworksareopentohistoricaltreatment—thatis,totreat-mentbyaphilosophicalhistorianofphilosophy.(Toputthematterabittoosimply,Itakeaphilosophicalhistorianofphilosophytobesomeonewhopostponesuntiltheverylastmomenttheabandonmentofbeliefinthereasonablenessoftheviewsofthephilosophersshestudies;apieceofphilo-sophicalhistoryofphilosophyisanattempttoreconstructthejustiﬁcationforaphilosophicalview.Anon-philosophicalintellectualhistorian,bycontrast,willbehappytoappealtonon-justiﬁcatoryexplanatoryfactorsatamuchearlierstageinheraccountofaview,orofachangeofview.)Theana-lytictraditionhasrecentlynoticedthatitsowncoreworksarenotmerelycontributionstoacurrentdebate:theyexpressviewsthatarepeculiarenoughtostandinneedofjustiﬁcationfromfurtheroutthanthat.AtthecoreofthisburgeoninginterestinphilosophicalscholarshipoftheanalytictraditionhasbeenarevivalininterestinBertrandRussell,inparticular.Thisrevivalhasbeenfedby—aswellasfeeding—thepublicationoverthelastfewyearsofRussell’sphilosophicalpapers.OfparticularimportancefortheTractatushasbeenthepublicationofpaperswrittenbothbeforeandafterthegreatpaper‘OnDenoting’of1905,andofthemanuscriptentitledTheoryofKnowledge,whichwaswritteninafewweeksin1913,andthenabandoned—apparentlybecauseRussellcouldnotseehowtogetroundWittgenstein’scriticism.Atthesametime,seriousworkhasbeencontinuingintotheactualhistoryofthecompositionoftheTractatusanditsmoreinformal\n10INTRODUCTIONpredecessors,theNotesonLogicandthewartimeNotebooks.MoreisnowknownabouttheviewswhichWittgensteinwasreactingto,andthecircumstancesofhisreaction,thanperhapshaseverbeenknowntoanyoneotherthanthework’sauthorsincethebookwaspublished.Inadditiontotheﬂourishingofscholarlyworkonearlyanalyticphilosophy,interestintheTractatushasbeengal-vanizedrecentlybyadisputeovertheinterpretationofthework.Ifonebelievesthepopularaccounts,thedisputeisbetweentwoschoolsofinterpretation:thosewhodescribethemselvesaspresentinga‘newWittgenstein’,ora‘resolute’reading,ontheonehand,andthosewhoarethoughtofasinsomeway‘traditionalists’,ontheother.Infact,therearemorethantwopositionsinplayhere,andtheycentreondifferentinterpretativeproblems.AtthecoreofallofthemistheapparentparadoxoftheTractatus,andthedismissalofphi-losophyasnonsensewhichformspartofthat.Onedisputeisoverexactlywhatismeantby‘nonsense’here:isthereadistinctionbetweenplainnonsenseandnonsensewhichis,somehow,signiﬁcant?Andisplainnonsensejustgibberish?AnotherisoverwhetherWittgensteinintheTractatusholdsthatthereareineffabletruths—truthswhichcannotbestated,butwhosecommunicationmightbethoughttobethepurposeofthework.AnotheragainisconcernedwiththerelationbetweenWittgenstein’sattitudetophilosophyintheTractatus,andhisattitudeinthelaterwork,inparticularinthePhilosophicalInvestigations.Agoodproportionofthosewhodescribethemselvesaspresentinga‘newWittgenstein’,ora‘resolute’reading,takethelaterworktoembodyarejec-tionofaparticularkindofwayofdoingphilosophy,whichtheycall‘metaphysics’;and,furthermore,theytendtothinkthatWittgensteinisrightinthisrejection.TheythenreadtheTractatusasifitwerefundamentallyinagreementwiththePhilosophicalInvestigations—andthem—inthisrejectionof‘metaphysics’.Againsttheseproponentsofa‘new’or‘resolute’interpretationoftheTractatustherearethosewhothinkthatthereisaradicaldisagreementinviewbetweenWittgenstein’searlyandlaterwork.\nINTRODUCTION114THEAPPROACHOFTHEPRESENTWORKItwouldbefoolishtoignoretheenormousamountofrecentscholarshipontheTractatus,andimpossibletoavoidtakingastandonthelargeinterpretativedisputes.Butmyaimhasbeentoavoidoverloadingthetextwithhistoricaldetail,andtopresentsomethingwhichmightbeofuseeventothosewhoendupdisagreeingwithmeonthemajorpointsofinterpretativedispute.Thisbookisdesigned,aboveall,tomakecomprehensibleatextwhichisdifﬁculttomakeanysenseofatall.Itsfocus,therefore,isonthedetailsofthetextitself—andinparticular,onthosedetailswhichareinitially(andoftenpersistently)verypuzzling.Theproblemsarepresentedbythepoeticstyleofthework,whichIhavealreadyremarkedon,inconjunctionwithaveryobviousfact:Wittgensteincontinuouslypresentssomeepigrammaticclaimsasbeinglogicallydependentonothers.Ifthereisalogicaldependence,thereoughttobesomeargumentwhichmakesthatdependenceclear.ButwithWittgenstein’simpatienceandhisconcernforpoeticexpression,theargu-mentisveryseldomexpressed.Itisthisabsenceofexpres-sionofargumentswhichistheprincipalsourceofthework’sdifﬁculty.Accordingly,ithasbeenmyprincipalconcerntoexpressasclearlyandexplicitlyaspossibletheargumentswhicheverybodyfeelsaretheretobefound.Clearlythiswillinvolvealossofthework’spoetry,andwillsometimesalsoleadtoalossofsubtletyandnuance.Butthereisaveryﬁnelinebetweensubtletyandevasion,andwheneverIfeltthatlinewasclose,Ihavetriedtobeexplicitandunambig-uous,attheriskofbeingunsubtle.Itseemstomethatthisisthebestwayofservingbothstudentsandscholars.TheargumentswhichItrytopresentexplicitlyhavebeenthesubjectofscholarlydisputeeversincetheworkwasﬁrststudied.Thereisnothingwhichdeservestobecalledthe‘standard’viewofanyofthem,soitisimpossibletoavoidcontroversyinpresentinganexplicitinterpretation.Thismeansthatthisbookcannotbemerelyintroductory,asstudyguidesaresometimesexpectedtobe.ButIhavetriedtomakethe\n12INTRODUCTIONstepsintheargumentasclearasstudentsneedthemtobe,whilealsoindicatingdifferencesfromotherinterpretations.Ofcourse,inpresentingtheargumentsexplicitlyItakeseriously—atleastfortheperiodofpresentingthem—theargumentswhichIpresent.Thisinevitablyinvolvesmeinsomeoftheissueswhicharisefromtheapparentpara-doxicalityofthebook,butIdonotdwellonthoseissueswhilelayingoutthearguments.Instead,theirpropertreat-mentispostponeduntilthelastchapter,wheretheyaredealtwithatsomelength.ThereisonequestionofinterpretationwhichIhavenotpursuedhereinanydepth.ThisconcernstherelationbetweentheearlyandthelateWittgenstein.ThereasonwhythiscannotbediscussedproperlyhereisthatitisnoeasiertounderstandthelaterworkthanitistounderstandtheTractatus,althoughthereasonsforthedifﬁcultyarealittledifferent.Buteventhoughthisisnottheplacetoargueforaninterpretation,itmayhelpreaderstounderstandtheorientationofthisbookifIsaybrieﬂywhatIaminclinedtothink.Iaminclinedtothink,ﬁrst,thatWittgensteinislessanti-philosophicalinhislaterworkthanheisoftentakentobe.And,second,Iaminclinedtothinkthereisatleastonesimplebutdecisivephilosophicaldisagreementbetweentheearlyandthelaterwork:theearlyworkendorses(thoughinawaymadecomplicatedbyitsparadoxicality)andthelaterworkrejectsthecentralthesisoftheTractatus’sphilosophyoflanguage,thattheformoflanguageisthesameastheformoftheworld.5AKANTIANOVERVIEWInaddressingadifﬁcultwork,asynopticoverviewalwayshelps.TheTractatusitselfinvitesaparticularkindofsum-mary,becauseofthenumericalarrangementofitsremarks.Thebookpresentsitselfashavingsevenkeytheses:1Theworldiseverythingthatisthecase.2Whatisthecase,thefact,istheexistenceofatomicfacts.\nINTRODUCTION133Thelogicalpictureofthefactsisthethought.4Thethoughtisthesignificantproposition.5Propositionsaretruth-functionsofelementarypropositions.(Anelementarypropositionisatruth-functionofitself.)–––6Thegeneralformoftruth-functionis:[p,n,N(n)].Thisisthegeneralformofproposition.7Whereofonecannotspeak,thereofonemustbesilent.Everythingelseinthebookispresentedasacommentonorexplanationofoneoftheseseventheses,oracommentonacomment,oracommentonacommentonacomment,andsoon,accordingtothenumberingschemesetoutinafootnotetotheﬁrstthesis.Thechapterswhichfollowcanbeassignedroughlytotheseremarks,asfollows.Chapter1isconcernedwiththeses1and2.Thenotionofa‘picture’whichisusedinthesis3isexplainedinChapter3,anditsapplicationtolanguageinthesis4isthesubjectofChapter4.Thistreatmentoflan-guagehasacertainhistory,whichisthesubjectofChapter2.Chapter5dealswiththeses5and6.Wittgensteinthinkstheseclaimshaveanimportantconsequencefortheissueofsolipsism,andthatisthetopicofChapter6.Thefurtherconsequencesofthesis6forphilosophy,astheyleaduptothesis7,aredealtwithinChapter7.Butthiskindofoverviewisunlikelytoprovidesomeonewhoreadsthebookfortheﬁrsttimewiththehelpsheneeds.Wewanttoknowwhatthewholethingisreallyabout,andtheseseventhesesdonotrevealthatveryclearly.HereithelpstorememberthattheprojectwasﬁrstaddressedinWittgenstein’swartimenotebookswiththisremark:Logicmusttakecareofitself.(NB2;TLP5.473)IthinkthesigniﬁcanceofthisismostsimplyunderstoodasderivingfromaconcernwithabroadlyKantianproblemwithphilosophy.(ThereisuncertaintyabouthowmuchKant—indeed,howmuchofanything—Wittgensteinhad\n14INTRODUCTIONactuallyread;butthereislittledoubtthathisapproachtophilosophyhasabroadlyKantianorientation.)WhatfollowsisabriefoverviewoftheTractatusfromthisslightlydif-ferentperspective.Itiscontroversial,ofcourse,likeevery-thingelseintheinterpretationofTractatus.Butthosewhoreadtheworkfortheﬁrsttimeneedittobegivensomeshape;anditisbetterthatitshouldbegivenashapewhichislaterrejectedasacaricature,thanthatitshouldhavenovisibleshapeatall.Here,then,isawayofraisingsomeoftheissuesthatconcernedKant.Amathematicianfriendofmineoncesaidtomesomethinglikethis:‘Isn’titamazingthatthenumbers,whichstandinallthecomplicatedrelationstoeachotherthatmathematiciansareinterestedin,canbeusedtocountordinarythingsintherealworld,likesheepandcows?’Itseemsimmediatelyclearthatthereissomethingveryoddaboutmyfriend’swayoflookingatthings,butitislesseasytoexplainwhatexactlyhasgonewrong,andmoredifﬁcultstilltoarticulatewhathastobeacceptedifwearetoavoidgoingwronginthatway.Theﬁrstthingweareinclinedtosayissomethinglikethis:itisnotanykindofaccidentthatthenumberscanbeusedtocountordinarythingsintherealworld;rather,themomentwehavethings,wemustbeabletodistinguishbetweendifferentthings,andhencedistinguishbetweenonethingandtwo,andthisprovidesuswiththepossibilityofcountingthem.Inshort,itisnotthatthenumbershavealifeoftheirown,andarethenusedtocountthings;itisratherthattheiroriginliesinthecountingofthings,andonlybecauseofthatdotheygettohavetheinterestingpropertieswhicharethemathematician’sconcern.Thisreplyisnotaltogetherwrong,butitisinadequateintwocrucialrespects.First,justdistinguishingbetweenthingsisnotenoughforcounting,andhencenotenoughforarithmetic.Whatweneedisacrucialextranotion—thatofasuccessorinaseriesofacertainkind.Andthenwecanask:wheredoesthatnotionofasuccessorcomefrom?And,sec-ondly,itisallverywellsayingthattheoriginofnumbers\nINTRODUCTION15liesinthediscriminationofthings,butthatnowputsacer-tainpressureonourconceptionofthings:thenotionofathingneedstobringwithitthenotionofidentity(and,correlatively,distinctness).Furthermore,thatnotionofidentitylooksasifitisconnectedwithclassiﬁcation:ifweidentifyathing,wehavetoidentifyitasathingofacertainkind.Andthenwecanask:wheredoesthenotionofathing,withtheseconnectednotionsofidentityandclassiﬁcation,comefrom?Whateverwesayaboutthis,weneedtotakeaccountofanimportantfactaboutthesefundamentalconcepts(likeallconcepts):theybringwiththemcertaincommitments,whichweareinclinedtothinkofasnecessarytruths.Somethingsseemtobenecessarilytrueofanyrelationwhichcanbedescribedasthatofsuccession.Somethingsseemtobenecessarilytrueofanythingwhichcanbecountedasathing.Thereseemtobesomenecessarytruthsaboutidentity.Andthereseemtobesomethingswhicharenecessarilytrueofanythingwhichcanbesaidtobelongtoagivenkindofthing.Itistemptingtosaythatwhatarerevealedwhenweconsiderwhatispresupposedintheapparentlysimpleprac-ticeofcountingarenothinglessthannecessarytruthsabouttheworld.Thetaskofunderminingtheamazementofmymathematicianfriendseemstoleadustoconsiderthenecessarystructureoftheworld—howtheworldabsolutelyhastobe,ifcounting,oreventalking,istobepossibleatall.Andthis—toputitverycrudely—ishowthingsstruckKant.Therearesomethingswhicharenecessarilytrueoftheworld,andthesearerevealedwhenweconsiderwhatisrequiredformathematics—indeed,thinkingingeneral—tomakesense.Butthisispuzzlinginitself.Itisnaturaltothinkthatourunderstandingofwhatistrueoftheworldisfurnishedbyexperience—byourperceptionofthingsaroundususingoursenses.Butexperienceseemsonlytopresentuswithcontingenttruths:withthingswhicharetrue,butnotnecessarilytrue.Weobservetheactualposi-tionofasheeponahill,orofaneedleonadial:wedonotobservehowsheep,hills,needlesanddialsmustbe.Sohow\n16INTRODUCTIONcanwepossiblyhaveknowledgeofhowthingsmustbeintheworld,ofwhatisnecessarilytrueoftheworld?Kant’sanswer—stillputtingthingscrudely—wassomethinglikethis.Foratruthtobenecessary,hethought,ithadtobecapableofbeingknownwithoutrecoursetoexperience:thatis,ithadtobeapriori.Butforittobeatruthabouttheworld,ithadtorunbeyondwhatcouldbederivedfromamereanalysisoftheconceptsinvolved:ithadtohavesomethingsuppliedbytheworld,ratherthanbyourconcepts.Inhisterms,thismeantthatithadtobesynthetic,ratherthananalytic.SoKantthoughtthatinordertodealwithmuddleslikethatofmymathematicianfriend,weneedtoappealtotruthsofaspecialkind:thosewhicharebothsyntheticandapriori.Thisis,initself,apuzzlingnotion.Itlooksasifthereneedstobesomekindofencounteroracquaintancewiththeworld,fortheworldtosupplyany-thingwhichoutrunsourconcepts:Kantcalledsuchanacquaintanceanintuition.Butthisacquaintanceorintuitionmustnotbeallowedtocompromisethefactthatthetruthswhichitdeliversareapriori:itmustnotinvolveanyrecoursetoexperience.Kantaccordinglythoughtthattherehadtobesomekindofaprioriacquaintancewith,orintui-tionof,theworld.Thechallengeisthentounderstandhowsuchathingispossible,andthatisthebeginningofKant’sownpositivephilosophy.WecanunderstandwhatWittgensteinisdoingintheTractatusifweseehimasreactingagainstthisposition—evenifhisreactionwasnot,ornotinitially,againstKant’sownpresentationofit.Necessarytruthisthebusinessoflogic,onaviewoflogicwhichWittgensteininheritedfromRussell.Toinsistthat‘logicmusttakecareofitself’istoinsistthatnecessityis,inasense,independentoftheworld,andthatwecanhaveknowledgeofwhatwethinkofasnecessaryorlogicaltruthswithoutanykindofacquaintancewith,orintuitionof,theworld.Whatneedstoberesisted,onthisview,istheideaofsyntheticaprioritruth.Thereisawayofavoidingappealingtosyntheticaprioritruthswhilestillallowingboththattherearenecessary\nINTRODUCTION17truthsabouttheworldandthatwecanhaveknowledgeofthem.Weavoidappealtosyntheticaprioritruthsbyinsistingthataprioritruths,insofaraswecanspeakoftruthshereatall,areknownsimplybyunderstandingthesysteminwhichwerepresenttheworldtoourselves:ifwhatweappealtoissimplythenatureofthesystemofrepre-sentation,thenwearestillwithintherealmoftheanalytic,inKant’sterms,ratherthanthesynthetic.Butthisunder-standingofthesystemcan,ineffect,giveusknowledgeoftheworldifacertainconditionismet.Weneedtoinsistthatthewaythesystemmustbeeithermirrors,orismirroredin,thewaytheworldmustbe.Ifwehaveacorrespondenceofthiskindbetweenthesystemofrepresentationandtheworldwhichisrepresented,wecanhaveaprioriknowledgeofwhatare,ineffect,necessarytruthsabouttheworld,butwithoutanyaprioriintuitionof,oracquaintancewith,theworld.Whatiscrudelyexpressedhereis,Ithink,theviewpre-sentedintheTractatus—insofarastheTractatuscanbesaidtopresentanyviewatall.Atitscoreisathesisabouttherelationbetweenasystemofrepresentation—anysystemofrepresentation—andtheworld:eachmust,inacertainsense,mirrortheother.Thisistheassumptionthatasystemofrepresentationandtheworldmustbothhavethesameform.ItisthecentralthesisofthephilosophyoflanguagepresentedintheTractatus,theviewwhichissomewhatmisleadinglydescribedasthe‘picture’theory—whichisexpressedintheses3and4ofthesevenmainclaimsofthebook.Thisassumptionofsamenessofformcanonlybetrueifboththeworldisacertainwayandlanguageisacertainway.Thewaytheworldhastobeforthesame-formassumptiontobetrueiselaboratedintheses1and2,andtheirdependentcommentsandexplanations.Thewaylan-guagehastobeisworkedoutintheses3,4,5,and6,andtheremarkswhichexplainanddevelopthem.Butifthesame-formassumptionistrueitturnsoutthattherewillbeproblemsstatingit:wecannot,asitwere,uselanguageto\n18INTRODUCTIONstepoutsidethemirroringrelationbetweenlanguageitselfandtheworld.AndthatmeansthatthewholeKantianphi-losophicalenterpriseturnsouttobeimpossible;andthesamegoesforanyphilosophywhichisconcernedtosaysomethingaboutourrelationshiptotheworld—includingtheTractatusitself.Andthatexplainsthelatercommentsonthesis6,aswellasthesis7.Itturnsout,then,thattheonlywayofproperlyaddressingtheKantianproblemendsupdemolishingallphilosophy.Somuchforanoverview:thedevil,ofcourse,isinthedetail,whichthechapterswhichfollowwilltrytoexplain.6NOTEONTRANSLATIONMuchofthetimeitisimportanttolookattheverywordsWittgensteinuses—ortheclosestyoucangettothemifyoudonotactuallyspeakGerman.Iquotethetextintranslationextensivelyinthechapterswhichfollow.Ithereforehadtoconsiderwhichtranslationtouseforthesequotations.Therearetwowell-establishedandauthoritativetransla-tionscurrentlyincirculation.OneisthetranslationwhichwasoriginallypublishedoppositeWittgenstein’sGerman—thetranslationbyC.K.Ogden(thoughlargelytheworkofFrankRamsey).Arevisedversionofthisisstillavailable,stillalongsidetheGermaninaparalleltext.TheotheristhelatertranslationbyDavidPearsandBrianMcGuinness,whichappearswithouttheGerman.Russell’soriginalintroductiontotheworkisprintedbeforebothtranslations.Therelativemeritsofthetwotranslationsare,brieﬂy,these.TheOgdentranslationwasactuallyapprovedbyWittgenstein,anditsﬁnalformistheresultofmodiﬁcationsmadeinthelightofcommunicationsbetweenOgdenandWittgensteinhimself.AndtheGermanisprintedalongsidetheEnglish.Butthetranslationisclumsy,attimesasaresultofbeingdog-literal.Itisalsoinsensitivetosomenuances(thereisafamousfailuretonoticethedifference\nINTRODUCTION19between‘sinnlos’—withoutsense—and‘unsinnig’—nonsense).Ontheotherhand,itsliteralnessdoessomethingsnicely—forexamplethedetailedprogressionof6.54.ThevirtuesofthePearsandMcGuinnesstranslationaretheoppositeofthoseofOgden’s.IdiomaticGermanisren-deredintoidiomaticEnglish,andthebookcanbereadrela-tivelyeasily.Moreover,someofthenuancesoftheoriginalareproperlymarked(theirtreatmentof‘sinnlos’and‘unsinnig’isafamousimprovementoverOgden’s).Thereare,however,placeswheretheiridiomaticEnglishismis-leadingaboutwhatWittgensteinmeans(forexample,thestatementofthegeneralformofthesentencein4.5).TheindexismoreusefulthanOgden’s.IntheendIhavechosentouseOgden’stranslationwhenIquotefromthetext,bothinthechapterswhichfollow,andinthisIntroduction.IhavechosentheOgdenlargelybecauseofitsfaults.Itsveryclumsinessandthefactthatitissounidiomaticmeanthatitoffersrelativelyfewofthe‘falsefriends’whichcansoeasilylureareaderintomis-understanding.SinceIdonotquotewithoutcommentingonwhatisquoted,IamabletodrawattentiontothemoreobviouswaysinwhichOgden’stranslationfailstocapturesomethingimportantinthetext.AndthefactthatWittgensteinhimselfapprovedOgden’stranslationmeansthatitcanbetreated,intheparalleltextinwhichitappears,aspartofaprimarytext.Forallthat,astudentshouldhavenodifﬁcultyworkingthroughthisbookifshehaseitherofthesetwotranslations:itisnotdifﬁculttoﬁndyourplaceinthePearsandMcGuinnesstranslationifyouhavetheOgdentranslationandthenumberoftheremarkwhichisquoted.AseriousstudentwhoreadsEnglishbutnot(ornotyet)GermanwillwanttohaveboththeOgdenandthePearsandMcGuinnesstranslations:usebothtogetahandleonwhatWittgensteinisdoing,playingidiomaticagainstunidiomaticEnglish;useOgdentokeyintotheGerman;andusePearsandMcGuinnessfortheirindex.\n20INTRODUCTION7REFERENCESQuotationsfromthemainbodyoftheTractatusarerefer-encedbysectionnumber—‘4.0312’forexample.ReferencestoworksbyWittgensteinareingeneralmadebymeansofabbreviations,thekeytowhichistobefoundintheBibliography.ReferencestothePrefaceoftheTractatususebothabbreviationandpagenumber—thepagenumberbeingthepagenumberintheOgdenedition—as,forexample‘TLP,p.29’.\n1THENATUREOFTHEWORLD1AANOUTLINEOFMETAPHYSICSTheTractatusbeginswithafamouslygnomicpronouncement:11.Theworldiseverythingthatisthecase.Mostpeople,onﬁrstreadingthis,havenoideawhattomakeofit.Isitsupposedtobeadeﬁnition,ﬁxingthemeaningoftheterm‘world’?Isitsupposedtobejustobvious?Orisitmeanttobeacontentiousclaim,adeliberatemarkingoutofapositionwhichWittgensteinexpectstobeattacked,butwhichheispreparedtodefend?Again,ifitisadeﬁnition,whatprojectmightWittgensteinhaveinmind,forwhichitwasappropriatesimplytodeﬁneawordlike‘world’?Andifitisnotadeﬁnition,whatreasoncouldWittgensteinhavehadforthinkingitistrue?TheonlyreasonforthinkingthatWittgenstein’sclaimmightbeadeﬁnitionisthatheintroducesitwithoutjustiﬁ-cation.Ifaworkofphilosophybeginswithastrikingclaim—anditiscertainlythat,whateverelseitis—forwhichno\n22THENATUREOFTHEWORLDjustiﬁcationisoffered,weareinclinedtoassumethattheclaimitselfisthebasisofthephilosophywhichistofollow.ButtheopeningclaimoftheTractatuscannot,infact,bereadlikethat.IftheclaimwereadeﬁnitionalbeginningtothephilosophyoftheTractatus,wewouldexpectthetermswhichareusedtostatethedeﬁnitiontobeclearthemselves,inadvanceofthephilosophywhichfollows.Buttheyarenot.Wedonotyetunderstandwhatsomething‘thatisthecase’is.Wewillknowveryshortly(in1.1)thatitisa‘fact’,andnota‘thing’;butatthisstagewehavelittleideawhatthedifferencebetween‘facts’and‘things’is,andthisissome-thingwhichcannotreallybemadeclearindependentlyofthegeneralconceptionoflanguagewhichfollowsinlatersections.Furthermore,iftheclaimwereadeﬁnition,itwouldimmediatelyrobtheworkofmuchofitssigniﬁcance.SinceWittgensteinwouldnolongerbemakingaclaimabouttheworld,aswenormallyunderstandthenotion,wecouldsimplyrespondtohim:Yes,yes,thismayallbetrueofthe‘world’,inyourpeculiarsense,butwhatabouttheworld,astherestofususetheterm?Itisbesttoacceptthattheclaimisnotadeﬁnition.Theterm‘world’isherebeingusedinafamiliarsense.TheopeningclaimoftheTractatusissupposedtobeasub-stantiveclaimabouttheworldweallknowabout,theworldwhichwehaveexperienceof.Anditissupposedtobecon-tentiousinatleastthissense:Wittgensteinishereproposingaviewofthenatureoftheworldwhichhasnotbeenrea-lizeduntilnow.Heexpectsthisviewtobenewandstrikingtomanyofus,evenifhesupposesthatitwillseemobviousenoughoncewehaveunderstoodhisreasonsforit.Heisheredeliberatelyopposinghimselftoalongtraditionofphilosophy.Theopeningclaimbeginsthepresentationofaverygen-eralaccountofthenatureofrealityasawhole,whichextendsfromthisﬁrstremarkupuntil2.063.(Atleast,averygeneralaccountofthenatureofrealityiswhatitseemstobe:aworryaboutthisisaddressedattheendofsection1Fbelow.)Butalthoughageneralaccountofrealityispresented\nTHENATUREOFTHEWORLD23here,norealargumentforthisaccountispresentedinthesesections.Somepointsareelaborated,andsomeargumentsarepresentedwhichpointforwards,beyond2.063—butitwillonlybeinlatersectionsthatthoseargumentsarecom-pleted.Why,then,doesWittgensteinholdtheviewswhichhepresentsaboutthenatureofrealityintheseearlysectionsoftheTractatus?Ultimately,becausehethinkstheyarerequiredbytheverypossibilityoflanguage:hethinksthatlanguagewouldnotevenhavebeenpossibleiftheworldhadnotbeenashepresentsitasbeingintheseearlysections.Butwhy,then,doeshebegintheTractatuswiththisgeneraloutlineofthenatureofreality,ifthereasonforthinkingthatrealityislikethatistobeofferedlater?WecangetasenseofwhatisgoingonintheearlypartoftheTractatusifwethinkinthefollowingway.Philosophersaresupposedtowanttounderstandthenatureofreality:thisisthetraditionaltaskofphilosophy,andaboveall,ofthequeenofallphilosophy,metaphysics.Itisthebusinessofmetaphysicstoexplainhowtheworldmustbe.Verywell,then:Wittgensteinwilltellushowtheworldmustbe.Hetellsusintheseﬁrstsections,upto2.063.Youwillthenwonderwhyweshouldacceptthisparticularmetaphysicalview.Theexplanationwillemergegradually,asthenatureoflanguage—anypossiblelanguage—isexplained.Evenso,wemayfeelthatwehavenotreallyunderstoodwhyWittgensteinshouldbeginthebookwithanaccountofthenatureoftheworld,ofwhichheoffersnoexplanation,andthejustiﬁcationforwhichhebringsinonlyafterwards.Thereasonforthisstyleofpresentationwillonlyemergeproperlylater,oncewehaveworkedthroughthewholebook;butwecananticipateitalittlehere.Thepenultimatesentenceofthebookreads:Hemustsurmountthesepropositions[i.e.thepropositionsoftheTractatus];thenheseestheworldrightly.Wehavehere,intheopeningsectionsoftheTractatus,ananticipationofthevisionoftheworldwhichisonlyproperly\n24THENATUREOFTHEWORLDavailabletosomeonewhohasunderstoodwhatWittgensteinisdoinginthebook.And,aswillbeclearwhenwehaveworkedthroughthewholebook,itisimportantthatthereshouldbesomethingmysterious(touseacrudeterm,forthetimebeing)aboutthevisionwhichispresented.TheopeningsectionsaredesignedtogiveusanimperfectglimpseofwhataproperunderstandingofWittgenstein’spurposewillenableustoseerightly,andtogiveusatasteofthemysterywhichbelongswiththatvision.Bypresentingtheoutlineofhisviewofthenatureoftheworldwithonlyminimalexplanationandjustiﬁcation,Wittgensteinisabletogeneratesomethingclosetowhatheregardsasaproperfeelingfortheworld.IwillfollowWittgenstein’sprocedureinmyownpresenta-tioninthischapter.InthischapterIwillpresentverylittleinthewayofjustiﬁcationforthemetaphysicalviewwhichWittgensteinpropoundsinthebook’sopeningsections.IwilldipintoWittgenstein’sgeneralconceptionoflanguageonlyinsofarasthatisnecessarytoexplainwhatWittgensteinisclaiming,ratherthanhisreasonsforclaimingit(thoughatonepointthatwillitselfinvolvesomequiteextensiveantici-pation).IwillaimtomakeclearexactlywhatWittgensteinholds,andwhatheisdisagreeingwithinholdingjustthat.Thisshouldgiveusaclearviewofpreciselywhatneedstobejustiﬁedbytheaccountoflanguagewhichfollows.1BTHEWORLDASTHETOTALITYOFFACTSBacktothebeginning,then:1.Theworldiseverythingthatisthecase.Whatdoesthismean?Whatisbeingruledout?Thenextremarkexplainsit:1.1.Theworldisthetotalityoffacts,notofthings.Afactissomethingwhichisthecase,sofortheworldtobeeverythingwhichisthecaseisjustfortheworldtobethe\nTHENATUREOFTHEWORLD25totalityoffacts.Butthisstilldoesnotgetusveryfar.InordertomakesenseofWittgenstein’sclaimhere,weneedtounderstandtwothings:ﬁrst,whatthedifferencebetweenfactsandthingsis;andsecond,whytheworldshouldbesaidtobethetotalityoffactsandnotofthings—asopposed,forexample,tobeingthetotalityoffactsaswellasofthings.Thedifferencebetweenfactsandthingscanbestbeunderstood—perhapscanonlybeunderstood—bymeansofacomparison,whichwillalreadyrequireustopeepaheadintothelaterpartsofthebook.Wearefamiliarwithadis-tinctionbetweenwordsandwholesentences.Wordsare,inacertainsense,thebasiccomponentsofsentences:theyarenaturallytakentobethesmallestmeaningfulpartsofsen-tences.Sentencesarecomposedofwords,but(aswenatu-rallyputit)inaspecialway.Asweordinarilyunderstandthings,thewayinwhichasentenceiscomposedofwordsisdifferentfromthewayinwhichalistiscomposedofwords,forexample.Considerthedifferencebetweenthesetwostringsofwords:(S)Wittgensteinwasrich;(L)Wittgenstein;was;rich.(S)isacompletesentence,while(L)isjustalist—eventhoughboth(S)and(L)consistofexactlythesamewords.Thedifferenceisthatwordscanbeaddedtoorsubtractedfrom(L)quitearbitrarily,withoutmakinganydifferencetowhetherwehavealist;whereasonlyveryparticularsub-tractionsfromoradditionsto(S)wouldstillleaveuswithasentence.Asentenceisacomplete,organicunit,inawaythatalistisnot.Therelationbetweenfactsandthingsisexactlysimilartothatbetweensentencesandwords(oratleast:certainbasicwords),accordingtoWittgenstein.Factsarecomposedofthings;andafactisnotjustanassemblageofthings:ithasacertainorganicunityofitsown.ThefactthatWittgensteinisrich,forexample,isnotjustanassemblageofWittgenstein(theman)andthepropertyofbeingrich.Thereasonforthis\n26THENATUREOFTHEWORLDprecisecorrespondencebetweenthesentence–wordrelation,ontheonehand,andthefact–thingrelation,ontheother,willbeexplainedbyWittgenstein’sgeneralaccountoflan-guage.Buttheparallelismisclearalready,intheseearlypas-sages,beforetheaccountoflanguageispresented.Evenherewehaveremarksaboutthenatureofrealityjuxtaposedwithremarksaboutlanguage(see,e.g.,2.0122and2.02–2.0201).Whatkindofentityisafact?Itissomethingwhichisessentiallycharacterizedbyawholesentence.Afactis,asitwere,athatsuchandsuchisthecase(thatWittgensteinwasrich,thatRusselllivedtoagreatage,thatRamseylikedclimbingmountains,andsoon).Anentitywhichisathatsuchandsuchisthecaseseemsentirelydifferentinkindfromanentitywhichwemightrefertowithanordinaryname(anentitysuchasWittgenstein,orRussell,orRamsey).Thisdifferenceextendstowhatwemightthinkofasthelocationoffacts.Ordinarythingsexistinspace,andaredistributedinspace.Thattheyarespatialisafunda-mentalconditionoftheirnature.Butitishardtoseewhatitwouldbeforathattohaveaspatiallocation.Iffactsexistinaspace,wemightexpectittobeadifferentkindofspace.Wittgensteinsays:1.13Thefactsinlogicalspacearetheworld.What,then,islogicalspace?Logicalspaceisaspaceofpos-sibilities.ItisafactthatWittgensteinwasrich;anotherfactthatRusselllivedtoagreatage;anotherthatRamseylikedclimbingmountains.ButWittgenstein’sparentsmighthavelosttheirmoney;Russellmighthavediedyoung;Ramseymighthavehadasearingexperiencewhichlefthimwithahorrorofthehills.Thereare,asitwere,lotsofotherfactswhichmighthaveexisted,butdonot.Theactualfactsareonlysomeofthepossiblefacts;theyexist,inasense,amongallthepossiblefacts.Whatispossiblemarksouttheextentoflogicalspace.Eachpossibilityis,asitwere,alocationinaspaceofpossibilities.Onlysomeoftheselocationsareactuallyoccupied—bywhatisactuallythecase.\nTHENATUREOFTHEWORLD27Sofactsarequitedifferentfromthings.Why,though,shouldWittgensteinhaveinsistedthattheworldisthetotalityoffacts,butnotthetotalityofthings?Whycouldtheworldnotbethoughttobefundamentallyconstitutedbythethings,evenifthesethingsthemselvescanbecombinedtoformfacts?ItissometimessuggestedthatthereasonisthatWittgensteinisthinkingoftheworldinaratherspecialsense:aswhatmakestruthstrue.2Certainlyveryfewtruthsaremadetruebythemereexistenceofthings:theexistenceofWittgenstein,theman,forexample,makestrueveryfewtruthsabouthim.Itseemsthattogetallthetruthsﬁxedweneedmorethanthethings:weneed,asitwere,thewaythingsare—thatistosay,thefacts.Ithink,though,thatthisisnottherealmotivationfortheclaimthattheworldisthetotalityoffacts,notofthings.IthasthedisadvantagethatitmakesWittgensteinseemtochangethesubjectfromwhatheseemedtobeconcernedwith:itmakeshimstopdealingwiththeworld,asweordinarilyunderstandit,andstartconsideringinsteadsomeconceptionoftheworldwhichsuitsphilosophers.Andifthatiswhatheisdoing,then,asinthecaseoftheearliersuggestionthattheopeningclaimismerelydeﬁnitional,wewanttorespond:Yes,yes,that’sallverywellforyourspecialnotionof‘world’—butwhatabouttheworldasweordinarilythinkofit?Moreover,weonlythinkthatWittgensteintakestheworldtobe,bydeﬁnition,whatmakestruthstrue,becausewecannotthinkofanyotherreasonforhimtosaythattheworldisthetotalityoffacts,notofthings.Andtheresponsetothatisjust:bepatient;therealreasonwillemergesoonenough.3Indeed,thereasonforthinkingthattheworldisthetotalityoffacts,notofthings,beginstoemergeintheimmediatelyfollowingremark,whichisparallelto1.1,anditselfispartoftheexplanationoftheopeningclaimthattheworldiseverythingthatisthecase:1.2Theworlddividesintofacts.Thatremarkinturniselaboratedasfollows:\n28THENATUREOFTHEWORLD1.21Anyonecaneitherbethecaseornotbethecase,andeverythingelseremainthesame.WhatWittgensteinhasinmindhereisakindofconceptionofthingswhichformspartofanancient(originallyAristotelian)viewofthemostbasicentities.4ThetraditionalAristotelianmetaphysicalsystemsupposesthattheworldismadeupofentitiesofvariouskinds,beginningwiththemostbasic,andincludingthosewhoseexistenceisinsomewaydependentonorderivativefromtheexistenceofthemostbasicentities.Whatmustanentitybelikeifitistoqualifyasoneofthesebasicentities?Theconceptionofthemostbasicentitiesintraditionalmetaphysicscombinesanumberoffeatures(anddideveninAristotle).Hereisonenaturalcondition,aconditionofindependenceofexistence:(Ind)Abasicentityissomethingwhichdoesnotdependforitsexistenceontheexistenceofanyotherentity.(Ind)isacentralfeatureofbroadlyAristotelianmetaphysicsandtheology,rightupuntilthemodernera(untilroughlytheeighteenthcentury).5AccordingtoLeibniz,forexample,theuniverseisﬁlledwithaninﬁnitenumberofindependententities,ormonads,noneofwhichiscausallyrelatedtoanyother(sincecausalrelationsinvolveakindofdependence).AccordingtoSpinoza,ontheotherhand,thereisreallyonlyonesuchindependententity,God,sinceeverythingbutGoddependsonGodforitsexistence,whileGoddependsonnothing.Itissomethinglike(Ind)whichisinplayintheopeningclaimoftheTractatus.WhatWittgensteinseemstobeclaimingisthatitisonlyoffactsthatwecanmakeanythingliketheclaimofindependentexistencewhichisexpectedofthefundamentalconstituentsofreality(thoughwewillseeinthenextsectionthatthisclaimwillhavetobequaliﬁedalittle).Nofact—strictly,nobasicfact(wewillcometothisshortly)—dependsforitsexistenceonanyotherfact.Things,bycontrast,canonlyexistwithsomequalities:there\nTHENATUREOFTHEWORLD29cannotbeathingwhichhasnoqualities(thiswouldbelikehavingRussell,theman,withnocharacteristicsatall).Forathingtohavequalities,onWittgenstein’sview,isforittoexistaspartofafact:thefactthatithasthosequalities.Andforittoexistaspartofafactis,accordingtoWittgenstein,forittoexistincombinationwithotherthings.Thatmeansthattherecannotbeanyonethingwithoutsomeotherthingexisting.WhatWittgensteinisdoinghereistakingatraditionalkindofview,andradicalizingit.Wecangiveaﬂavourofthisbyconsideringaparallelmovewhichweourselvesmightbetemptedtomake.InatraditionalAristotelianmetaphysics(ononeorthodoxinterpretation),thebasicentitieswereindividualthings:thingslikeWittgenstein(theman),orthetableinmyroom,ortheLeaningTowerofPisa.Theseindividualthingshavequalities:Wittgensteinhadthequalityofbeingrich((S)istrue);mytablehasthequalityofbeingmessy;theLeaningTowerofPisahasthequalityofbeingveryfamous.Individualthings,ontheonehand,andqualities,ontheother,correspondtolinguisticexpressionswhichbelongtodifferentgrammaticalcategories.Individualthingscorrespondtosingularterms(expressionswhichfunctionlikepropernames).Qualitiescorrespondtopredicates(forthetimebeing,wecantakeapredicatetobewhatyouhaveleftwhenyouknockoneormoresingulartermsoutofasentence).ThetraditionalAristotelianviewisthatindividualthingsarebasic,anddonotdependfortheirexistenceonanythingelse.Qualities,however,aretakentobedependentbeings:aqualitycannotexistexceptasthequalityofsomeindividualthing.Otherphilosophers(Humeisanexample)haveadoptedanoppositepriority:theyhavesupposedthatindividualthingsarejustbundlesofqualities.Onthisview,qualitiesarethebasicentities,andindividualthingsaredependentonthem.Itisnaturaltorespondtobothoftheseviewsthatthedependenceismutual:itisexactlyashardforanindividualthingtoexistwithnoqualities,asitisforaqualitytoexistexceptasthequalityofsomeindividualthing.WemayhesitatetosaythatWittgensteinmakespreciselythismove,becauseitisquitehardtounderstandWittgenstein’sviewof\n30THENATUREOFTHEWORLDqualities(wewillreturntothistopicinsection4Fbelow).Butwhathedoesisatleastsimilartothis:individualthingscanonlyexistsomehowqualiﬁed,andthiswillrequirethemtoexistincombinationwithotherthings.Ifthereistobeanythingwhichisareallybasicbeing,inanythinglikethesenseof(Ind),itcannotbeeitherwhatweantecedentlythinkofasanindividualthingoraquality:itcanonlybeafact.Hereisthepointoftheopeningremark,then.Ifwearetryingtocharacterizetheconstitutionoftheworld,wewanttounderstandthebasicentitiesofwhichitiscomposed.Whenwearetalkingofbasicentities,weareinterestedinentitieswhichareindependentofeachother.Theonlyenti-tieswhichmeetthatconditionarefactsofacertainkind.Sotheworldisfundamentallycomposedoffacts.This,inturn,meansthatweneedtoreviseourintuitiveortraditionalunderstandingofwhattheworlditselfis.Ifwethinkthattheworldisfundamentallycomposedofindividualthings,wewillthinkthattheworlditselfisalargecompo-sitething—perhapssomethinglikethephysicaluniverse,asweordinarilythinkofit,boundbythelimitsofspaceandtime.Butiftheworldisthetotalityoffacts,theworlditselfwillbealargecompoundfact,theconjunctionofalltheotherfacts.Theworldwillbe,asitwere,agrandthat.Itisperhapsforthisreason—toemphasizethattheworldisnotanykindofthing—thatWittgensteinchoosestobeginthebookwithremark1,ratherthan1.1:eventotalkof‘facts’,intheplural,suggeststhatfactsareakindofthing.Iftheworldisagreatthat,ratherthananall-encompassingobject,itwillbedelimitedbythefacts,togetherwiththefactthattheyareallthefacts,andnotbythelimitsofspaceandtime,asWittgensteinsaysin1.11.Theworldisanaltogetherdifferentkindofentityfromthings(thougheventosaythatisproblematic).1CFACTSANDTHINGSItisnot,however,thattherearefactsandnotthings.Factsarecomposedofthings,and,aswewillsee,thiscomplicatesthepicturewhichseemstobepresentedin1–1.21:infact,\nTHENATUREOFTHEWORLD311.1mayenduplookinglikeanoverstatement.Thecompo-sitionoffactscanbebrokendownintotwostages.First,weshouldnote:2Whatisthecase,thefact,istheexistenceofatomicfacts.Theclaimhereisthatallfactsarecomposedofcertainbasicfacts,called‘atomicfacts’inOgden’stranslation.Somefactsarejustatomicfacts;othersarecompoundsofseveralatomicfacts.Itisthese‘atomicfacts’whicharethebasicconstituentsoftheworld,theentitiesintowhichtheworld‘divides’(1.2),theentitiesofwhichWittgensteinsays:1.21Anyonecaneitherbethecaseornotbethecase,andeverythingelseremainsthesame.Theseatomicfactsarethefundamentalorganicunitiesintheworld,theentitieswhoseexistencedependsonnootherentityofthesamekind.Butawordonthetranslationhere.‘Atomicfact’isOgden’stranslationofWittgenstein’sGermanword‘Sachverhalt’.‘Sachverhalt’means,etymologically,somethinglike:com-portmentorarrangementofthings.PearsandMcGuinness’salternativetranslationoftheterm—stateofaffairs—istherefore,muchclosertothesenseoftheGermanword.Asaresult,insomeplacesinthetext—forexampletheverynextremark,2.01—Pears’sandMcGuinness’stranslationdoessomethingwhichOgden’sdoesnotdo.Butthemove-mentofphilosophysincetheTractatusmakestheirtransla-tionawkwardinotherways.Thephrase‘stateofaffairs’isnowsometimesusedtomeanpossiblefact,including,thereforewhatmighthavebeenthecase,aswellaswhatactuallyisthecase.So,onthisuse,‘stateofaffairs’hasawiderapplicationthan‘fact’.ButWittgensteinmeanshistermtohaveanarrowerapplicationthan‘fact’:aSachverhaltisafactofaveryspecialkind,onewhichisbasicintheconstitutionoftheworld.AndalthoughOgden’sterm‘atomic’reﬂectsnoelementoftheGermanword,it\n32THENATUREOFTHEWORLDdoescapturesomethingofWittgenstein’sreasonforsinglingoutSachverhalten.Tobe‘atomic’,etymologically,istobeindivisible.WhenWittgensteinsaysthattheworld‘divides’intofacts,hemeansthatitdividesintoSachverhalten,andnofurther.IwillcontinuetouseOgden’stranslation—Wittgensteinhimselfapproveditafterall—butitisaswelltobeawarebothofwhatitomitsandofwhatitinterpolates.Whatareatomicfacts?WittgensteingavethefollowingexplanationinalettertoBertrandRussell:Sachverhaltis,whatcorrespondstoanElementarsatzifitistrue.(CL:125)An‘Elementarsatz’isanelementaryproposition,orbasicsentence.Thistellsusthatthenotionofanatomicfactistiedtolanguage,justasthenotionoffact,ingeneral,is.6Anditalsoemphasizesthebasicnessofatomicfacts.ButbeyondthistheexplanationreliesonthefullconceptionoflanguagewhichiselaboratedlaterintheTractatus.Facts,ingeneral,arecompoundsofatomicfacts.Andatomicfacts,Wittgensteincontinues(2.01),arecombinationsofobjects.Thenotionofanobjectwillshortlybegivenfullerelaboration,but,forthetimebeing,Wittgensteinishappytotakeittobeequivalentto‘entity’(‘Sache’)or‘thing’(‘Ding’).ThingsentertheTractatus’spictureoftheworldonlywhencombined—boundorlinked—withoneanothertoformatomicfacts.Theremainderofthe2.01s(upuntil2.0141)areconcernedwiththerelationbetweenobjectsandatomicfacts;andWittgensteinreturnstothetopicinthe2.03s.Wittgensteinisconcernedtoexplainherecertaincomplicatedrelationsofdependenceandindependence.Objectsareboth,inonesense,dependenton,and,inanothersense,independentof,atomicfacts.Atomicfactsare,inasense,dependentonobjects,despitethemselvesbeingthemostbasicorganicunitiesintheworld.Objectshavetobe,inasense,independentofatomicfacts,ifwearetomakesenseoftheideathatatomicfactsarecomposedofobjects.Theyareindependentofatomicfactsin\nTHENATUREOFTHEWORLD33thefollowingsense.Objectsappearincombinationwithoneanother,inatomicfacts,buttheverysameobjectscouldhaveexistedevenifthoseparticularatomicfactshadnotexisted.SupposethatthereisanatomicfactthatBillistotheleftofBen,inwhichtheobjectsBillandBenstandinrela-tiontoeachother.BillandBencouldhaveexisted,eveniftheyhadnotstoodinthatparticularrelationtoeachother(ifBillhadbeentotherightofBen,forexample).Thecrucialpointhereisthatatomicfactsarecontingent:theyarewhatisactuallythecase,butmightnothavebeen.Theindepen-denceofobjectsfromatomicfactsconsistsinthis:theexistenceofobjectsdoesnotdependonwhatisactuallythecase,butsimplyonwhatispossible.ButWittgensteinisconcernedtoinsistthatthisindepen-denceshouldnotbeoverstatedormisunderstood.Itisnotthattheobjectsmighthavelainarounduselessly,uncom-binedwitheachother.Forifthathadbeenpossible,wewouldhaveneededsomekindofspecialglue,tojoinobjectstightlyenoughtogethertoformtheorganicunitieswhichareatomicfacts.Butnoglueisneeded:2.03Intheatomicfacttheobjectshangoneinanother,likethelinksofachain.Therearetwoseparatepointshere.First,theobjectsarebuilttolinkup,tobecombinedinatomicfacts.And,second,theircombinationdoesnotrequireanyextrinsicjoiningagent:theobjectsalwayscomeinparticularcombinations;theyarealwaysalreadyjoined,withnoexternalassistance.Thismeansthatobjectscannotbethoughtofasself-standingentitieswhichjusthappentobejoinedtogetherinstatesofaffairs.ThisiswhatWittgensteinisrulingoutwhenhesays:Itwould,sotospeak,appearasanaccident,whentoathingthatcouldexistaloneonitsownaccount,subsequentlyastateofaffairscouldbemadetofit.(2.0121)\n34THENATUREOFTHEWORLDAndthereasontherecannotbesuchanaccidentisthis:2.012Inlogicnothingisaccidental:ifathingcanoccurinanatomicfactthepossibilityofthatatomicfactmustalreadybeprejudgedinthething.Andagain:(Alogicalentitycannotbemerelypossible.Logictreatsofeverypossibility,andallpossibilitiesareitsfacts.)(2.0121)WhatisWittgenstein’spointhere?Insayingthatinlogicnothingisaccidental,orthatalogicalentitycannotbemerelypossible,Wittgensteinseemstoberulingouttheideaofsomethingwhichispossible,butmightnothavebeenpossible.Thatis,heseemstobeinsistingonthisprinciple:(NP)Whateverispossibleisnecessarilypossible.(NP)isabasicandintuitiveprincipleofmodallogic:itisthecoreprincipleofthemodernmodallogicalsystem(S5).ItseemsclearthatWittgensteincommitshimselftoit.(NP)hasacounterpartwhichrelatestowhatisessentialtothings,providedwearepreparedtocountenancetheveryideaofthingshavingessences.7Theessenceofsomethingis—oratleastentails—whateverisnecessarytothatthing’sexistence.Ifweacceptboth(NP),andthatthingshaveessences,wewillacceptthis:(NPE)Ifsomethingcanbetrueofanobject,itisessentialtotheobjectthatthatcanbetrueofit.Wecansee(NPE)atworkinoneofWittgenstein’sfundamentalclaimsaboutobjects:2.011Itisessentialtoathingthatitcanbeaconstituentpartofanatomicfact.\nTHENATUREOFTHEWORLD35Thesepointsarethenelaboratedinthefollowingremarks:2.0123IfIknowanobject,thenIalsoknowallthepossibilitiesofitsoccurrenceinatomicfacts.(Everysuchpossibilitymustlieinthenatureoftheobject.)Anewpossibilitycannotsubsequentlybefound.AndthatliesattheheartofadistinctionwhichWittgensteinmakesbetween‘internal’and‘external’qualities:2.01231Inordertoknowanobject,Imustknownotitsexternalbutallitsinternalqualities.Theexternalqualitiesofathingarethosequalitieswhichithasonlycontingently;theinternalqualitiesarewhatisessentialtoit.Inourtrivialexample,itisanexternalqualityofBillthatheistotheleftofBen,becauseheneednothavebeentotheleftofBen.ButitisinternaltoBillthathecanbetotheleftofBen:thisispartofhisessence.ThesamepointsareusedagaintointroducefortheﬁrsttimeoneofthecrucialnotionsoftheTractatus,thenotionofform:2.0141Thepossibilityofitsoccurrenceinatomicfactsistheformoftheobject.Thenotionofformisonewithahugephilosophicalreso-nance.ItharksbacktoPlatoandAristotle:inAristotle,forexample,theformofathingiswhatisessentialtoit,whatmakesitthethingitis.8AnditrecallsKant,forwhomspaceandtimeweretheformsofintuition(roughly:basicexperi-entialawarenessofthings),whichmeans(atleast)thattheyarepresupposedinallintuitions(oftherelevantkinds).Infact,Wittgenstein’sconcernsareevenclosertoKantthanthis.Kantsays:[T]hatwhichallowsthemanifoldofappearancetobeintuitedasorderedincertainrelationsIcalltheformofappearance.9\n36THENATUREOFTHEWORLDWittgenstein’sclaimisthatwhatisessentialtoanobjectisjustthefact(aswemightputit)thatitcancombinewithotherobjectstoformaparticularrangeofatomicfacts:thatistheformoftheobject.Thisisinitselfadramaticclaimaboutobjects:thereisnomoretotheiressence,ortowhatisinternaltothem,thanwhichother(kindsof)objectstheycancombinewith,toformatomicfacts.ThisleadsWittgensteintosay:2.0232Roughlyspeaking:objectsarecolourless.Whichpicksupanearlierpoint:Aspeckinavisualfieldneednotbered,butmusthaveacolour;ithas,sotospeak,acolourspacearoundit.(2.0131)Thepointisnotthatobjectsdonothaveanymorematerialqualitiesthanthefactthattheycancombinewithparticularrangesofotherobjectstoformparticularrangesofatomicfacts:itisnotthattheydonotactuallyhaveanycolour(literallyspeaking)—althoughthatmaybetrue.Itisjustthatthesematerialqualitiesarenotpartoftheformoressenceoftheobjects.Materialproperties,hesays,‘areﬁrstpre-sentedbythepropositions—ﬁrstformedbytheconﬁgurationofobjects’(2.0231).10Thisiswhatliesbehindthelimitsoftheindependenceofobjectsfromatomicfacts:Thethingisindependent,insofarasitcanoccurinallpossiblecir-cumstances,butthisformofindependenceisaformofconnexionwiththeatomicfact,aformofdependence.(2.0122)11Therearetwothingsworthnotingaboutthisclaim.First,thewordtranslated‘connexion’hereis‘Zusammenhang’:thisisanordinaryword,meaningconnectionorcontext,butetymolo-gicallyitmeansahangingtogether.Itthusemploysthevery\nTHENATUREOFTHEWORLD37imageofhangingtogetherwhichWittgensteinusestoexplaintherelationofobjectstooneanotherinanatomicfact,whichwehavealreadyseenin2.03(italsoappearsin2.032).Second,thisremarkabouttheindependenceofobjectsactuallybeingaformofdependenceisjustiﬁedbythefollowingparenthesis:(Itisimpossibleforwordstooccurintwodifferentways,aloneandintheproposition.)HereweseeanexplicitappealtothenatureoflanguagetojustifyWittgenstein’smetaphysicalclaimaboutthenatureoftheworld.Theclaimis,apparently,thatwecanseethatobjectsmustbedependentonatomicfacts,becausewordsessentiallyoccurinsentences.Itisimportant,however,torecognizethatthedependenceofobjectsuponatomicfactsdoesnotrequiretheretobeanyactualatomicfacts.Allthatisneededisthattherelevantatomicfactsbepossible.ThisisthepointWittgensteinismakinginthisremark:2.013Everythingis,asitwere,inaspaceofpossibleatomicfacts.Icanthinkofthisspaceasempty,butnotofthethingwithoutthespace.ThisisaclearechoofKant.HereiswhatKantsays,insupportoftheclaimthatspaceisapriori:Onecanneverrepresentthatthereisnospace,althoughonecanverywellthinkthattherearenoobjectstobeencounteredinit.12Thereisariskofbeingmisledbythisecho,however.IfwehaveKantinourearswhenweread2.013,wemighttakeWittgensteintobeclaiminginthesecondsentencethatwecouldhaveaspaceofpossibleatomicfacts,evenifthatspacewereemptyofobjects.Hewouldthenbeclaimingthatthoseatomicfactswouldhavebeenpossibleeveniftheobjectshadnotexisted,buttherecouldnothavebeenthoseobjectswithoutthoseatomicfactsbeingpossible.Butthisisincon-sistentwithWittgenstein’sowntheory.Hedoesnotthink\n38THENATUREOFTHEWORLDthattheverysameatomicfactscouldhavebeenpossiblewithouttheobjectsexisting.Aswewillsee,hisviewisthatnothingatallwouldhavebeenpossibleiftheobjectswhichconstituteatomicfactshadnotexisted.WittgensteindoesnotmeanwhattheKantianechomightleadonetothinkhemeans.Hedoesnotmeanthatthespaceofpossibleatomicfactscouldhavebeenemptyofobjects,butthatitcouldhavebeenemptyofatomicfacts.Thatistosay,itmighthavebeenthatnoneoftheatomicfactswereactual,oractuallyexisted.Thiswouldnotbeasituationinwhichtherewerenoactualfacts,ofcourse:itwouldsimplybeasituationinwhichnoneoftheactualfactswasatomic.Asweknowfrom1.21,eachatomicfactcaneitherbethecaseornotbethecase.Ifanatomicfactisnotthecase,thenthereisafactallright:thefactthattheatomicfactisnotthecase.Butthisfact(whichWittgensteincallsa‘negativefact’in2.06)isnotanatomicfact.Wittgenstein’spointin2.013isthattheexistenceofanobjectdoesnotrequirethatanyatomicfactbeactual:itsimplyrequiresthattherelevantatomicfactsbepossible.Furthermore,althoughthereisaclearechoofKantin2.013,therelationsofdependenceandindependencebetweenobjectsandatomicfactsaremorecomplexthananysimpleparallelwithKant’sconceptionofempiricalspacewouldsuggest.Atomicfactsare,ofcourse,thebasicorganicunitiesoftheworld,andobjectscanonlyexist,combinedwithotherobjects,inatomicfacts.Butbeyondthat,thereisreallyamutualdependence.Thus,Wittgensteinclaims,ontheonehand,thatthething’scapacitytooccurinallpossiblecir-cumstancesisaformofdependenceofobjectuponatomicfact.But,ontheotherhand,thefactthatthepossibilityofitsoccurrenceinatomicfactsmustbe‘prejudged’inanobjectmeansthatthisistrue:2.014Objectscontainthepossibilityofallstatesofaffairs.13Andthisgivesusasenseinwhichobjectsarebasic:theyare,inasense,thegroundofallpossibilities.Thisbasicnessof\nTHENATUREOFTHEWORLD39objectsisfurtherelaboratedinWittgenstein’sclaimthat‘objectsformthesubstanceoftheworld’(2.021).Iwillturntothatclaiminthenextsection.Butwecannotenowthatthepicturewebeganwithhasbeencomplicated.Itremainstruethattheworldisthetotalityoffacts,andnotofthings(1.1),becausethethingsdonotappearintheworldasself-standingentities;butitisclearlythecase,onWittgenstein’sview,thatobjectsarejustasbasicinonewayasfactsareinanother.1DTHESUBSTANCEOFTHEWORLDWehaveseenthatWittgensteinbeginstheTractatuswithageneralcontrastbetweenfactandthing.Attheoutsetthecontrastisquiteschematic,andtheterminologynotusedwithgreatprecision.Thussomeofhiscoreclaims(forexample,1.2and1.21)aremadeintermsoffacts(Tatsachen),whentheyarestrictlytrueonlyoffactsofaspecialkind,theatomicfacts(Sachverhalten).Similarly,hebeginswithrela-tivelyvaguetalkofthings(Dingen),apparentlyswappingthenotioneasilywiththatofanobject(Gegenstand)oranentity(Sache).Butitbecomesgraduallyclearthatthethingswhicharehisprincipalfocushavetomeetcertainquitedemandingconditions.Tworemarksinparticulararestriking:2.0232Roughlyspeaking:objectsarecolourless.2.0233Twoobjectsofthesamelogicalformare—apartfromtheirexternalproperties—onlydifferentiatedfromoneanotherinthattheyaredifferent.Bythisstageitisclearthatwearedealingwiththingswhicharenotatalllikethethingsweusuallytakeourselvestohaveexperienceof.ThesearethethingswhichWittgensteincallsobjects(Gegenständen).Wittgensteinmakesthefollowingcentralclaimaboutobjects:2.02Theobjectissimple.\n40THENATUREOFTHEWORLDThatistosay,objectshavenoparts;theyarenotcomposedofthings;theyarenotcomplex.ThismeansthatWittgenstein’sobjectscannotbeanythinglikethe‘things’whichweordinarilytakeourselvestoexperienceandtounderstand.Theyarenotlikepeople,ortables,orroads,orcities:allofthese‘things’arecompound;theyhaveparts.Strictlyspeaking,therearenosuchthings,onWittgenstein’sview.Sentenceswhichseemtorefertosuch‘things’needtobere-understood,sothatwedonotletourselvesadmitthattherearecomplexobjects:2.0201Everystatementaboutcomplexescanbeanalysedintoastatementabouttheirconstituentparts,andintothosepro-positionswhichcompletelydescribethecomplexes.Wherewemighthavethoughtthatwehadacomplexobject,accordingtoWittgensteinthereisnothingbutthefactthatitsconstituentpartsarerelatedtoeachotherinacertainway.Thisisstrikingenough,butitisnomorestrikingthanthereasonWittgensteinoffersfortheclaimthatobjectsaresimple:2.021Objectsformthesubstanceoftheworld.Thereforetheycannotbecompound.WhatdoesWittgensteinmeanby‘substance’?Hisansweristhis:2.024Substanceiswhatexistsindependentlyofwhatisthecase.HerewecanseethatWittgensteinisappealingtoakeystrandinthetraditional(Aristotelian)notionofsubstance.14Wemightexpressitasfollows:(Sub)Asubstanceissomethingwhichremainsthesamethingthroughchange.ButWittgensteinisnotconcernedwithanythingsovulgaraschangeintheempiricalworld.Hisconcerniswithalternativepossibilities,withthefullrangeofpossibleatomicfacts.\nTHENATUREOFTHEWORLD41Wittgenstein’sconceptionofsubstanceisexpressed,notbythetraditional(Sub),butbysomethinglikethis:(Sub*)Substanceiswhatisconstantacrossallpossibledifferencesintheatomicfacts.Thereisasigniﬁcantclaimembodiedinthis:thattheremustbesomethingwhichisconstant,ﬁxed,acrossallpossiblevariationsinwhatiscontingent.Wittgensteindoes,indeed,makethissubstantialclaim:2.022Itisclearthathoweverdifferentfromtherealoneanimaginedworldmaybe,itmusthavesomething—aform—incommonwiththerealworld.15Everypossibleworldmustshareaformwiththeactualworld.Wittgensteincontinues:2.023Thisfixedformconsistsoftheobjects.Andhesaysofsubstance:2.025Itisformandcontent.Thethinkinghereissomethinglikethis.Theremustbesomethingcommon,somethingconstantacrossallpossiblealternativescenarios.Thisis(atleastcloseto)whatisknowntraditionallyassubstance.Butwhatisactuallyrequired,accordingtoWittgenstein,isacommonform.Whatmightbemeantby‘form’here?Thenotionofformhasalreadybeenintroducedintheideaoftheformofanobject:itisthewaysinwhichthatobjectcancombinewithotherobjectstoformatomicfacts.Wittgensteinintroducesarelatednotioninconnectionwithatomicfacts:2.032Thewayinwhichobjectshangtogetherintheatomicfactisthestructureoftheatomicfact.2.033Theformisthepossibilityofthestructure.\n42THENATUREOFTHEWORLDThestructureofanatomicfactissomethingcontingent:itisthefactthatitsconstituentobjectsareactuallycombinedinthewaytheyare.Theatomicfact’sformisquitedifferent:itis(asitwere—thereasonforthiscautionwillhaveemergedbythetimewehavereachedtheendofthebook)thefactthattheconstituentobjectscanbearrangedlikethat.Thislatter‘fact’—theformoftheatomicfact—clearlyhasitsrootsintheformoftheconstituentobjects,since‘objectscontainthepossibilityofallstatesofaffairs’(2.014).Sotherecanonlybeaﬁxedform,commontoallpossibleworlds,iftheobjectswhoseformistherootoftheformofatomicfactsarealsocommontoallpossibleworlds.Thisiswhysubstanceisbothformandcontent.Itisform,becausetheformofatomicfacts—thepossibilityoftherebeingsuchfacts—iswhatiscommontoallpossibleworlds.Anditiscontent,becausetheformofatomicfactsiscarriedintheformoftheirconstituentobjects,sotheremustbethingsaswellasforms,iftherearetobetheappropriateforms.HenceWittgensteinsays:2.026Onlyifthereareobjectscantherebeafixedformoftheworld.2.027Thefixed,theexistentandtheobjectareone.Wehavehereadramaticconceptionofobjects.Itturnsoutthattheworldismadeupofatomicfactswhoseconstituentsareentitieswhichexistnecessarily,ineverypossibleworld.Theobjectscanonlybeindependentofwhatisthecase,inthewaytheyhavetobetoformthesubstanceoftheworld,iftheyexistnomatterwhat:if,thatis,theyarenecessaryexistents,notdependingfortheirexistenceonanycon-tingentfact.Andthisiswhyobjectsmustbesimple:anobject’sbeingcompoundrequiresittobepossibleforitnottoexist(beforeitscomponentsarecombined,forexample,oraftertheyarebrokenapart).Thisconceptionofobjectsmaybedramaticandclear,butthereasoningwhichunderliesitisnotentirelyobvious.ForthesakeofsimplicityIwilljustpresentmyownreading\nTHENATUREOFTHEWORLD43here—leavingthedifﬁcultiesofinterpretationtobeconsideredmorefullyintheAppendix.AsIunderstandit,then,theTractatus’sconceptionofobjectsdependsonthefollowingtwoclaims:(FF)Theremustbeafixedformwhichiscommontoallpossibleworlds;(FO)Therecanonlybesuchafixedformifthereareobjectscommontoallpossibleworlds.Whymightwehold(FF)?(FF)isawayofstatingthemodalprinciple(NP)(thatwhateverispossibleisnecessarilypos-sible),whichisitselfnaturalandintuitive:wehavealreadyseenthisprincipleinplayinWittgenstein’sconceptionoftheessenceofobjects(as(NPE)).ButdoesWittgensteinhaveanindependentreasonforholding(FF)?Well,hecertainlyproducesanargument:2.0211Iftheworldhadnosubstance,thenwhetherapropositionhadsensewoulddependonwhetheranotherpropositionwastrue.2.0212Itwouldthenbeimpossibletoformapictureoftheworld(trueorfalse).Thewordingof2.0211suggeststhatwhatWittgensteinwantstoinsistonisthatthesenseofallpropositionsmustbeindependentofthetruthofanyofthem.ThisisreminiscentofthefollowingremarkfromtheNotebooks:Astatementcannotbeconcernedwiththelogicalstructureoftheworld,forinorderforastatementtobepossibleatall,inorderforapropositiontobeCAPABLEofmakingSENSE,theworldmustalreadyhavejustthelogicalstructureithas.Thelogicoftheworldispriortoalltruthandfalsehood.(NB:14)In2.0212Wittgensteininsists,ineffect,thatitmustbepossibletoforma‘picture’oftheworld.Thecentralclaimofthetheoryoflanguagewhichisdevelopedlaterinthe\n44THENATUREOFTHEWORLDTractatusisthatsentencesarepicturesormodels.Itisnat-ural,therefore,totaketheuseof‘picture’(‘Bild’—pictureormodel)in2.0212tobeananticipatoryreferencetothattheory.WewillconsiderthetheoryitselfindetailinChapters3and4;forthemoment,however,Iwillanticipatethatexplanation,andsaythatthetheoryinvolvesacom-mitmenttothesethreeclaims:(a)Inthebasiccase,asentenceisacombination(ahanginginoneanother)ofsymbols(names);(b)Inthebasiccase,forasentencetohavesenseisfortwocondi-tionstohold:(i)Itssymbolsarecorrelatedwithobjectsintheworld;(ii)Itispossibleforthesymbolstobecombinedinthewayinwhichtheyareactuallycombinedinthesentence;(c)Itispossiblefortheconstituentsymbolsofasentencetobecombinedinthewaytheyare,andbecorrelatedwiththeobjectswithwhichtheyarecorrelated,ifandonlyifitispossibleforthecorrespondingobjectstobecombinedinthesamewayinreality.Armedwiththeseassumptions,wecanreconstructanargu-mentforthekeyassumption(FF)whichitisnaturaltothinkliesbehind2.0211and2.0212.Wemaybeginwithageneralmodalassumption:(1)Ifanypossibilityisanecessarypossibility,theneverypossibilityisanecessarypossibility.Thisisextremelynatural:itsimplyinsistsonauniformapproachtomodality.Given(1),wecanpickonanarbitrarypossibilityandtrytoarguefor(FF)forthatcase.LetustakeasentenceofthekindwhichWittgensteinwillregardasbasic:accordingtoassumption(a),itconsistsjustofacom-binationofnames.Wecanusetheletters‘a’,‘b’,‘c’,etc.,assamplenames,andwecanjustwritesuchlettersinastringtoindicatetheirbeingcombined.Abasicsentence,then,mightlooklikethis:\nTHENATUREOFTHEWORLD45(P1)abcde(P1)assertsthatsomethingisthecase:itassertsthatabcde.Weassumethat(P1)statesagenuinepossibility(somesentencesmust,andthiscanbetakentobeanarbitrarilychosenexampleofonewhichdoes).Given(1),wecannowassert:(2)Ifthepossibilityexpressedby(P1)isanecessarypossibility,theneverypossibilityisanecessarypossibility.Ouraimwillthenbetoshowthatthepossibilityexpressedby(P1)isindeednecessarilypossible(grantedthatitisatleastpossible).Consider,ﬁrst,thestatementthatthepossi-bilityassertedby(P1)isindeedapossibility.Wemightwriteitlikethis:(P2)Itispossiblethatabcde.Ifwhatisexpressedby(P1)ispossible,butnotnecessarilypossible,then(P2)mustbecontingent.Soinordertoprove(FF)weneedtoshowthat(P2)isnotcontingent.Nowhereisanaturalprincipleaboutcontingency:(3)Ifasentenceiscontingent,itshavingsensemustnotdependuponitsbeingtrue.Thisisnatural,becauseitisnaturaltothinkthatifasen-tenceiscontingent,itstruthcouldnotbeworkedoutjustfromitsmeaning.Atthispoint,weshouldrecallassumption(b)oftheTractatus’sgeneraltheoryoflanguage.Itfollowsfromthisthat(P1)hassenseifandonlyif‘abcde’isapossiblecom-binationofsymbols,providedthatthenamesarecorrelatedwithobjectsinreality.Butbyassumption(c)oftheTractatus’sgeneraltheoryoflanguage,‘abcde’isapossiblecombinationofsymbolsifandonlyifthecorrespondingobjectscanbecombinedinthesameway—thatis,justin\n46THENATUREOFTHEWORLDcase(P2)istrue.SotheTractatus’stheoryoflanguageentitlesustoclaim:(4)(P1)hassenseifandonlyif(P2)istrue.Butnowlookat(P2):thesentence‘abcde’occurswithinit—andinitsownright,notmerelyquoted.Itisclearthat(P2)cannothavesenseifthisintegralpartofithasnosense.Furthermore—ifweassumeforthemomentthatitislegitimatetotalkaboutpossibilityatall—therecanbenootherproblemabout(P2)’shavingsense.Thatmeansthatwecanassertthis:(5)(P2)hassenseifandonlyif(P1)hassense.Butfrom(4)and(5)togetherwecanderivethis:(6)(P2)hassenseifandonlyif(P2)istrue.Butby(3),thenaturalprincipleaboutcontingency,(6)impliesthis:(7)(P2)isnotcontingent.Butwealreadyknow:(8)If(P2)isnotcontingent,whatisassertedby(P1)isnecessarilypossible.Puttingthisalltogetherwith(2),wecanconclude:(9)Everypossibilityisanecessarypossibility.Whichis,ineffect,theﬁxed-formassumption(FF).How,precisely,doesthisargumentrelatetothetext?Thesuggestionisthat2.0212,ineffect,bringsinassumptions(a),(b),and(c)fromtheTractatus’sgeneraltheoryoflan-guage—theso-called‘picturetheory’.Andtheargument\nTHENATUREOFTHEWORLD47canbeseenasshowingthatitisimpossibleforthesenseofonesentencetodependonthetruthofanother(whichiswhat2.0211saysisproblematic).(P2)assertsacertainpos-sibility.Byassumptions(b)and(c)fromthepicturetheory,itsassertingthatpossibilityisthesamethingas(P1)’shavingsense.So(P2)istantamounttoanassertionthat(P1)hassense:onthisinterpretation,(P2)isthe‘otherproposi-tion’onwhosetruththesenseof(P1)depends.Butofcourse(P2)’struthisnotindependentofitsownsense,whichmeansthatitcannotbecontingent,asitwouldhavetobefortheworldnottohavea‘ﬁxedform’.Wemayalsonote,moreover,thatthereasoningfromstep(4)tostep(5)isreasoningwhichisnaturallyattributedtoWittgenstein.Aswewillseeinthenextchapter,WittgensteinobjectedtoRussell’s‘multiple-relation’theoryofjudgementonthefollowingground:5.5422Thecorrectexplanationoftheformoftheproposition“Ajudgesp”mustshowthatitisimpossibletojudgeanonsense.(Russell’stheorydoesnotsatisfythiscondition.)Thepointhereisatleastclosetothethoughtthatasentencewhichcontainsapieceofnonsenseasanintegralpartmustitselfbenonsense.16Theargumentisclearlyvalid,andseemsclosetoWittgenstein’sthought,butisitsound?Themostobviouslyquestionableassumptions—apartfromthosewhichderivefromtheTractatus’stheoryoflanguage—arethegeneralmodalprinciples(1)and(3).Iwillnotquestion(1)here,butitisworthpausingforamomentover(3).What(3)assumes,ineffect,isthattherecannotbecontingentaprioritruths.Nowthiswasstandardlyassumedbyphilosophers:itisconnectedwithKant’sinsistencethatphilosophyandmathematicsareapriori,andthereforewithhisclaimthattheyinvolvesyn-theticaprioriknowledge.ItisalsonaturaltothinkthatitisconnectedwithWittgenstein’sowninterestintheapriori.ButithasbeenquestionedbySaulKripke,inhisground-breakinglecturesonnamingandnecessity(Kripke1980).\n48THENATUREOFTHEWORLDKripkepointsoutthatthetwodistinctions—betweentheaprioriandtheaposteriori,ontheonehand,andbetweenthenecessaryandthecontingent,ontheother—aremadeinquitedifferentways.Thedistinctionbetweentheaprioriandtheaposterioriisanepistemicdistinction:itconcernswaysinwhichtruthscanbeknown.Butthedistinctionbetweenthenecessaryandthecontingentismetaphysicalorontolo-gical:itisconcernedwithwhetherthingscouldinfacthavebeenotherwise.WewouldprobablyrejecttheargumentIhavepresentedhere,therefore,whateverourviewoftheTractatus’stheoryoflanguage,butthisisnoreasonnottoascribesomesuchargumenttoWittgenstein:Wittgensteinwouldcertainlyhaveassimilatedthetwodistinctions.Alloureffortsofarhasbeendirectedtowardstheﬁxed-formassumption(FF).Butwhatabouttheotherkeyassumption,(FO),theassumptionthataﬁxedformrequiresobjectswhicharecommontoallpossibleworlds?Wittgenstein’sviewsherehaveacertainhistory.17Russellatonepointthoughtthattheformofabasickindofsentencewasexpressedinaverygeneralstatement:sotheformofasentencesuchas‘Fa’wouldbecapturedintheverygeneralstatement‘(9x,u).ux’(thereisauandthereisanxsuchthatxisu;or:thereisatleastoneobject,andatleastoneproperty,suchthattheobjecthastheproperty).18AndWittgensteinseemsatonepointtohaveagreed(NB:17).19Unfortunately,thatgeneralstatementseemstobetrueonlyifsomeparti-cularsentenceoftheappropriateformistrue.Soonesen-tence’shavingtheformithasseemstodependoneitheritoranother(ofthesameform)beingtrue.20Thisseemsarbitraryinitself,anditviolatesWittgenstein’sgeneralinsistencethatquestionsofsensemustbesettledinadvanceofquestionsoftruthandfalsity.Wittgensteinseemstohavethoughtthattheonlywayofavoidingthisproblemwastosaythis:Thelogicalformofthepropositionmustalreadybegivenbytheformsofitscomponentparts.(NB:23)\nTHENATUREOFTHEWORLD49Andsince,accordingtotheTractatus’sgeneralconceptionoflanguage,thelogicalformofaproposition(sentence)isthesameasthelogicalformofanyrealityitcanrepresent,theformofatomicfactsmustbegivenbytheformsoftheircomponentparts—whichistosay,theobjects.Theremightseemstilltobeagap,however,betweenthisandwhatWittgensteinclaimsaboutobjects:2.027Thefixed,theexistentandtheobjectareone.ThisseemstocommitWittgensteinunambiguouslytotheideathatgenuineobjectsexistindependentlyofwhatisthecase—thatis,necessarily.ButitmightseemthatwhatWittgensteinneedsinordertoestablishthepossibilityof‘formingapictureoftheworld’,whilegroundingtheformsofpropositionsintheformsoftheirparts,couldbegrantedhimwithoutadmittingthisstrongconclusion,thattheobjectswhichembodytheformoftheworldexistnecessa-rily.Forhismainpurposes,Wittgensteinneedsthefollow-ingthreeclaims:(d)Theformoftheworld(thewaysinwhichobjectscanbecom-bined)isindependentofwhatisthecase;(e)Theformoftheworldiscontainedintheformsofobjects(thewaysinwhichtheycancombinewithoneanother);(f)Theformsofobjectsareessentialtothem.Anditmightseemthat(d),(e),and(f)couldallbetrue,eveniftheobjectsthemselveswerenotnecessarilyexistententities.Itmightseemthatwhatisnecessaryisjustthatthereshouldbesomeobjectsineachworld—perhapsjustthisnumberofobjects—withjusttheformsoftheobjectswhichactuallyexist.Butthenitisnotatallobviousthattherecouldnothavebeenotherobjectswhichhadessen-tiallytheformswhichtheobjectswhichactuallyexisthave.And,aswehaveseen,Wittgensteinhimselfseemstoallowjustthispossibility:\n50THENATUREOFTHEWORLD2.0233Twoobjectsofthesamelogicalformare—apartfromtheirexternalproperties—onlydifferentiatedfromoneanotherinthattheyaredifferent.Infact,however,itisnotclearthatWittgenstein’sactualcommitmentsreallydooutrunwhathisphilosophyoflan-guagerequires.Thisonlyseemstobethecaseifwemis-understandwhat(d)hereinvolves.21Inrequiringtheformoftheworldtobeindependentofwhatisthecase,Wittgensteinisrequiringthepossibilitiestobeindependentofwhatisthecase:thatistosay,howeverelsethingsmighthavebeen,theremustatleasthavebeenthesamepossibi-lities.Butaccordingtothephilosophyoflanguagetobeexpoundedlaterinthebook,thepossibilitiesarejustwaysinwhichtheobjectscorrelatedwiththenamesmighthavebeenarranged.Sowewouldnothavethesamepossibilitiesunlesswehadthesameobjects.Withdifferentobjects,wemighthaveformallyparallelpossibilities,buttheywouldnotstrictlyhavebeenthesamepossibilities.SoitseemsthatifwegrantWittgensteinhisphilosophyoflanguage,togetherwithhisgeneralprinciplesofmodality,hereallydoeshaveanargumentfortheclaimthatthefundamentalobjectsexistnecessarily.1ETHEWORLDASAWORLDOFFACTS:ARECAPITULATIONWittgensteincompleteshisoutlineofthenatureoftheworldbyrestatingthepointsof1–1.21explicitlyintermsofatomicfacts.Thushesays:2.04Thetotalityofexistentatomicfactsistheworld.Thislookslikejustarestatementof1,butthingsarenotquitesosimple.Thereasonisthattherearefactsotherthantheactualatomicfacts.Inparticular,weneedtobearinmindthattherearealotofatomicfactswhichmighthaveexisted,butdonot.Ifweconsideranatomicfactwhichmighthave\nTHENATUREOFTHEWORLD51existed,butdoesnot,andsaythatitdoesnotexist,weseemtohavereportedanotherfact.Factsofthiskind—factsthatsuchandsuch(somethingatomic)isnotthecase—Wittgensteincalls‘negative’facts:Theexistenceofatomicfactswealsocallapositivefact,theirnon-existenceanegativefact.(2.06)Negativefactswillnotbeincludedinthelistofalltheexis-tentatomicfacts,buttheywillbeincludedin‘everythingthatisthecase’.22WhatthisrevealsisthatitisnotatallstraightforwardtorestatetheopeningclaimoftheTractatusjustintermsofatomicfacts.Butthereseemstobeawayaroundthedifﬁculty,forthecaseofnegativefacts,atleast.Thisisbecause,ifwehavealistofalltheexistentatomicfacts(thepositivefacts),wewillhaveﬁxedthefulllistofnegativefactsaswell.Oncewehaveﬁxedwhichofallthepossibleatomicfactsactuallyexists,wemustalsohaveﬁxedwhichdonotexist—alltherest.Thatistosay:2.05Thetotalityofexistentatomicfactsalsodetermineswhichatomicfactsdonotexist.Onceweﬁxallthepositivefacts,wehavetherebyﬁxedallthenegativefactsaswell.Sowenowhave,asitwere,amuchlargerlistoffacts:alltheatomicfactsandallthefactswhichare,asitwere,negations,ofpossiblebutnotactualatomicfacts.Butiseventhislargerlistenoughtoﬁxalltheexistentfactsthereare?Onlyifitiscantheclaimof2.04holdgood.ItisoneofWittgenstein’sdistinctiveclaimsthatthislargerlist—thelistofalltheatomicfactsandallthenega-tionsofpossiblebutnotactualatomicfacts—sufﬁcestoﬁxthefullrangeoffacts.Sincethatlargerlistisﬁxedbyﬁxingwhichatomicfactsexist,theclaimisthatoncewehaveﬁxedwhichofallthepossibleatomicfactsactuallyexist,wewill\n52THENATUREOFTHEWORLDhaveﬁxedallthefactsthereare.IthinkthatitistomakepreciselythispointthatWittgensteinintroducesthenotionof‘reality’,astheOgdentranslationhasit(‘Wirklichkeit’).Butwefaceapuzzle,createdbythreesentenceswhicharealmostnexttooneanotherinthetext:2.04Thetotalityofexistentatomicfactsistheworld.2.06Theexistenceandnon-existenceofatomicfactsisthereality….2.063Thetotalrealityistheworld.WhydoesWittgensteinnotsimplyusetheword‘world’inplaceof‘reality’in2.06,anddispensewith2.063altogether?Itisonlyifthereisadifferenceinthemeaningofthewordsthattherecanbeanypointinusingbothofthem;buthow,then,cantheclaimof2.063betrue?Theproblemisthat2.04suggeststhattheworldisrestrictedtotheexistentatomicfacts,whereas2.06and2.063togetherseemtorequirethattheworldalsoinclude(insomesense)thenon-existentatomicfacts.IthinkthattheWittgenstein’spointhereismademoreobscurethanitneedbebyanawkwardnessoftranslation:‘Wirklichkeit’wouldbebetterrenderedactuality,ratherthanreality.‘DieWirklichkeit’iswhatisactuallythecase—asopposedtowhatismerelypossible.Ifweadoptthissuggestion,2.04–2.063canbeseentoconstituteanargu-ment:or,rather,2.05–2.063canbeseentoconstituteanargumentfor2.04.Onceitisdeterminedwhichofthepos-sibleatomicfactsactuallyexistitisalsodeterminedwhichdonotexist(2.05).Thesubstantialclaimof2.06isthenthatlistingwhichatomicfactsexist,andwhichdonotexist,isenoughtodeterminecompletelywhatisactuallythecase—whichofallthepossiblefactsofanykind(notjustatomicfacts)isactual.And2.063canthenbeseenasmakingthesimplepointthatthismeansthatwewillhavedelimitedthewholeworld:theworldis,afterall,thetotalityofwhatisactuallythecase(as1claims).IthinkthismustbeWittgenstein’sargument,butitisnotenoughtosolveourproblemwith2.04,2.06,and2.063:howcantheworldconsistbothjustoftheexistentatomicfactsand\nTHENATUREOFTHEWORLD53oftheexistenttogetherwiththenon-existentatomicfacts?Thebestthatcanbesaid,Ithink,isthatWittgenstein’swritinghereisloose.Heseemstobeconﬂatingthesetwoclaims:(i)Thetotalityofexistentatomicfactsis(constitutes)theworld(everythingthatisthecase);(ii)Thetotalityofexistentatomicfacts,togetherwiththesebeingalloftheexistentatomicfacts,determineseverythingthatisthecase(theworld).(ii)iswhathemustmean;but(i)iswhatheactuallysays,at2.04.ThiskindofloosenessisactuallynotuncommonintheTractatus.Itis,Ithink,partofwhatintheIntroductionIcalledthe‘poetic’characterofthework.Weshouldsimplyacceptit,andmaketheminormodiﬁcationsneededtodealwiththepuzzlesitcreates.Thepuzzleof2.04,2.06,and2.063shouldnotdistractusfromthesubstantialclaimthatWittgensteinmakeshere—theclaimthatﬁxingwhichpossibleatomicfactsdoanddonotexistisenoughtoﬁxwhichpossiblefactsofanykindexist.Thereseemstobeaconnectionbetweenthissubstantialclaimandtheclaimofthemutualindependenceofatomicfacts.ForinthemidstofthisargumentWittgensteinwrites:2.061Atomicfactsareindependentofoneanother.2.062Fromtheexistenceornon-existenceofanatomicfactwecannotinfertheexistenceornon-existenceofanother.Thisis,ofcourse,arestatementoftheearlyclaimwhichlayattheheartoftheideathatfacts—atomicfacts,atleast—arethebasicorganicunitiesintheworld:1.21Anyonecaneitherbethecaseornotbethecase,andeverythingelseremainsthesame.Butwhatistheclaimdoinghere,rightinthemiddleoftheargumentforthepointthatﬁxingwhichatomicfactsexistisenoughtodetermineallthefacts?\n54THENATUREOFTHEWORLDThereisareason:itisonlyifatomicfactsareindependentofeachotherthatitcanbeplausibletomakethesubstantialclaimwhichWittgensteinmakesat2.06.Forsupposethatsomeatomicfactsdiddependonotheratomicfacts.Thentherewouldbefactsofthefollowingform,where‘p’and‘q’expressatomicfacts:(D)Itsbeingthecasethatpdependsonitsbeingthecasethatq.Wemightcallfactsofthisformdependencefacts.Theobviousexamplesofdependencefactswouldbeexplanatoryfacts:factsexpressedbysentencesoftheform‘pbecauseq’.Therecouldonlybeapointinmakingdependenceclaimsorexplanatoryclaimsifdependencerelationsandexplanatoryrelationsheldbetweensomepairsoffactsandnotothers.Forexample,supposethat‘Thehousecaughtﬁre’,‘Thecir-cuitblew’,and‘Garydroppedhiscigarette’allexpressatomicfacts.Weonlyhavereasontosaythatthehousecaughtﬁrebecausethecircuitblewifweareconcernedtoruleoutotherdependencerelations—suchasthatthecir-cuitblewbecausethehousecaughtﬁre,orthatthehousecaughtﬁrebecauseGarydroppedhiscigarette.Ifdependencerelationsholdbetweensomepairsoffactsandnotothers,thenwhetherornotaparticulardependencefactexists—whetherornottherelevantdependenceclaimistrue—willnotdependjustonwhethertheatomicfactsinvolvedactu-allyexist.Itcanbetruethatthehousecaughtﬁre,thatthecircuitblew,andthatGarydroppedhiscigarette,andstillnotbetruethatthecircuitblewbecausethehousecaughtﬁre,orthatthehousecaughtﬁrebecauseGarydroppedhiscigarette.Soifsomeatomicfactsdependedonothers,therewouldbesomefurtherfacts—dependencefacts—whoseobtainingwasnotdeterminedbytheexistenceandnon-existenceoftheatomicfacts.Thatistosay,ifsomeatomicfactsdependedonothers,theclaimof2.06wouldnotbetrue.Itturnsout,then,thatthefundamentalmetaphysicalclaimoftheopeningsectionsoftheTractatus—thatitis\nTHENATUREOFTHEWORLD55factswhicharethebasicorganicunitiesintheworld—isinterconnectedwiththesubstantialclaimof2.05and2.06,thatonceitisdeterminedwhichatomicfactsexist,allofthefactsaredetermined.ItisonlybecauseoftheclaimthattheatomicfactsareindependentofoneanotherthatWittgensteincanrestatetheopeningstatementoftheTractatusintermsofatomicfacts,andclaimthatthetotalityofexistentatomicfactsistheworld.1FTHEMETAPHYSICALCOMMITMENTSOFTHETRACTATUSAswewillsee,themetaphysicsoftheTractatusisjustiﬁed—insofarasitisjustiﬁedatall—bythetheoryoflanguagewhichfollowsitinthetext.Letustakestockhereofwhatwewillhavetoﬁndsupportforinthattheoryoflanguage:(T1)Thebasicorganicunitiesoftheworldarefacts;(T2)Factsaredifferentinkindfromthings(objects);(T3)Factsareeitheratomicfactsorcombinationsofatomicfacts;(T4)Theexistenceofanyatomicfactisindependentoftheexis-tenceofanyotheratomicfact;(T5)Atomicfactsarecombinationsofobjects;(T6)Whichatomicfactsarepossibleisdeterminedbythenatureofobjects;(T7)Itisessentialtoanobjectthatitcancombinewithotherobjects,inthewaysitcan,toformatomicfacts;(T8)Nothingisessentialtoanobjectbeyondthefactthatitcancombinewithotherobjects,inthewaysitcan,toformatomicfacts;(T9)Objectsexistnecessarily;(T10)Itisnecessarythatjustthoseatomicfactsarepossiblewhichare,infact,possible.(T6),(T7),(T9),and(T10)havealreadybeenshowntofollow(givenasmallpinchofsalt)fromthetheoryoflan-guage—providedthatthattheoryoflanguageturnsouttorequirethetruthofthefollowingclaims:\n56THENATUREOFTHEWORLD(a)Inthebasiccase,asentenceisacombination(ahanginginoneanother)ofsymbols(names);(b)Inthebasiccase,forasentencetohavesenseisfortwocondi-tionstohold:(i)Itssymbolsarecorrelatedwithobjectsintheworld;(ii)Itispossibleforthesymbolstobecombinedinthewayinwhichtheyareactuallycombinedinthesentence;(c)Itispossiblefortheconstituentsymbolsofasentencetobecombinedinthewaytheyare,andbecorrelatedwiththeobjectswithwhichtheyarecorrelated,ifandonlyifitispossibleforthecorrespondingobjectstobecombinedinthesamewayinreality.Weneedthentoensurethat(a)–(c),togetherwith(T1)–(T5)and(T8),canbeextractedfromtheaccountoflanguagewhichtheTractatusprovides.ThataccountoflanguagewillbethetopicofChapters3,4,and5.Butbeforeweturntoit,weneedtounderstandsomethingofthephilosophicalback-groundfromwhichthetheorysprang,whichwillbeourconcerninChapter2.Evenbeforeturningtothat,however,itisaswelltoraise—ifonlytopostpone—anissuewhichhasstruckseveralpeopleinconnectionwiththeseopeningsections.Itiscom-monlyassumedthattakingWittgensteintobepresentingametaphysicalaccountofthenatureoftheworldintheopeningremarksoftheTractatusrequiresustoattributetohimaformofrealism.23AndthisissometimesfelttobeafalsiﬁcationofWittgenstein’sviews.24Weneedtobeclear,atleast,aboutwhatisbeingsuggestedhere.First,hereisastatementofrealism:(R)Thenatureoftheworldasitisinitselfisaltogetherindepen-dentofanythingtodowithanythoughtorrepresentationofit.Anyreluctancetoaccept(R)isaformofanti-realism.Apositivedenialof(R)(involvinganassertionofsomedependenceoftheworlduponsomethingtodowiththoughtorrepresentation)isaformofidealism.\nTHENATUREOFTHEWORLD57Second,hereisadeﬁnitionofmetaphysics,asIhavebeenusingthetermsofar:(M)Metaphysicsisconcernedwiththewaysinwhichtheworldmust,can,andcannotbe.Thatistosay:metaphysicsisconcernedwiththemodalityoftheworld.Justas(R)isarelativelytraditionalstatementofrealism,so(M)isafairlyconventionaldeﬁnitionofmetaphysics.Whatistheconnectionbetweenmetaphysicsandrealism?Somearetemptedtomakethissimpleconnection:(MR)Onlyarealistcanengageinmetaphysics.25GiventhedeﬁnitionsofrealismandmetaphysicswhichIhaveoffered(andwhich,asIsay,arequiteuncontroversial),(MR)shouldseemunobvious,tosaytheleast.Infact,onthefaceofit,idealism(asIhavedeﬁnedit)islikelytobeametaphysicalthesis(onthedeﬁnitionofmetaphysicspro-videdby(M)).Theidealistholdsthatthereissomedepen-denceoftheworlduponsomethingtodowiththoughtorrepresentation,andisunlikelytothinkthatthisdependenceisaccidental:idealismisitselflikelytobeastatementofhowtheworldmustbe(viz.,dependentonsomethingtodowiththoughtorrepresentation).Ithink(MR)isfalse.Weshouldalsobewareofaclaimwhichmightseemtorunintheotherdirection.IhavesaidthatthemetaphysicsoftheopeningpagesoftheTractatusisjustiﬁed,insofarasitisjustiﬁedatall,onlybythecon-ceptionoflanguagewhichispresentedlater.Someonemightsupposethatthisrequiressomeformofidealism.Thatis,someonemightthinkthatthiswastrue:(MLI)Ifametaphysicaltheoryisjustifiedbyaphilosophyoflanguage,thenthewaytheworldmust,can,andcannotbe(whichisdescri-bedinthemetaphysicaltheory)mustdependonthenatureoflanguage(whichisdescribedbythephilosophyoflanguage).\n58THENATUREOFTHEWORLDBut(MLI)isfalsetoo:thedirectionofjustiﬁcationneednotmirrorthedirectionofanyrealdependence.Thispointabouttheseparabilityofthedirectionofjustiﬁcationfromthedirectionofdependenceisveryobviousinscience:areadingonaninstrumentwilljustifyajudgementaboutthecurrentﬂowingthroughawire,eventhoughtheinstrumentreadingobviouslydependsuponthecurrent,ratherthanviceversa(thecurrentcausesthereading).Thereisnomorereasontoexpectthedirectionofjustiﬁcationtomatchthedirectionofdependenceinphilosophythanthereisinscience.Someonemightreacttothis,however,andtakethepar-allelIhavejustdrawnbetweenphilosophyandsciencetoshowsomethingelse,namelythis:(MLR)Ifametaphysicaltheoryisjustifiedbyaphilosophyoflan-guage,thenthenatureoflanguage(whichisdescribedbythephilosophyoflanguage)mustdependonthewaytheworldmust,can,andcannotbe(whichisdescribedinthemeta-physicaltheory).Thismightbereasonableifthenatureoflanguageweremerelyevidenceforametaphysicaltheory,buttherelationbetweenthephilosophyoflanguageandmetaphysicsneednotbethoughtofinthisway.So(MLR)—whichisanotherwayoftryingtogetrealismoutofthegeneralshapeoftheTractatus—isnottrueeither.WhatthisallmeansisthatatleastonesetofworriesabouttheattributiontoWittgensteinofanysubstantialmetaphysicalviewscanbesetaside.ThegranddescriptionofthestructureofrealitywithwhichtheTractatusbeginscanbeacceptedatfacevalue,withoutprejudgingthequestionwhetherWittgensteinwasarealistornot.Theseremarksaresimplyneutralontheissue.Iwilladdressthegeneralques-tionofrealismandidealismdirectlyinChapter6,aspartofadiscussionoftheissueofsolipsismintheTractatus.Andinthemeantime,IwillnotehowviewstobefoundintheTractatusﬁtwithrealistandanti-realistinterpretations,asthoseviewsareencountered.\n2THELEGACYOFFREGEANDRUSSELL2ATHEIMPORTANCEOFLANGUAGETheTractatusbeginswithavisionofthenatureoftheworld.Thatvisiondependsontheconceptionoflanguagewhichiselaboratedinthework’smainbody.Butwhathaslanguagegottodowithit?Whyshouldaphilosophyoflanguagehaveanythingtocontributetoaviewofthenatureofreality?Whatmakeslanguagerelevantissomethingwhichisnaturallythoughttodeﬁnewhatisdistinctiveaboutlan-guage—incontrast,forexample,withanyotherkindofrepresentationalorexpressivesystem.Almosteveryonethinksthatlanguagesaresystemsofsignswhicharearbi-traryinthefollowingsense:whateveranyparticularsigndoes,adifferentsigncouldhavedonejustaswell(soitis,inasense,arbitrarythatthisparticularsign,ratherthananother,isactuallyused).Theviewthatlanguagesaresys-temsofarbitrarysignsisinterdependentwithaverygeneralconceptionofwhatitisforlanguagestobemeaningful,\n60THELEGACYOFFREGEANDRUSSELLwhichisseldomformulatedexplicitly,butcanbetracedbackthroughthewholehistoryofphilosophy.Thisgeneralapproachtolinguisticmeaning,withslightvariations,continuestoshapebothphilosophicalandnon-philosophicalconceptionsoflanguage.Wecanattempttoexpressthisapproachtolinguisticmeaningasamatterofbeingcommittedtoacertainassumption,whichwemightcallthecorrelationassumption:(Corr)Languagesdependfortheirmeaningfulnessoncorrelationsbetweencertainlinguisticitems,ontheonehand,andextra-linguisticitems,ontheother.Ifthisistoexpressanattitudetolanguagewhichisalmostuniversal,weneedtotakesomecareaboutwhatismeantby‘correlation’.Hereisanaturalcharacterization:(C)Acorrelationisanypairingofitemswhichmeetsthiscondition:itdoesnotmatterforthepurposesofthepairinghowthepairingisachieved.Thecorrelationassumption,withcorrelationunderstoodinthemannerof(C),clearlysupportstheviewthatlanguagesaresystemsofarbitrarysigns.Itisworthdwellingamomentontheformulationof(Corr)and(C).First,weshouldnotethat(C)explicitlyallowstherelevantcorrelationstobemadeinanynumberofways.Somewillthinkofthembeingmadedeliberatelyandself-consciously:‘Hereisasign,’wemightimaginesomeonesaying,‘andthereanextra-linguisticitem;letmecorrelatetheonewiththeother.’Others,however,willthinkofthecorrelationsasnomorethanassignmentsofmeaningwhicharerecognizedexplicitlyonlyafterthefact,inordertomakesenseofthosewhospeaksomelanguage(andthespeakersthemselvesmayhavenoconsciousconceptionofthecorre-lationswhichgivemeaningtotheirwords).(C)isneutralonthis.Inasimilarspirit,someviewsmightholdthattheextra-linguisticitemswithwhichlinguisticitemsarecorrelated\nTHELEGACYOFFREGEANDRUSSELL61canberecognizedashavingthecharactertheyhave,quiteindependentlyofthinkingofthemascorrelatesoftherele-vantlinguisticitems.Otherviews,ontheotherhand,mightdenythis,supposingthatwecanonlybeinapositiontoidentifythecorrelatesoflinguisticitemsinvirtueofspeak-ingalanguageofanappropriatekind.1Bothkindsofviewcanbeunderstoodtoaccept(Corr)withcorrelationunder-stoodasitischaracterizedin(C).Further,(C)allowsthattheremaybewhatwemightcallderivedcorrelations:theobviousexampleswouldbecorrelationsbetweencomplexlinguisticitemsandextra-linguisticitemswhicharesimpleconsequencesofantecedentpairingsofthecomponentsofthosecomplexlinguisticitemswithcertainotherextra-linguis-ticitems.Thatacorrelationisactuallyestablishedinapar-ticularwaydoesnotmeanthatitisessentialtothepurposesofthecorrelationthatitbeestablishedinthatway.Finally,itisworthpointingoutthat(Corr)doesnotholdthatthemeaningfulnessofeverylinguisticitemdependsonacorre-lationwithsomeextra-linguisticitem:itmerelyrequirestheretobesomesuchcorrelationsforalanguageasawholetobemeaningful.(Corr)allows,inparticular,thatsomelinguisticitemsmightbemeaningful,eventhoughtheythemselvesarenotcorrelatedwithanythingextra-linguistic,justinvirtueofotherlinguisticitemsbeingcorrelatedwithextra-linguisticitems.Withcorrelationunderstoodinthisway,(Corr),Ithink,isalmostuniversallyaccepted—oratleastwasuntilrelativelyrecently.2Butitiscomparativelyunspeciﬁc.Wegetsome-thingmoresubstantialifwespecifythekindofthingwemightincludeastherelevantextra-linguisticitemswithwhichlinguisticitemsneedtobecorrelated.Theinterpreta-tionof(Corr)whichunderliesWittgenstein’sconceptionoflanguageintheTractatuscanbeformulatedasacommitmenttothefollowingobjectivityassumption:(Obj)Theextra-linguisticitemswithwhichlinguisticitemshavetobecorrelatedforlanguagestobemeaningfulareitemsintheworld(objects).\n62THELEGACYOFFREGEANDRUSSELL(Obj)seemsmoreobviouslydeniablethanthecorrelationassumption,(Corr):indeed,awholetraditioninthephilo-sophyoflanguagehasdeniedit.JohnLocke,forexample,heldthatlinguisticitemsweremeaningfulinvirtueofacorrelationwithsomethingextra-linguistic(inlinewith(Corr)),butthoughtthattheextra-linguisticitemsinques-tionwerethingsinthemindofeachspeaker—thespeaker’s‘ideas’(Locke1700:III,ii).Wittgenstein’sgreatpredecessorsandphilosophicalinspirations,GottlobFregeandBertrandRussell,playedadecisivepartintheturntowardstheworld,awayfromthemind,which(Obj)represents;almosteveryonesincehasfollowedthem.Thecorrelationandobjectivityassumptions((Corr)and(Obj))togetherexpressthegeneralapproachtolanguagewhichWittgensteintookoverfromFregeandRussell.Andthesetwoassumptions,takentogether,makelanguageimmediatelyanddirectlyrelevanttoanunderstandingofthenatureofreality.Toseewhy,weneedﬁrsttorecognizehowlittlemerecorrelation(ascharacterizedby(C))canachieve.Correlationisnotaprocessoftransformation:ifwemerelycorrelatelinguisticitemswithsomethingextra-linguistic,theextra-linguisticisnottherebyreconﬁguredasitisinitself.Allthatwecandoisgetlinguisticitemstoreﬂectcertainpropertiesoftheextra-linguistic—whicheverpropertiesarenotlostinaprocessofcorrelation.Ofcourse,iflinguisticitemsreﬂectcertainpropertiesoftheextra-linguistic,lan-guagemustrevealsomethingofthenatureoftheextra-linguistic.Wecanexplainthisalittlemorecarefully.Ifweacceptthecorrelationassumption,(Corr),wecandividethepropertiesoflanguageinuseintothreecategories.First,therearethecoreintrinsicpropertiesofthemostbasiclin-guisticitemsthemselves—typically,theirshapeandsound.Thesewecansimplysetaside,asirrelevanttothesig-niﬁcanceoflanguage.Second,thereisthemerefactthatthebasiclinguisticitemsarecorrelatedwiththeextra-linguisticitemswithwhichtheyare,infact,correlated.Andthen,third,thereiseverythingelse:ifwearerightinourdeter-minationbothofthephilosophicallyirrelevantintrinsic\nTHELEGACYOFFREGEANDRUSSELL63propertiesofthelinguisticitems,andinouraccountofwhichextra-linguisticitemstheyarecorrelatedwith,every-thingelseaboutlanguageinusemustinsomewaybeareﬂectionoftheextra-linguistic,andmust,therefore,showussomethingaboutthetruenatureoftheextra-linguistic.Ifweaddtheobjectivityassumption,(Obj),tothispicture,weensurethattheextra-linguisticwhosetruenaturelan-guagecanrevealisnothinglessthantheworld.Itthenappearsthatanyfeatureoflanguagewhichcannotbesetasideasphilosophicallyirrelevant,andwhichisnotjustthefactofcertainlinguisticitemsbeingcorrelatedwithitemsintheworld,mustitselfbeinsomewayareﬂectionofthetruenatureofreality.Onceweacknowledgethesetwocoreassumptions,wecanseewhythephilosophyoflanguagemightplaysuchacen-tralroleintheTractatus.But(Corr)and(Obj)aremoredeeplyembeddedinthebookthanthatsuggests.Theyarenotmerebackgroundassumptions.Infact,thewholecon-ceptionoflanguagewhichformstheheartoftheTractatuscanbeseenasnothingmorethanaworkingoutof(Corr)and(Obj),inthelightofdifﬁcultieswhichWittgensteinfoundwiththeviewsofFregeandRussell.TheimportanceoftheworkofFregeandRussellforanunderstandingoftheTractatusishardtoexaggerate.Mostoftherestofthischapterwillbeconcernedwiththeback-groundwhichtheirworkprovidesforthephilosophyoflanguageoftheTractatus.3FregeandRussellweredecisiveinformingWittgenstein’sviewofthewayinwhich(Corr)and(Obj)mustbetrue.Theirwork—whetherdirectlyorindirectly4—ledhimtoconsidertherangeoflinguisticexpressionswhicharemeaningfulinvirtueofacorrelationwithsomethingextra-linguistic,thenatureoftheextra-linguisticitemswithwhichtheyarecorrelated,andthemannerofthecorrelation.ButtheinﬂuenceofFregeandRussellwasalsocrucialinshapingthelargerphilosophicalmotivationsfortheoverallviewoftheTractatus.TheirworkinthephilosophyofmathematicsengagedexplicitlywithKant’sconceptionofthetaskofphilosophy,5andthisKantian\n64THELEGACYOFFREGEANDRUSSELLbackgroundintersectswithWittgenstein’slonger-standingphilosophicalinterests.62BTHEOBJECTIVETURNIhavealreadyremarkedthatFregeandRussellplayedadecisiveroleintheestablishmentoftheobjectivityassump-tion,(Obj).Inadopting(Obj)FregeandRussellwererejectingalong-standingalternativeinterpretationofthecorrelationassumption,(Corr).Thesimplestversionofthisalternativeinterpretationof(Corr)istobefoundinLocke’sclaimthat‘wordsintheirprimaryorimmediatesigniﬁca-tion,standfornothing,buttheideasinthemindofhimthatusesthem’(Locke1700:III,ii,2).Thislookslikeacom-pletelygeneralclaim—itseemstobemeanttoapplytoallwords—butaswewillseeinsection2D,Lockedoesmakesomeexceptions.Theword‘idea’isatechnicaltermforLocke:hetakesittomean‘whatsoeveristheobjectoftheunderstandingwhenamanthinks’(Locke1700:I,8),withthe‘objectoftheunderstanding’beingassumedtobesomethinginthemind.ThecrucialthingaboutLocke’sview,forthetraditionofwhichhewasapartandwhichfollowedhimdowntothenineteenthcentury,isthatwordssignify(intheﬁrstinstance,atleast)itemsinthemind.Thesementalitemsarecomponentsofthoughts—whichonthisviewwillbetakentobecompositementalitems—anditisthoughtwhichlanguageis(intheﬁrstinstance,atleast)about.Ifwordssignifymentalitemswhicharecomponentsofthoughts,wholesentences—thethingsofwhichwordsarecomponents—willsignify(insomesense)wholethoughts.Andrelationsbetweenwholesentenceswillhavetobeexplainedintermsofrelationsbetweenwholethoughts.Someoftheserelationsareofparticularinteresttophiloso-phers.Consider,forexample,thefollowinglinguisticsequence:BertielovedOttoline.SoBertielovedsomeone.\nTHELEGACYOFFREGEANDRUSSELL65Ifthesentencesheresignify(insomesense)wholethoughts,therelationbetweenthem—whichisembodiedintheword‘so’—willnaturallybetakentoexpressarelationbetweenthoughts.Therelationhereisalogicalrelation;logicalrelationswillthenberelationsbetweenthoughts.Sincethoughtsareherebeingunderstoodtobecompositementalitems,onthisviewlogicwillbeconcernedwiththerelationsbetweencompositementalitems.Itwillthenbetemptingtotaketheserelationstobethebusinessofpsychology,andtotreatthelawsoflogicaspsychologicallaws.Fregeobjectedtoeverypartofthisview,whichherefer-redtoaspsychologism.Hehadtworeasonsforthinkingthatwordswerenotmeaningfulinvirtueofcorrelationswithideas.First,becauseideas(heassumed)areprivatetoeachindividual,sothatoneperson’sideasarenotaccessiblebyanother,ideasmustbeirrelevanttothemeaningofthewordsofpubliclanguages,whichwecanallunderstand(Frege1884:vi).Second,hetookitthatourwordsaremeaningfulinvirtueofcorrelationswithwhatwearecon-cernedwithwhenweusethem,andwearealmostneverconcernedwithideas(Frege1892a:28,31–32).Intheareainwhichhehadaparticularinterest,mathematics,Fregeclaimedthatweareconcernedwithnumbers,andnotwiththeideasofnumbers(Frege1884:v).Ingeneral,ourconcerniswiththingsintheworld,ratherthanthingsinthemind,anditmustbethingsintheworldwhichlinguisticitemsarecorrelatedwith.Astotheideathatthelawsoflogicmightbepsychologicallaws,Fregetakesittoderivefromanambiguityinthenotionofalaw.Thereare,ontheonehand,lawswhichprescribewhatoneshoulddo,andthereare,ontheother,lawswhichdescribewhatisthecase.Itisinthelattersensethatlawsofnaturearelaws.Ifwedescribethelawsoflogicas‘lawsofthought’,wewillbetemptedtotakethemaslawsinthisdescriptivesense.Theywillthenbecomepsychologi-callaws.Butpsychologicallawscanonlybeconcernedwithwhatisheldastrue,whereaslogicisconcernedwithtruth.Treatingthelawsoflogicas‘lawsofthought’—as\n66THELEGACYOFFREGEANDRUSSELLpsychologicallaws—forcesustoconﬂatebeingheldtruewithbeingtrue(Frege1893:xv).Frege’shostilitytothepsychologicalinterpretationof(Corr)waspartofhislifelongattempttosetmathematicsstraightandgiveitrigorousfoundations.AsimilarconcernmotivatedRussell,thoughhecameatitdifferently.Intheﬁrstinstance,heapproachedtheproblemsofcoherencewhichseemedtoinfectthefoundationsofmathematicsintheexpectationofﬁndingtheminsoluble.Theirinsolubilitywastobepartofthemotiveforthereinforcementoftheneo-Hegelianphilosophyinwhichhewasﬁrstschooled.Butfurtherresearchshowedhimthatmanyoftheseproblemshad,infact,beensolvedbyanumberofGermanmathema-ticianswhomhehadnotpreviouslystudied;andreadingtheworksofHegelhimselfseemstohavelefthimdisillusioned.ThementionofHegelisrelevanthere,becausetheneo-HegelianviewwhichwasdominantinRussell’scircleduringtheearlypartofhisacademiccareerwascertainlyatleastcontinuouswithLocke’sinitsapproachtolanguage.Andtheparticularneo-HegelianviewsofF.H.BradleywerethesubjectofcriticismbyG.E.MooreatjustthemomentwhenRussell’scommitmenttoneo-Hegelianismhadbeenwea-kened(Moore1899).MoorepointstotheconfusingfactthatBradleyusestheterm‘idea’intwodifferentsenses:torefertoakindofstateofmind,ontheonehand;andtoa‘uni-versalmeaning’,ontheother.MooretakesBradleytobeconfusingthesetwosenseswhenhetakesideasinthesecondsense—thatis,‘universalmeanings’—tobedependentonourstatesofmind,andwhenheconsequentlythinksthattruthinvolvessomerelationbetweenourstatesofmindandreality(Moore1899:177).Toavoidsuchaconfusion,Moorereplacestheuseoftheword‘idea’inthesecondsense—referringto‘universalmeanings’—withtheword‘concept’.Concerning‘concepts’,sounderstood,Mooresaysthis:Conceptsarepossibleobjectsofthought;butthatisnodefinitionofthem.Itmerelystatesthattheymaycomeintorelationwithathinker;andinorderthattheymaydoanything,theymustalreadybe\nTHELEGACYOFFREGEANDRUSSELL67something.Itisindifferenttotheirnaturewhetheranybodythinksthemornot.(Moore1899:179)Ifweunderstand‘concepts’(inthissense)tobewhataremeantbywords,wehavehereaﬁrstmoveawayfrompsy-chologismaboutmeaning.And,insomesense,thismoveawayfrompsychologismisamovetowardstheworld.Mooresays:‘Itseemsnecessary…toregardtheworldasformedofconcepts’(Moore1899:182).Likewise,hetakeshisviewtobeawayofholdingthat‘therelationofpre-missestoconclusionisanobjectiverelation’(Moore1899:183)—thatis,thatitdoesnotdependatallontheconclu-sionandpremisesbeingconnectedinourthoughts.Moorehererejectspsychologismaboutlogic.ThisearlytheoryofMoore’sdoesgivesomeendorsementto(Obj),butitisanoddkindofendorsement,sinceitdependscruciallyonanunorthodoxconceptionoftheworld—assomething‘formedofconcepts’.AndMoore’s‘con-cepts’arepeculiarentities.AccordingtoMoore,‘concepts’are‘incapableofchange’(Moore1899:179).Hedescribesitas‘perfectlyobvious’that‘theconceptcanconsistentlybedescribedneitherasanexistent,noraspartofanexistent,sinceitispresupposedintheconceptionofanexistent’(Moore1899:181).Moreover,accordingtoMoore,concepts‘cannotberegardedfundamentallyasabstractionseitherfromthingsorfromideas;sincebothalikecan,ifanythingistobetrueofthem,becomposedofnothingbutconcepts’(Moore1899:182).Inthisrespect,Russell’sviewwasclearer,andmoreclearlydistinctfromanyformofidealism.Hisviewchangedovertime,andseveraltimes,butinalltheversionsofhisviewwhichhadsomebearingonWittgenstein’sphilosophyintheTractatus,heseemstohaveheldthatlinguisticitemsarecorrelatedwiththingswhichareobjectsintheworldinarelativelyunproblematicsense.Therangeoftheseobjectsmaychange:earlyontherangeisextremelyextensive—‘aman,amoment,anumber,aclass,arelation,achimaera,or\n68THELEGACYOFFREGEANDRUSSELLanythingelsethatcanbementioned’(Russell1903:43)—whereaslateritseemstoberestrictedtothingswithwhichasubjectmaybeacquainted(Russell1984).Butthesechangesmaybeunderstoodaschangesofviewaboutwhatobjectsthereareintheworld:thesenseinwhichtheobjectsareobjects,theworldistheworld,andtheobjectsareintheworld,seemsconstantandrelativelyorthodox.FregeandRussellbothendorse(Obj)aswellas(Corr);andonce(Obj)isaccepted—onceitisacceptedthatwordsaremeaningfulinvirtueofacorrelationbetweenlinguisticitemsanditemsintheworld—itishardtoretreatfrom.AsFregeinsisted,itissoobviouslyitemsintheworldwhicharetheobjectsofourconcern,ratherthananythinginourminds.But,forallthat,acceptanceof(Obj)isnotpainfree.Itbringswithittwolargeproblems,inparticular.Thesewillbethesubjectsofthefollowingsections.2CTHEOBJECTIVETURNANDTHINNESSOFMEANINGFregeandRussellheld(Obj),thatlanguagesaremeaningfulinvirtueofcorrelationsbetweenlinguisticitems—signs—andthingsintheworld.Theﬁrstproblemthisviewfacesisthatitseemstomakemeaningtoothin:itseemstoallowtoolittletobeinvolvedinthemeaningofwords.If—inthebasiccase,atleast—wordsaremeaningfulinvirtueofbeingcorrelatedwiththingsintheworld,itseemsthatanytwowordswhicharecorrelatedwiththesamethingintheworldwillhavethesamemeaning,andanywordwithwhichnothingintheworldiscorrelatedwillhavenomeaning.Butthisis,onthefaceofit,implausible.Considerthefollowingtwosentences:(1)Everestisthehighestmountainintheworld;(2)Chomolungmaisthehighestmountainintheworld.Itisnaturaltothinkthatthesetwosentencesdifferinmeaning,becausesomeonecouldunderstandbothandyet\nTHELEGACYOFFREGEANDRUSSELL69thinkthatoneofthemwastrueandtheotherfalse.Andyettheonlydifferencebetweenthemisthatonehasthename‘Chomolungma’wheretheotherhasthename‘Everest’,andthesetwonamesinfactrefertothesamemountain.Again,considerthissentence:(3)GreenkryptoniteisfataltoSuperman.Wearelikelytothinkthatthissentenceismeaningful—perhapseventrue—eventhoughitseemsthatthereisnoobjectatallwithwhichthename‘Superman’iscorrelated.ThisthinnessofmeaningwasespeciallyproblematicforFrege,whoseviewcombinedthreethings:averysimpleviewofthegrammarofsentences;arelativelyunrestrictedconceptionofthekindsoflinguisticitemwhosemean-ingfulnessdependsontheirbeingcorrelatedwithsomethingextra-linguistic;andaveryaustereviewofthethingswithwhichdifferentkindsoflinguisticitemarecorrelated.Atbase,histheoryrecognizesthreeclassesofexpression:sin-gularterms,sentences,andpredicates(theresultofremov-ingoneormoresingulartermsfromasentence).Heisverygenerousinwhathecountsasasingularterm:anyexpres-sionatallwhichpicksoutanindividualobjectcountsasasingularterm.Bythiscriterion,ordinarypropernames(suchas‘Everest’and‘Chomolungma’)aresingularterms;butsoaremorecomplexexpressions,like‘theleastrapidlyconvergingseries’,‘whoeverdiscoveredtheellipticformoftheplanetaryorbits’,and‘(223)+2’.Thethreebasickindsofexpressionarecorrelatedwiththreedistinctivekindsofitemintheworld,onFrege’stheory.Singulartermsrefertoobjects,whichmaybeofvariouskinds:people,series,numbers(forexample).Sentencesrefertoentitiesofaveryspecialkind:truthvalues.AlltruesentencesrefertotheTrue,andallfalsesentencesrefertotheFalse.Sentences,infact,becomeaspecialkindofname,onFrege’stheory,withtheTrueandtheFalsebeingobjectsofaspecialkind.Predicatesrefertoentitieswhicharedifferentagain:accordingtoFrege,they\n70THELEGACYOFFREGEANDRUSSELLrefertoakindofincompleteentitywhichhecallsaconcept.Thisisanotherconfusinguseofadifﬁcultword:forFrege,a‘concept’isafunction,whichyieldsatruth-value(eithertheTrueortheFalse)asoutput,givenaparticularobject,orclassofobjects,asinput.OnFrege’sview,itseemsthatallpredicateswhicharetrueofexactlythesameobjectswillrefertothesame‘concept’,thesamefunctionfromobjectstotruth-values.ThesebasicassumptionsmaketheproblemofthinnessofmeaningverysharpforFrege.Theexpressions‘(223)+2’and‘18’refertothesamething,onhisview:thenumbereighteen.Butsurelytheydifferinmeaning?Heholdsthatalltruesentencesrefertothesamething—theTrue—asdoallfalsesentences—totheFalse:butsurelydifferenttruesentences,anddifferentfalsesentences,candifferinmeaning?Andsurelytwopredicatescouldbetrueofexactlythesamethingswithouthavingthesamemeaning?Fregeintroducedatechnicalnotion,whichhecalledsense,preciselytodealwiththisdifﬁculty(Frege1892a).Fregean‘sense’isdeﬁnedpreciselytobewhateveritisthatmarksadifferenceinmeaningbetweensuchpairsofsentencesas(1)and(2),despitethefactthat,onFrege’stheory,thewordsinthem(and,indeed,thesentencesthemselves)allrefertothesamethings.The‘sense’ofanexpressionissupposedtobedeterminedbythewayinwhichtheentitywithwhichtheexpressioniscorrelatedisgiventoone—by,asthetech-nicalterminologyhasit,the‘modeofpresentation’oftheentitytheexpressionrefersto.Sothenames‘Everest’and‘Chomolungma’expressdifferentwaysinwhichthesamemountainispresentedtous;similarly,theexpressions‘(223)+2’and‘18’presentthesamenumberindifferentways.AndFregeclaimedthatanexpressioncouldhave‘sense’eveniftherewasinfactnothingwithwhichitwascorre-lated.Sothephrase‘theleastrapidlyconvergingseries’has‘sense’,accordingtoFrege—andthereforeakindofmeaning—eventhoughtherecanbenosuchseries.Andsentence(3)canhave‘sense’—andthereforestillbe\nTHELEGACYOFFREGEANDRUSSELL71meaningful—eventhoughthereisnotreallysuchapersonasSuperman,andconsequently(accordingtoFrege)thesentenceasawholeisneithertruenorfalse.Allkindsofexpressionhave‘sense’(inhissense),accordingtoFrege.Hegivesaparticularnametothe‘sense’(inhissense)ofsen-tences:the‘sense’ofasentenceisathought(inthesenseofwhatisthought,ratherthanthethinkingofit).OnFrege’sviewthe‘sense’ofanexpressionisdistinctfromitsreference—distinctfromtheentityintheworldwithwhichitiscorrelated.Butitisstillbothpublicandobjective:itisnotmeanttobepsychologicalinanyway.SoFregean‘thoughts’—the‘senses’ofsentences—areunlikethoughtsasMooreunderstoodtheterm,intwocrucialrespects:iftwopeoplethinkthat(223)+2=18,theyboththinkthesamethought;andthatthought—thethoughtthat(223)+2=18—existed,andwastheretobethought,evenbeforeanyoneentertainedit.Fregean‘sense’ismeanttobeobjectiveandnon-psychologicalinmuchthesamewayasMoore’s‘concepts’are.Frege’sresponsetotheproblemofthinnessofmeaningis,then,toofferaratherricheraccountofwhatisinvolvedin(Corr)and(Obj).Atbase,languagesdependfortheirmean-ingfulnessonlinguisticitemsbeingcorrelatedwithitemsintheworld.Butthecorrelationsaremadeindifferentways—theitemsintheworldaregiventousindifferentways—andthesedifferencesinmannerofcorrelationarereﬂectedinanaspectofmeaningwhichgoesbeyondthemerefactofcorrelation.7Indeed,insomecasesthisaspectofmeaningcanbepresentevenwhennoactualcorrelationhasbeenmade.RusselldistrustedFrege’snotionof‘sense’.HisattitudeismadeclearinalettertoFregewrittenattheendof1904:Inthecaseofasimplepropernamelike‘Socrates’,Icannotdistin-guishbetweensenseand[reference];Iseeonlytheidea,whichispsychological,andtheobject.Orbetter:Idonotadmitthesenseatall,butonlytheideaandthe[reference].Iseethedifferencebetweensenseand[reference]onlyinthecaseofcomplexeswhose[reference]\n72THELEGACYOFFREGEANDRUSSELLisanobject,e.g.,thevaluesofordinarymathematicalfunctionsliken+1,n2,etc.(Frege1980:169)8AndwithinayearhehadgivenuptheappealtoFregean‘sense’eveninthecaseofthe‘complexes’hementionshere.HisrevisedviewmadenoappealtoFregean‘sense’atall.Hisresponsetotheproblemofthinnessofmeaninghad,therefore,tobequitedifferent.Inessence,itinvolvedchan-gingthosefeaturesofFrege’stheorywhichmadethepro-blempeculiarlysharpforhim.Hetookamuchlesssimpleviewofgrammar,anddistinguishedasbelongingtofunda-mentallydifferentgrammaticalcategoriesexpressionswhichFregehadgroupedtogether.Hetookamorerestrictiveviewoftherangeoflinguisticitemswhosemeaningfulnessdependsontheirbeingcorrelatedwithsomethingextra-linguistic.Andhehadalessaustereconceptionofthenatureoftheentitiesintheworldwithwhichlinguisticitemsmaybecorrelated.Russell’scrucialadvancecamewithhisinventionofhistheoryofdescriptions,presentedfortheﬁrsttimeinhisclassicpaper,‘OnDenoting’(Russell1905).Thistheoryinvolvedmakingaradicaldistinctionbetweensingulartermsproperlysocalled(whatRussellhimselfwouldlatercall‘logicallypropernames’)anddeﬁnitedescriptions.Deﬁnitedescriptionsarecomplexexpressionswhichservetopickoutparticularindividualthings:expressionssuchas‘theleastrapidlyconvergingseries’,‘whoeverdiscoveredtheellipticformoftheplanetaryorbits’,and‘(223)+2’.WhereasFregehadtreatedtheseassingularterms,onaparwithsemanticallysimplepropernames,Russelltookthemtobequantiﬁerexpressions.Ifwetakethestandardformofdeﬁ-nitedescriptiontobegiveninaphraseoftheform‘TheF’,wecanpresentRussell’sviewofthem,astheyoccurinsentencesoftheform‘TheFis…’,asbeingthattheyareparaphrasablewithsomethingofthisform:‘ThereisexactlyoneobjectwhichisanF,andthatobject…’.Thus,‘theleastrapidlyconvergingseries’canberendered(asitoccursin\nTHELEGACYOFFREGEANDRUSSELL73appropriatesentences)as‘Thereisexactlyoneobjectwhichisaleastrapidlyconvergingseries,andthatobject…’.And‘(223)+2’becomessomethinglike‘Thereisexactlyoneobjectwhichisaresultoftakingthecubeof2,multiplyingitby2,andadding2totheproduct,andthatobject…’.Sounderstood,themeaningfulnessofadeﬁnitedescrip-tion(orofasentenceinwhichsuchadescriptionoccurs)doesnotdependinanywayonthedescription’sbeingcor-relatedwithanobject.WhereasonFrege’sviewacorrelationwithanobjectispresupposed,andthereissomethingdefec-tiveaboutthemeaningofadescriptionwhenthereisnoobjectwithwhichitiscorrelated,onRussell’sviewdescrip-tionstowhichnoobjectscorrespondarefullyandunpro-blematicallymeaningful.Theirusesimplyinvolvestheassertion(ratherthanmerelythepresupposition)thatexactlyonethingsatisﬁesacertaincondition.ThistheoryenabledRusselltoexplaindifferencesinmeaningbetweendifferentdeﬁnitedescriptions,andbetweendeﬁnitedescrip-tions,ontheonehand,andsemanticallysimplepropernames,ontheother.Differentdescriptionswillinvolvetheassertionthatdifferentconditionsareuniquelysatisﬁed;andsemanticallysimplepropernameswillnotinvolvetheassertionthatanyconditionisuniquelysatisﬁed.Muchoftheproblemofthinnessofmeaning—atleastasitappliestowhatFregecountedassingularterms—isthusavoided.Partofthisproblemstillremains,however.Whatarewetodoabouttheapparentdifferenceofmeaningbetween(1)and(2),whichdifferonlyinthedifferentapparentlysimplepropernameswhichtheycontain?HintsofRussell’sapproachtosuchsentencesaretobefoundintheclosingparagraphsof‘OnDenoting’.Russellsawthatheneednotcountanyexpressionasdependingforitsmeaningonacorrelationwithanobject,unlesstheobjectandourmodeofaccesstoitmeetwhatevertheoreticalconditionsourphilosophymightdemand.Forexample,ourphilosophymightinvolvedeny-ingthatthereareanyunrealobjects;inthatcasewewillnotcounttheapparentlysimplepropernamestobefoundinﬁctionasdependingfortheirmeaningoncorrelationswith\n74THELEGACYOFFREGEANDRUSSELLobjects.Instead,theywillberegardedasbeingequivalenttodeﬁnitedescriptions,andwillbemeaningfulinjustthesamewayasdeﬁnitedescriptionsare,onRussell’saccount.WhatRussell’saccountallowsisthatwemaysetasidetheindicationsofsurfacegrammar,andtakealinguisticexpres-siontofunctioninwhateverwayourunderlyingphilosophyrequires.RussellhimselfmarriedhistheoryofdescriptionstoabroadlyCartesianepistemology.Attheendof‘OnDenoting’weﬁndhimproposingthatweneedonlyregardanexpressionasmeaningfulinvirtueofacorrelationwithanobject,iftheobjectinquestionisonewithwhichweare‘immediatelyacquainted’—where‘immediateacquaintance’isrestrictedtothingswhoseexistencewecannotdoubt(principallyqualitativefeaturesofourexperience).Allotherexpressions,whatevertheirapparentform,canbetreatedasequivalenttodeﬁnitedescriptions.ItisarguablethatthismethodenablesRusselltodealevenwithproblemssuchasthoseraisedby(1)and(2),whichturnonapparentdifferencesofmeaningbetweensentenceswhichinvolvedifferent,butapparentlyunstructured,propernames.Differentpropernamescanberegardedasbeingequivalenttodifferentdeﬁnitedescriptions,andthedifferentdescriptionswillinvolvetheassertionthatdifferentcondi-tionsareuniquelysatisﬁed.Sothename‘Everest’in(1)mightbetakentobeequivalenttothedescription‘themountainnamedafteraSurveyor-GeneralofIndia’,andthename‘Chomolungma’in(2)mightbetakentobeequivalenttothedescription‘themountainreveredbyTibetansasthemotheroftheworld’.Ifweonlyregardanexpressionasmeaningfulinvirtueofacorrelationwithanobjectiftheobjectinquestionisonewithwhichweare‘immediatelyacquainted’,andwecounteveryotherexpressionasequiva-lenttosomecompoundofsuchbasicexpressions,itisnotimplausiblethatwewillbeabletodealwiththeproblemsofthinnessofmeaningwhichariseforexpressionswhichFregewouldhavecountedassingularterms.Buttheproblemofthinnessofmeaningaffectsmorethanjustthoselinguisticexpressions.HowdoesRusselldealwith\nTHELEGACYOFFREGEANDRUSSELL75itelsewhere?HerethecrucialfeatureofRussell’saccountisitsrejectionofFrege’saccountofthereferenceofsentences.Fregetookthefullmeaningfulnessofsentencestodependontheirbeingcorrelatedwithaspecialkindofobject—atruth-value,eithertheTrueortheFalse.(Asentencewhichhasnotruth-valuemustbedefectiveinmeaning,havingsense,butnoreference.)Russellrejectedthisviewfortworeasons(Russell1903:504).First,itcouldbeseenby‘directinspection’thattherelationbetweenasentenceandatruth-valuewasquitedifferentfromthatbetweenanordinarysingulartermandanobject.And,second,Frege’sviewmustﬁndinsufﬁcientdistinctionbetweenalltruesentences,or,alternatively,betweenallfalsesentences.ButalthoughherejectedFrege’saccountoftheentitywithwhichsentencesarecorrelated,heagreedwithFrege—earlyon,atleast—thatwholesentenceswereindeedcorrelatedwithentities.Whileheheldthistheory,hecalledtheentitiesinquestionpropositions:theyaresupposedtobesomekindofobjectivecorrelateofwholesentences.Propositions,inthissense,theobjectivecorrelatesofwholesentences,arecomposedoftheobjectivecorrelatesofthewordsofwhichsentencesarecomposed.Theobjectivecorrelatesofwordsareconstituentsofthepropositionswhicharetheobjectivecorrelatesofwholesentences.ThusRussellwrotetoFrege(intheletterfromwhichIhavealreadyquoted):IbelievethatinspiteofallitssnowfieldsMontBlancitselfisacom-ponentpartofwhatisactuallyassertedintheproposition‘MontBlancismorethan4000metreshigh’.Wedonotassertthethought,forthisisaprivatepsychologicalmatter:weasserttheobjectofthethought,andthisis,tomymind,acertaincomplex(anobjectiveproposition,onemightsay)inwhichMontBlancisitselfacomponentpart.(Frege1980:169)InhisearlyworkRussellsaysthattheobjectivecorrelatesofwordsingeneralareterms(Russell1903:43).‘Terms’clearlybelongtotheworld:theyarewhatevercanbe\n76THELEGACYOFFREGEANDRUSSELLcountedasone,andarealsodescribableasunits,individuals,orentities.Russelldescribes‘terms’asfollows:Atermis,infact,possessedofallthepropertiescommonlyassignedtosubstancesorsubstantives.Everyterm,tobeginwith,isalogicalsubject:itis,forexample,thesubjectofthepropositionthatitselfisone.Againeverytermisimmutableandindestructible.Whatatermis,itis,andnochangecanbeconceivedinitwhichwouldnotdestroyitsidentityandmakeitanotherterm.(Russell1903:44)Among‘terms’ingeneral,Russelldistinguishestwokinds.Ontheonehandtherearethings(whatwehavebeencallingobjects),whicharecorrelatedwiththeexpressionswecallsingularterms(suchaspropernames);ontheotherhandtherearewhatRussellcallsconcepts(yetanotheruseofthatslipperyword),whicharethecorrelatesofotherwords(Russell1903:44).WhatRussellherecallsconceptsincludeentitieswhicharemorefamiliarasqualitiesandrelations,theobjectivecorrelatesofpredicates.AcrucialdifferencefromFregeemergeshere:althoughneitherRussellian‘con-cepts’norqualitiesandrelationsareverytightlydeﬁnedbyRussell,itseemsclearthattherecanbedistinct‘concepts’,qualities,andrelationscorrelatedwithdifferentpredicateswhicharetrueofexactlythesamethings.Fregeseemstohavetakenpredicateswhicharetrueofexactlythesamethingstobecorrelatedwiththesame‘concept’inhissense(afunctionfromobjectstotruth-values).Butwithhisricherconceptionoftheentitiescorrelatedwithwholesentencesandpredicates,Russellisnotopentosuchacuteembarrass-mentovertheproblemofthinnessofmeaningasFregewouldhavebeenifhehadnotposited‘sense’asanextradimensionofmeaning.ThereisnosuggestioninRussell’sviewthatalltruesentences(orallfalsesentences)havethesamemeaning,northatallpredicateswhicharetrueofexactlythesameobjectshavethesamemeaning.Russellcertainlyhassomethingtosayinresponsetothegeneralproblemofthinnessofmeaning,bothbecauseofhis\nTHELEGACYOFFREGEANDRUSSELL77theoryofdescriptions,andbecauseofhisricherconceptionoftheentitieswithwhichsentencesandpredicatesarecor-related.Whetherwhathehastosayisﬁnallyadequateisamatterforfurtherdebate.Wehaveseen,forexample,thattheproblemledRusselltopositanexplicitversionofthedescriptiontheoryofnames,accordingtowhicheveryordin-arypropername(‘Socrates’,‘Everest’,and‘Chomolungma’areexamples)isequivalentinmeaningtosomedeﬁnitedescription.Thistheoryhasbeensubjectedtoseriouscriti-cism,andisnowgenerallyrejected.9Butsomeversionofthistheorywasacceptedalmostwithoutquestionformorethanhalfacentury:itwouldbenosurpriseifWittgenstein(forexample)thoughtitwasobviouslycorrect.2DTHEOBJECTIVETURNANDTHEUNITYOFTHEPROPOSITIONThereisaveryobviousfactaboutlanguagewhichiseasilymissedifwebeginfromthecorrelationassumption,(Corr),whichholdsthatthemeaningfulnessoflanguagesdependsoncorrelationsbetweenlinguisticitemsandsomethingextra-linguistic.Theobviousfactisthatwordscanbecom-binedtoformsentences,butsentencesarenotjustlistsofwords.Thecrucialdifferencebetweenasentenceandalististhis:wordscanbeaddedtoorsubtractedfromalistquitearbitrarily,whilestillleavinguswithalist;butonlyveryparticularadditionsofwordstoasentence,orsubtractionsofwordsfromasentence,willleaveuswithawholesentence.Sentenceshaveakindofcompletenessorunitywhichlistsdonothave.Wemightcallthistheunityofthesentence.(Corr)forcesusintoacertaindifﬁcultyovertheunityofthesentence.Accordingtothepicturewhich(Corr)expres-ses,languagesarecomposed,atbase,ofintrinsicallymean-inglessthings(marksorsounds),whichareinsomewaygivenmeaningbybeingcorrelatedwithsomethingextra-linguistic.Butsincethesemostbasiclinguisticitemsareintrinsicallymeaningless,thespecialunityandcompletenessofasentencecannotbeexplainedbytheircoreintrinsic\n78THELEGACYOFFREGEANDRUSSELLnature.Rather,theunityofsentencesmustbesomekindofreﬂectionofanextra-linguisticunity.Thisseems(initially,atleast)relativelyunproblematicinatheorylikeLocke’s.Whenheﬁrstintroduceshistheory,Lockeseemstosuggestthatallwordsaremeaningfulinvirtueofbeingcorrelatedwithitemsinthemind,butthisisanover-simpliﬁcation.Somewords,hethinks,workquitedifferently:Themind,incommunicatingitsthoughttoothers,doesnotonlyneedsignsoftheideasithasthenbeforeit,butothersalso,tosheworintimatesomeparticularactionofitsown,atthattime,relatingtothoseideas.Thisitdoesseveralways;as,Is,andIsnot,arethegeneralmarksofthemind,affirmingordenying.(Locke1700:III,viii,1)Theclaimhereisthatthecombinationofwordsinasentenceisanexpressionofanactofthemindincombiningthementalcorrelatesofthosewordsinthemind.Ineffect,theunityofthesentenceisanexpressionoftheunityofacertainkindofmentalitem—wemightcallitajudgement.Theunityofthesentenceisthereforeexplainedintermsofthemorebasicunityofjudgements,wherejudgementsarethoughttobethingsinthemind.Somethinglikethistheoryheldswaywellintothenineteenthcentury.AmongitsfamousadherentswasKant,whose‘transcendentaldeductionofthecategories’dependsonsomethingveryclosetothisthought.Butitlooksdifﬁculttoholdanysuchviewoncewehavetakentheobjectiveturn—oncewehavedeterminedthatwordsaremeaningfulinvirtueofcorrelationswithsome-thingobjective,ratherthansomethinginthemindofparti-cularindividuals.Itisthenhardtoseehowtheunityofthesentencecanbeanexpressionofanactofuniﬁcation:itlooksasifitmustbeanexpressionofthecompletenessofsomeobjectiveunity.Whatmightthatobjectiveunitybe?Frege’sviewmustbethatthecrucialobjectiveunitiesarethoughts,theobjectiveentitieswhichhetooktobethe‘senses’ofwholesentences.Thoughts,likesentences,havecomponents:the‘senses’ofsubsententialexpressions.And\nTHELEGACYOFFREGEANDRUSSELL79justassentencesarenotsimplylistsofwords,sothoughtsarenotmereaggregatesofthe‘senses’ofsubsententialexpressions.ButFregeanthoughtsare,infact,veryoddcandidatesforbeingthebasicunitieswhosecompletenessisexpressedintheunityofthesentence.Thereasonisthatitishardtounderstandtheirunityasbeingindependentenoughoftheunityofsentencestobecapableofbeingmerelyreﬂectedinsentences.Letusask:isathoughtessentiallythe‘sense’ofasentence?Thatis:couldtherebethoughtswithoutthesentenceswhichexpressthem?Ifthoughtsareessentiallythe‘senses’ofsentences,thentheyareclearlynotindependentenoughofsentencesfortheunityofsentencestobeareﬂectionoftheirunity.Iftheyarenotessentially‘senses’ofsentences,thenthenatureofthoughts,andof‘sense’moregenerally,dependsonthenotionofamodeofpresentation,whichwewillthenwantsomeindependentgraspof.Ingeneral,‘sense’is,orisdependenton,thewayinwhichsomeitemintheworld—thereferentoftherelevantexpression—isgivenorpre-sented.Sentencesrefertotruth-values,theTrueandtheFalse.SoifitistheunityofFregeanthoughtswhichisreﬂectedintheunityofsentences,theunityofsentenceswillhavetobeexplainedasareﬂectionoftheunitywhichisrequiredofsomethingifthatthingistobemodeofpre-sentationoftheTrueortheFalse.ButwhatkindofunityisrequiredofsomethingwhichisamodeofpresentationoftheTrueortheFalse?Wehavenogriponthisotherthanasthekindofunitywhichisexpressedinsentences.ThismakesitlookasiftheprospectsofexplainingtheunityofthesentencewithinaFregeantheory—atleast,inawaywhichiscompatiblewith(Corr)—arepoor.Weseemforced,then,totrytoexplaintheunityofthesentenceintermsofthepriorunityofsomethinglikeRussellianpro-positions,theobjectivecorrelatesofsentences.Iftheyaretodotheworkthatishererequiredofthem,Russellianpro-positionsmustthemselvesbeunities:theycannotbemereaggregatesoftheobjectivecorrelatesofpartsofsentences;theycannotbejustcollectionsofobjectsandrelations.\n80THELEGACYOFFREGEANDRUSSELLButthiscreatesaproblem.SupposethatthereisaRussellianpropositioncorrelatedwithsentence(1).Wemightrefertoitasfollows:(1p)Everest’sbeingthehighestmountainintheworld.Ifthenatureofthispropositionistoexplainhowitisthat(1)isacompletesentence,andnotamerelist,itmustbedifferentfromthemereaggregateoftheobject,Everest,andthequalityofbeingaman,whichwemightrefertobymeansofthefollowinglist:(1a)Everest,beingthehighestmountainintheworld.Whatisthedifferencebetweentheuniﬁedpropositionandthemereaggregate?Thenaturalthoughtisthatinthepro-positiontheelements—Everestandthequalityofbeingthehighestmountainintheworld—aresomehowjoinedtoge-ther.Butwhatmightsuch‘joiningtogether’amountto?Again,thenaturalthoughtisthis:theobject,Everest,mustactuallypossessthequality;thatis,Everestmustactuallybethehighestmountainintheworld.Butnowconsiderthissentence:(4)Everestisalake.WemightrefertotheRussellianpropositionwhichiscorrelatedwiththissentenceasfollows:(4p)Everest’sbeingalake.AndifRussellianpropositionsarecompleteunities—astheyhavetobe,iftheyaretobecapableofexplainingtheunityofsentences—theproposition(4p)mustbedistinctfromthemereaggregateofitsparts,whichwemightrefertoasfollows:(4a)Everest,beingalake.\nTHELEGACYOFFREGEANDRUSSELL81Butwhatcouldthatdifferencebe?Ifwefollowthenaturalthoughtweusedinconnectionwith(1p)and(1a),thedif-ferenceisthattheproposition(4p)consistsofEverest’sactuallybeingalake.But,ofcourse,(4)isfalse:Everestisnotactu-allyalake.Soitseemsthatthereisnosuchpropositionas(4p):thereisnosuchthingasEverest’sactuallybeingalake.Wemightourselvessuggestapossiblewayoutofthisdifﬁculty:perhaps,wemightsay,sentencesarecorrelatedwithpossiblesituations—possiblecombinationsofobjectsandqualitiesorrelations.Whenthesentenceistrue,thepossiblecombinationisactual,andnotjustpossible;andwhenitisfalse,thecombinationismerelypossible.(4p)mightindeedbethoughttorepresentapossiblecombinationofthings,andthismightseemtosolveourproblem.Russellhimselfseemsnottohaveconsideredthissolution,however,andtherearestronghintsthathewouldnothavefavouredit(Russell1910:152).Italsofacesafurtherdifﬁculty,whoseseriousnessdependsonthewayinwhichthecorrelationoflinguisticitemswiththeextra-linguisticisunderstood.Fregeand(early)Russellbothseemtohaveheldthatamongtheexpressionsforwhichsomekindofcorrelationconceptionofmeaningfulnessappliesare(atleastsome)sentences.(Itisaswelltorememberheretheliberalityoftheconceptionofcorrelationexpressedin(C),insection2Aabove.)ForFrege,thefullmeaningfulnessofsentencesdependsontheirbeingcorrelatedwithtruth-values:truth-valuesareobjects(ofadistinctivekind),andasentencewhichhasnotruth-valueisatbestdefectiveinmeaning.For(early)Russellthemeaningfulnessofsentencesdependsontheirbeingcorrelatedwithpropositions.Thereseemsnoclearreasonwhythemeaningfulnessoftruesentencesshouldbemorebasicthanthemeaningfulnessoffalsesen-tences.Inthatcase,ifanysentencesaremeaningfulinvirtueofcorrelationswithextra-linguisticitems,bothtrueandfalsesentenceswillhavetobemeaningfulinvirtueofsuchcorrelations.Andthatmeansthattherewillhavetobeextra-linguisticitemswhicharethecorrelatesoffalsesen-tences.Ifweholdthisview,wecanonlyadopttheproposed\n82THELEGACYOFFREGEANDRUSSELLsolutiontotheproblemraisedbyfalsesentencesforRussell’saccountoftheunityofsentencesifwecanmakesenseofsentencesbeingcorrelatedwithmerelypossiblecombinationsofobjects,qualities,andrelations.Butcanwemakesenseofsentencesbeingcorrelatedwithsomethingwhichismerelypossible?Thatdependsonthekindofcorrelationwehaveinmind.Indiscussingthecharacterizationofthenotionofcorrelationprovidedby(C)insection2A,above,Isaidthat(C)wasconsistentwithsomecorrelationsbeingderived,dependentonother,antecedentcorrelations.Derivedcorrelationscanobviouslybecontrastedwithnon-derivedcorrelations.Fregeseemsnottohavebeenmuchconcernedwiththedistinctionbetweenderivedandnon-derivedcorrelations,anditisquiteimplausibletosupposethatthecorrelationofsentenceswithtruth-valuesisanon-derivedcorrelation:ifitwere,itwouldbeimpossibletounderstandasentencewithoutknowingwhetheritwastrue.Russell,however,isplausiblyunder-stoodashavingbeenconcernedwiththiscontrast,andashavingthoughtthatatleastsomecorrelationsofsentenceswithpropositionswouldbenon-derived.Anditseemsthatanon-derivedcorrelationcanonlyintelligiblybemadebetweenalinguisticitemandsomethingnon-linguisticwhichactuallyexists,ratherthanonewhichismerelypos-sible.10Russellseemstohavethoughtthattherecanonlybeanappropriatecorrelateofasentenceiftherelevantpropo-sitionactuallyexists—thatistosay,ifthesentenceistrue.Andthismeansthathehadtogiveupthetheorywhichprovidedhimwithanaccountoftheunityofsentences.Theproblemherecanberephrasedlikethis.DespitethefactthatRussellhimselfrestrictedtheclassofsingularterms,properlyso-called,tolinguisticexpressionswhosemeaningreallydoesdependontheirbeingcorrelatedwithanobject—therebypreventingdeﬁnitedescriptionsfromcountingasgenuinesingularterms—heseems,ineffect,tohavetreatedwholesentencesascomplexsingulartermswhosemeaningfulnessistobeexplainedinfundamentallythesamewayasthemeaningfulnessofgenuinesingular\nTHELEGACYOFFREGEANDRUSSELL83terms—thatis,intermsofanon-derivedcorrelation.ItlooksasifthenaturalsolutiontoRussell’sproblemwiththeunityofthepropositionistorejectthisapproachtowholesentences,anddenythattheirmeaningfulnessdependsoncorrelationswithextra-linguisticitems.AswewillseeinChapter4,thisisindeedtheapproachWittgensteinadopted.2ETHEUNITYOFTHEPROPOSITIONANDTHEMULTIPLE-RELATIONTHEORYOFJUDGEMENTInthefaceofthedifﬁcultywithfalsesentences—aswellassomeothers11—Russellhimselfseems,ineffect,tohaverevertedtosomethingakintotheLockeanaccountoftheunityofsentences.12InPrincipiaMathematica,writtenwithAlfredNorthWhitehead,weﬁndhimdenyingthatpropo-sitionsareamongthebasicunitiesoftheworld—evenwhenthesentencestheycorrespondtoaretrue.Onereasonforholdingtheearlyaccountofpropositionsisthatitsup-pliesapleasantlysimpleaccountofpropositional-attitudeconstructions.Forexample,supposewesay:(5)OthellobelievesthatDesdemonalovesCassio.Thisisnaturallyparsedasinvolvingatwo-place,or‘dual’,relation(believing)whichholdsbetweenathinker,Othello,andtheobjectofhisbelief,thatDesdemonalovesCassio.Russell’stheoryofpropositionsgivesuspreciselythisana-lysis:theobjectofbeliefisthepropositionthatDesdemonalovesCassio—or,inthephrasingweusedbefore,Desdemona’slovingCassio.InPrincipiaMathematica,RussellandWhiteheadrejectthissimpleview:Whenajudgmentoccurs,thereisacertaincomplexentity,composedofthemindandthevariousobjectsofthejudgment.(WhiteheadandRussell1927:44;myemphasis)13Thereisnotasingleobjectofjudgement;thereisratherarelationbetweenathinkerandthecomponentsofpossible\n84THELEGACYOFFREGEANDRUSSELLpropositions—inourcase,betweenOthello,ontheonehand,andthethreeentities,Desdemona,Cassio,andtherelationofloving.Judgementsinvolvemultiplerelations,ratherthanmerely‘dual’relations(betweenathinkerandasingleobjectofjudgement).RussellandWhiteheadremark:Itfollowsfromtheabovetheorythata‘proposition’,inthesenseinwhichapropositionissupposedtobetheobjectofajudgement,isafalseabstraction,becauseajudgementhasseveralobjects,notone.(WhiteheadandRussell1927:44;originalemphasis).Andtheycontinue:Owingtothepluralityoftheobjectsofasinglejudgement,itfollowsthatwhatwecalla‘proposition’(inthesenseinwhichthisisdis-tinguishedfromthephraseexpressingit)isnotasingleentityatall.Thatistosay,thephrasewhichexpressesapropositioniswhatwecallan‘incomplete’symbol;itdoesnothavemeaninginitself,butrequiressomesupplementationinordertoacquireacompletemeaning.14(WhiteheadandRussell1927:44)Whatkindofsupplementationmightbeprovided?RussellandWhiteheadsaythis:[W]henIjudge‘Socratesishuman’,themeaningiscompletedbytheactofjudging.(WhiteheadandRussell1927:44)ThisisRussell’sfamous‘multiple-relation’theoryofjudge-ment.Itmayhavesolvedtheproblemofsentencestowhichnoactualcombinationofextra-linguisticentitiescorre-sponds,butitbroughtotherdifﬁcultiesinitsplace.Oneisaproblemoforder.15Thereisacleardifferencebetween(5)—whichmightexplainOthello’sjealousy—andthefollowingclaim:(6)OthellobelievesthatCassiolovesDesdemona.\nTHELEGACYOFFREGEANDRUSSELL85Withoutsomethinglike(5),thiswouldexplainonlyprideorpityonOthello’spart,nothisjealousy.Butifbelief—likealljudgement,onRussell’stheory—involvesarelationjustbetweenabelieverandthevariousthings,includingrela-tions,whichthebeliefconcerns,howarewetounderstandthedifference?Wecanhardlysay‘OthellostandsinthebelievingrelationtoCassio,loving,andDesdemona,inthatorder’:wordsmayhaveanorderinanywritingorspeakingofthem,butitishardtomakesenseofjudgingitselforderingthings.16And,inanycase,theorderingevenofwordsleadsusbacktotheproblemoftheunityofthesen-tence.Wordsmaybeorderedintwoways:eitherforsomeextraneouspurpose—asinalphabeticalordering,ororder-ingbynumberofletters—orbecauseofthedemandsofgrammar.Clearlytheorderingofthewordsin(5)and(6)isnotdesignedtosuitanyextraneouspurpose:theorderingishererequiredbythegrammarofEnglishifwearetosaypreciselythat.Butgrammaticalrequirementsarealwaysrequirementsfortheconstructionofcomplete,uniﬁedsen-tences;thissuggeststhatwewillonlybeabletomakesenseofthiskindoforderingofwordsinsofaraswecanmakesenseoftheunityofsentences.Themultiple-relationtheoryofjudgementfacesdifﬁcultyonthisscoreinanycase,becauseitattemptstocombineaLockean,mental-actconceptionoftheunityofsentenceswithanobjective,world-orientedconceptionofthemeaningof(most)words.AsRussellhimselflatersaid:Supposewewishtounderstand‘AandBaresimilar’.Itisessentialthatourthoughtshould,asissaid,‘unite’or‘synthesize’thetwotermsandtherelation;butwecannotactually“unite”them,sinceeitherAorBaresimilar,inwhichcasetheyarealreadyunited,ortheyaredissimilar,inwhichcasenoamountofthinkingcanforcethemtobecomeunited.(1984:116)Thisconﬁrmstheinitialthought(seesection2D)thatitisdifﬁculttocombineanobjectiveconceptionofthemeaning\n86THELEGACYOFFREGEANDRUSSELLofwordswiththissubjectiveconceptionofwhatmakessentencesunities.Oneﬁnaldifﬁcultyforthemultiple-relationtheoryisworthnoting.Atthetimewhenheproposedit,Russelldidnotwanttoinsistthattherewere,fundamentally,altogetherdifferentlogicalcategoriesofthing.(Thisissomethingtowhichwewillreturninthenextsection.)SoDesdemona,Cassio,andtherelationoflovingareallentitieswhicharecapable,inprinciple,ofbeingnamed(bythenames‘Desdemona’,‘Cassio’,and‘Loving’,forexample):theyareall,inRussell’searlyterminology,terms.WhilewemaythinktherelationoflovingasbeingafundamentallydifferenttypeofentityfromDesdemonaandCassio,onRussell’stheorytheyaretreatedasbeing,inasense,gram-maticallyonapar.Oneadvantageofthemultiple-relationtheoryofjudgement,fromRussell’spointofviewatthetime,isthatitdoesnotneedtheretobedifferencesoflogicaltypebetweentheentitiescorrelatedwithdifferentkindsofword.Theseentitiesﬁttogether,notbecausetheybelongtogetherinuniﬁed,completepropositions,butbecausetheyarebroughttogetherbyamentalactofajudgingsubject.Inprinciple,ajudgingsubjectcanuniteorsynthesizeanygroupofentitieswhatever—or,atleast(bearinginmindthelastcriticismmentioned),itsabilitytouniteorsynthesizegroupsofentitiesdoesnotdependatallontheirlogicaltype.Wittgensteinthoughtthisconsequencewasunacceptable.Heputthepointinthiswayinhis1913NotesonLogic:Everyrighttheoryofjudgementmustmakeitimpossibleformetojudgethat‘thistablepenholdersthebook’(Russell’stheorydoesnotsatisfythisrequirement).(NL:96)Thepointrecurs,slightlydifferentlyformulated,intheTractatus:5.5422Thecorrectexplanationoftheformoftheproposition‘Ajudgesp’mustshowthatitisimpossibletojudgeanonsense.(Russell’stheorydoesnotsatisfythiscondition.)\nTHELEGACYOFFREGEANDRUSSELL87Whatthisshowsisthatsomethingliketheunityofthepropositionmustbeacceptedasabasicgiven,priortoanyinterventionbyjudgement.Some,butnotall,combinationsofwordsmakeupwholesentences,andonlyawholegram-maticalsentencecanbeputinthe‘p’positionofasentenceoftheform‘Ajudgesp’.17Thisisaconstraintonthepossi-bilitiesofjudgementwhichisquiteindependentofanythingtodowiththecharacterofthejudgingsubject;anditrequiresanotionofsententialorpropositionalunitywhichisindependentofanyconsiderationofactsofjudgement.TheprecisedetailsofthehistoryofRussell’sviewandtheinterpretationofvariouspointsofhisworkareamatterofsomecontroversy,butitlooksasifRussellwasatleastonthewaytoabandoningthemultiple-relationtheoryofjud-gementinthefaceofsuchdifﬁcultiesasthese.In1913hesettoworkonamanuscript,provisionallyentitledTheoryofKnowledge,whichincorporatedwhatIthinkamountstoatleastthebeginningsofarevisedtheoryofjudgement,whateverRussellthoughtitsstatuswas.18Inessence,thisnewtheorydoestosentencessomethingakintowhatthetheoryofdescriptionsdoestosingularterms.Itsuggeststhat,inmanycasesatleast,sentencesshouldnotberegardedasnamesofcombinationsofentities.Instead,theyimplicitlyinvolveexistentialquantiﬁers.AsRussellputsit:Theproposition[here:sentence19]‘aisbeforeb’mustbeinterpretedasmeaning‘thereisacomplexinwhichaisearlierandbislater’.(1984:135)Thisbringswithitwhatlookslikeanewtheoryofjudge-ment:tojudgethataisbeforebisreallytojudgethatthereisacomplexinwhichaisearlierandbislater.Onthefaceofit,thisseemsaneatresolutionofthepro-blemswhichfacedRussell’searliertwotheories.Wedonothavetheproblemoffalsitywhichfacedtheearlyaccountofpropositions:sentencesingeneraldonotnamecomplexesinwhichentitiesarecombined,andjudgementsdonotinvolveusdirectlyinrelationstosuchentities.Asentence\n88THELEGACYOFFREGEANDRUSSELLcanmeaningfullyasserttheexistenceofacombinationofentities,evenifthereisinfactnosuchcombination;andasubjectcanbelievethatthereisacertaincombinationofentities,evenifthereisnone.Andtheunityofcomplexesisnotdependentonourjudgement:rather,wejudgethattherearesuchcomplexes,whoseunityiswhollyindependentofanyactofours.Nordowehavetheproblemoforderingwhichafﬂictedthemultiple-relationtheory:wheretheorderofsingulartermsmattersinlanguage,thiscanbetakentobeanexpressionoftheobjectivedifferenceofposition(inspaceandtime,forexample)ofthecorrelativeobjectsinacomplex.20Despitetheseattractions,Russellabandonedallattemptstoprovideatheoryofjudgement,includingthisproposalwhichIthinkamountstoanewtheory.Fromallaccounts,itappearsthatwhatmadehimabandonthesubjectwasacri-ticismofWittgenstein’s.Thecriticismwasmadeinperson,butWittgensteinlaterreformulateditinabriefletterdatedJune1913:Icannowexpressmyobjectiontoyourtheoryofjudgmentexactly:Ibelieveitisobviousthat,fromtheprop[osition]‘Ajudgesthat(say)aisintheRel[ation]Rtob’,ifcorrectlyanalysed,theprop[osition]‘aRb.v.~aRb’mustfollowdirectlywithouttheuseofanyotherpremises.Thisconditionisnotfulfilledbyyourtheory.(CL:29)Itispossibletounderstandthiscriticismasnomorethanareformulationofthecriticismwehavealreadyencountered,whichwasdirectedspeciﬁcallyagainstthemultiple-relationtheoryofjudgement.Interestingly,though,thecriticismintheletterofJune1913certainlyappliestoRussell’snewtheory,whichtheotherdoesnotobviouslydo.Intuitively,whatsomeonejudgeswhenshejudgesthataRbisthataRb,andthataRbis,sotospeak,somethingwhichcaneitherbethecaseornot.ButonRussell’snewtheory(asItakeittobe),whensomeonejudgesthataRb,whatshereallyjudgesisthatthereisanR-complexinwhichaﬁllsoneposition\nTHELEGACYOFFREGEANDRUSSELL89andbﬁllstheother.ItisimmediatelyclearthatthatthereisanR-complexinwhichaﬁllsonepositionandbﬁllstheotherissomethingwhichcaneitherbethecaseornot;butweneedafurtherpremise—totheeffectthatanR-complexisapropositionalcomplex—forittobeclearthatthecomplexitselfissomethingwhichcaneitherbethecaseornot.IsWittgenstein’scriticism(onthisinterpretationofit)sound?Aswillbecomeclearinlaterchapters,Wittgensteincametohavereasonsforobjectingtoaccountsoflanguagewhichrequiredthelogicalorgrammaticalstatusoflinguisticexpressionstobespeciﬁed.Buttherearereasonsforthink-ingthat,independentlyofthoseconsiderations,thereisevenmorereasontobeworriedaboutRussell’snewviewthanWittgensteinmakesexplicitlyclear.Toseethis,weneedtointroducethenotionofanatomicsentence.Anatomicsen-tenceisonewhichinvolvesnologicalconnectives(‘and’,‘or’,‘not’,‘if…,then…’,andtheirformalcounterparts,andthequantiﬁers).Russellnotesastrikingconsequenceofhistheory(perhapsafterreﬂectiononanearlyformofWittgenstein’scriticism):Theproposition[here:sentence]‘aisbeforeb’mustbeinterpretedasmeaning‘thereisacomplexinwhichaisearlierandbislater’.Thisinvolvestheword‘and’,whichisoneofthewordsthatindicatemolecular[i.e.,non-atomic]complexes….Thisresultiscurious,forthecomplex‘a-before-b’isatomic,andyetthecorrespondingproposi-tion[i.e.,sentence]isnotatomic.Itisnotveryeasytobelievethatsuchadifferencecanexist,andperhapssomeothertheoryof‘sense’[i.e.,direction]canbefoundwhichwouldavoidsuchadifference.(1984:135)AlittlereﬂectionsuggeststhatonRussell’snewtheorynosentencecanbegenuinelyatomic.21Thatmeansthatnoapparentlyatomicsentence(suchasWittgenstein’s‘aRb’)canhavetheformitseemstohave,andwecannotdeﬁneanatomiccomplex(suchasthesupposedR-complexinwhichaﬁllsonepositionandbtheother)asbeingpropositionalinformbysayingthatitisexpressedbyanatomicsentenceof\n90THELEGACYOFFREGEANDRUSSELLthatform.22Butifitisnotpropositionalinvirtueofhavingtheformofasentence,inwhatwaycanitbepropositional?ThismakesthedifﬁcultyraisedbyWittgenstein(ifIhaveunderstoodthatcorrectly)lookverydeep.Theproblemisnotmerelythatanextrapremiseneedstobeaddedtoensurethatthecomplexinquestionispropositional.Thedifﬁcultyisthatitisunclearwhatthecomplex’sbeingpropositionalamountsto,ifthereisnosentencewhichcanexpressit.Itisnotjustthatanextrapremiseisneeded:itlooksasifnoextrapremisewill,intheend,becapableofdoingthejob.ItisworthdwellingforamomentonRussell’sdisquietovertheasymmetrybetweentheatomicityofthecomplexandthemolecularityofitsexpression.WhatRussellishereﬁndingdifﬁcultyinswallowingisthesuggestionthat,forthecaseofatomiccomplexes,theformoflanguagedoesnotmatchtheformoftheworld.Aswewillsee,Wittgenstein’saccountintheTractatuspreciselydoesnotfacethisdifﬁculty.2FTHEUNITYOFTHEPROPOSITION,THECORRELATESOFWORDS,ANDTHECONTEXTPRINCIPLEIftheunityofsentencesissecuredbyanactofthemind,asitisonLocke’stheoryandonRussell’smultiple-relationtheoryofjudgement,thenthegrammarofwords—howtheycombinetoformsentences—isnotoffundamentalimportance.Whatthismeansisthatwordsdonotneedtobeoffundamentallydifferentkinds:or,atleast,thedifferenceofkindamongwordsneedonlybeasuperﬁcialdifference.Andifwehaveaconceptionoflanguageaccordingtowhichthefundamentallinguisticexpressionsaremeaningfulinvirtueofcorrelationswithsomethingextra-linguistic,thereneedbenofundamentaldifferenceinkindbetweentheextra-linguisticitemswhicharecorrelatedwithdifferentkindsofword.Thiswasboththedecisivedifﬁcultywiththemultiple-relationtheoryforWittgenstein(aswehaveseen),andacrucialadvantageinthetheoryforRussell.\nTHELEGACYOFFREGEANDRUSSELL91Throughouttheperiodofhismostadvancedtechnicalworkinphilosophy,itisplausibletoclaimthatRussellattemptedtomaintaintheideathattherewerenotfundamentaldifferencesoflogicalcategoryamongtheentitieswithwhichwordsarecorrelated.Thiscanbeseenasbeingcentraltotheramiﬁedtheoryoftypes,onwhichhislogicalconstructionofmathematicsdepended(atthetimeofPrincipiaMathematica,onwhichhecollaboratedwithWhitehead).23Butitisalsotobefoundinhisearlywork,ThePrinciplesofMathematics.Recalltheterminologyofthatwork:thecorrelatesintheworldoflinguisticexpressionsareterms;andamongtermsRusselldistinguishesbetweenthings(thetermscorrelatedwithpropernames)andconcepts(thecorrelatesofotherexpres-sions,includingpredicates).Intheﬁrstplace,Russellsays:Everyterm,tobeginwith,isalogicalsubject:itis,forexample,thesubjectofthepropositionthat[it]itselfisone.(Russell1903:44)Alogicalsubjectisanentitywhichasentencemaybeabout;itissomethingthatmaybereferredtowithaname.AlittlelaterRussellconsidersthefollowingissue:Itmightbethoughtthatadistinctionoughttobemadebetweenaconceptassuchandaconceptusedasaterm,between,e.g.,suchpairsasisandbeing,humanandhumanity,oneinsuchapropositionas‘thisisone’and1in‘1isanumber’.(Russell1903:45)Thisisalittledifﬁculttoconstrue,butItakeitthattheentitiesRussellisconsideringhereareallentitiesintheworld,ratherthanlinguisticitems.Sothequestioniswhether‘is’and‘being’,forexample,arecorrelatedwiththesameentity:whether,thatis,isandbeing(theentities)arethesame.Similarly,thepropositionwhichRussellherereferstoastheproposition‘thisisone’isauniﬁedentityintheworld:inthestyleIusedearlier,itisthisbeingone.NotethatRussellishereusingthenotionofa‘term’toreferto\n92THELEGACYOFFREGEANDRUSSELLentitiesintheworldonlywhentheyareactingas‘logicalsub-jects’.Inthisuseof‘term’,anentity’sbeingatermiscon-trastedwithitsbeinganadjective:andagain,beingan‘adjective’isnotbeingacertainkindoflinguisticentity;ratherthisisawayofreferringtoaworldlyentitywhenthatentityisplayingacertain‘adjectival’—thatis,qualifying—role.Should,then,one(theentitywhichmayﬁgureasaqua-liﬁer,an‘adjective’)bedistinguishedfrom1(theentitywhichmayﬁgureasalogicalsubject,a‘term’)?Russellsaysthat‘inextricabledifﬁcultieswillenvelopus’ifwesaythatitshould(1903:45).Hereistheargument:Forsupposethatoneasadjectivedifferedfrom1asterm.Inthisstatement[i.e.,thestatementmadebythislastsentence],oneasadjectivehasbeenmadeintoaterm[becauseitisthelogicalsubject];henceeitherithasbecome1,inwhichcasethesuppositionisself-contradictory;orthereissomeotherdifferencebetweenoneand1inadditiontothefactthatthefirstdenotesaconceptnotatermwhiletheseconddenotesaconceptwhichisaterm.Butinthislatterhypothesis,theremustbepropositionsconcerningoneasterm,andweshallstillhavetomaintainpropositionsconcerningoneasadjec-tiveasopposedtooneasterm;yetallsuchpropositionsmustbefalse,sinceapropositionaboutoneasadjectivemakesonethesubject,andisthereforereallyaboutoneasterm.(Russell1903:46)This,therefore,isafundamentalreasonforthinkingthattherearenofundamentaldifferencesinlogicalorgramma-ticalkindbetweentheentitieswhicharecorrelatedwithdif-ferentkindsofwords.Solongastheyareentities,theymustbecapableofbeinglogicalsubjects—whatpropositionsareabout—andthatrequiresthattheybewhatRussellcallsterms.Thisassimilationofallcorrelatesoflinguisticexpressionstothesamefundamentallogicalkind—theyareallterms—canalsobeseeninthenewtheoryofjudgementofthe1913manuscript(Russell1984).Theveryideaofacomplexistheideaofanentity,whichmaybealogicalsubject,\nTHELEGACYOFFREGEANDRUSSELL93whichisinsomeway—evenifitis,aswehaveseen,acuriousway—acorrelateofwholesentences.ThesameinsistenceonuniformityoflogicaltypeisfoundlateaswellasearlyinRussell’slogicalwork.Inthis,Russell’sviewisstrikinglyopposedtoFrege’s.Fregeheldthatdifferentkindsofsubsententialexpressioncorrespondtoentitiesintheworldofradicallydifferentkinds.Singularterms(suchaspropernames)refertoobjects,accordingtoFrege:objectsaredistinctiveinbeing‘saturated’,orcomplete.OnFrege’sview,predicatesrefertoaspecialkindoffunction,whichhecalleda‘concept’.Fregean‘concepts’are‘unsaturated’,orincomplete—injustthesamewayasapredicatemaybethoughttohaveoneormoregapswhichcanbeﬁlledbysingulartermstoformwholesentences.24ThisledFregeintoaparadoxwhichisnotunliketheparadoxwhichwehavejustseenleadingRusselltoinsistthattherearenofundamentaldifferencesoflogicaltypebetweentheentitieswhichdifferentkindsofexpressionarecorrelatedwith.Fregewantstoinsistthat‘concepts’,thecorrelatesofpredicates,arewhollydifferentinkindfromobjects,thecorrelatesofsingularterms.Consider,inparti-cular,thecaseofthe‘concept’horse—thecorrelateofthepredicate‘xisahorse’.Fregeseemscommittedtothis:(CH1)Theconcepthorseisnotanobject.Theproblemisthatthephrase‘theconcepthorse’functionsgrammaticallylikeasingularterm(atleastonFrege’sgrammar).Butthatmeansthat,ifitreferstoanythingatall,whatitreferstoisanobject,nota‘concept’.ItthusbecomesimpossibleforFregetostatetrulythefundamentaldistinc-tionbetweenobjectsand‘concepts’.Infact,solongaspre-dicatesaretakentorefertoentitiesatall,itlooksasifitwillbedifﬁcultforFregetosaywhatpredicatesarecorrelatedwith,andhencetosaywhatpredicatesmean.25Thefollowing,forexample,cannottrulysaywhatFregewantsittosay:(CH2)Thepredicate‘xisahorse’referstotheconcepthorse.\n94THELEGACYOFFREGEANDRUSSELLForthephrase‘theconcepthorse’canonlyrefertoanobject,ifitreferstoanythingatall;andnoobjectcanbewhatthepredicate‘xisahorse’refersto.Frege’sresponsetothisproblemisinfamous:Byakindofnecessityoflanguage,myexpressions,takenliterally,sometimesmissmythought;Imentionanobject,whenwhatIintendisaconcept.IfullyrealizethatinsuchcasesIwasrelyinguponareaderwhowouldbereadytomeetmehalf-way—whodoesnotbegrudgeapinchofsalt.(Frege1892b:204)Russellwasdismissiveofthis:hesays,‘Frege’stheory…willnot,Ithink,bearinvestigation’(Russell1903:510).ButFrege’scommitmenttohisview,despiteitspara-doxicalnature,isnotunmotivated.Itderivesfromthefol-lowingclaimaboutlinguisticitemsandtheentitieswithwhichtheyarecorrelated—aclaimofcorrespondenceofgrammar:(CG)Thedifferentgrammarofdifferentcategoriesoflinguisticexpressionmustbematchedbydifferencesbetweentheentitieswithwhichtheyarecorrelated.(CG)isboundtocreatedifﬁculties,sincetheexpressions‘theconcepthorse’and‘xisahorse’arethemselvesgrammati-callydifferent,butbothexpressionsmustbecorrelatedwiththesameentityifthemeaningofpredicatesistobeexplainedbytheirbeingcorrelatedwithentitiesintheﬁrstplace.Butaslongasweholdthatthemeaningofbothsingulartermsandpredicatesessentiallyinvolvessomecorrelationwithnon-linguisticentities,itishardtoseehowwecanabandon(CG)—atleastforthecaseofsomeexpressionsforwhichthesameproblemswillarise—with-outadoptingsomequasi-Lockeanaccountoftheunityofsentences.OnaviewlikeLocke’s,theunitywhichunderliestheunityofasentenceiscreatedbyanactofjudgement:the\nTHELEGACYOFFREGEANDRUSSELL95wordsthemselvesneedcontainnothingwhichmakesthemsuitedtoﬁttogetherinthewaytheydo;andnordoesanycomparablesuitabilityforcombinationneedtobefoundinthecorrelatesofthosewords.Toputthepointalittlecru-dely,thegrammarofsentencesisnottobeexplainedbywhatistobefoundineitherthewordsthemselvesortheirextra-linguisticcorrelates:itderivesjustfromtheactofjudgement.Onceweabandonthatkindofview,however,wehavetoacceptthatpartsofsentencescanonlycombinetogethergrammaticallyiftheyare,insomeway,ﬁtbynaturetobesocombined.Ifwethinkthepartsaremeaningfulonlyinvirtueofacorrelationwithsomethingextra-linguistic,itisnaturaltothinkthatitisonlyinthecorrelation,orelseinwhatisrequiredforthecorrelationtobepossibleatall,thatthevariouslinguisticitemscometobesuitedtotheirvariousgrammaticalroles.Butcorrelationitselfissobruteanasso-ciationthatthecorrelatingitselfcannotprovidegrammar.Rather,wemustsupposethatgrammarinvolvessomekindofrelationbetweenlinguisticitemswhicharesuitedtoformwholesentences,andnon-linguisticitemswhichhaveamatchingcapacitytoﬁttogether.Whatwehavehereis,ofcourse,justaparticularapplica-tionofthegeneralpointaboutthecorrelationassumption,(Corr),whichwasmadewhenthatassumptionwasﬁrstintroduced(insection2A,above).Sincecorrelationcannotbeaprocessoftransformation,allitcandoisenablelin-guisticitemstoreﬂectfeaturesoftheextra-linguisticentitieswithwhichtheyarecorrelated.Thismeansthatfeaturesthatweﬁndinlanguageinusemustbeeither(i)irrelevanttomeaning(becauseintrinsicfeaturesofintrinsicallymean-inglessentities—marksandsounds),(ii)themerefactofthesignsbeingcorrelatedwithextra-linguisticentities,or(iii)reﬂections,insomeway,ofthenatureofthoseextra-linguisticentitiesthemselves.Grammarcannotberegardedassimplyirrelevanttomeaning;norisanexpression’shavingaparticulargrammarthemerefactofitsbeingcor-relatedwithaparticularentity.Consequently,thegrammarofanexpressionmustbeareﬂectionofthenatureofthe\n96THELEGACYOFFREGEANDRUSSELLextra-linguisticentitywithwhichitiscorrelated,ifthereisone—orofthenatureoftheextra-linguisticentitieswithwhichitcanbecorrelated,ifnocorrelationhasyettakenplace.Nowthatwehave,ingrammar,aspeciﬁcinstanceofthewayinwhichthecorrelationassumption,(Corr),entitlesustosupposethatlanguagerevealsthenatureoftheworld,itisaswelltoconfrontexplicitlyanissuewhichwillhaveoccurredtomanywhentheideawasﬁrstbroached.Ihavesuggestedthat(Corr)requiresthatlanguagereﬂectcertainfundamentalfeaturesoftheworld.Itmightbethoughtthatthiscommitsanyonewhoaccepts(Corr)toasimpleformofrealism,whererealismisunderstoodinlinewiththedeﬁni-tionIgaveinChapter1,asacommitmenttothefollowingthesis:(R)Thenatureoftheworldasitisinitselfisaltogetherindependentofanythingtodowithanythoughtorrepresentationofit.26But—focusingforthemomentonthecaseofgrammar—itisimportanttorecognizethattheideaofextra-linguisticcategoriesbeingreﬂectedinthegrammaroflanguagemaybeunderstoodinanyoneofatleastthreeways.Theﬁrstwayisthemostobviousone:wesupposethattheworldasitisinitselfcomescomposedofitemswhicharealready,asitwere,suitedtobecombinedincertainwayswitheachother(grammatically,asitwere).Onthisview,wesupposethatcorrelatinglinguisticitemswiththeseitemsintheworldenablestheantecedentlymeaninglesslinguisticitemssimplytoborrowfromtheitemsintheworldtheircapacitiesforcombination.Onthisﬁrstaccount,thegrammar,sotospeak,oftheworld,isbasic,andlanguagedoesnomorethancopythat.Thisisthemostobviousview,butitispossibletocon-structanalternativetoit.Onthisalternative,webegin,asitwere,withmeremarksandsounds.Somethinghastohappentothesetomakethemintomeaningfulwords.Whathappens,onthealternativeview,isthattheyare(eithersimultaneouslyorsuccessively)27providedwithagrammar\nTHELEGACYOFFREGEANDRUSSELL97andprojectedontotheworld.Thisprojectionis,ineffect,theprojectionofagrammarontotheworld.Theworldasitisinitselfhasnogrammar,onthissecondview,butintheestablishmentofmeremarksandsoundsasmeaningfulwords,whatwedoisreadagrammarintotheworld.Andhavingreadthatgrammarintotheworld,weﬁndinthisnowgrammaticallyviewedworlditemswhichcanbepropercorrelatesofthegrammaticalwordswhichwehavejustcre-ated,andwhoseobjectivegrammar(sotospeak)thewordsthemselvescannowreﬂect.Bothofthesetwoviewsarerealist,ontheconceptionofrealismwhichIdeﬁnedinthelastchapter(commitmentto(R)).Inthecaseoftheﬁrstview,thenatureoftheworldasitisinitselfincludesaworldlycorrelateofgrammar,fromwhichthegrammaroflanguagecanjustbederived.Inthecaseofthesecondview,theworldasitisinitselfdoesnotcontainanycorrelateofgrammar:itisgrammaticallyamor-phous.Butthesecondviewpermitsustomakesenseofwhatwemightcalla‘worldoflanguage’—nottheworldasitisinitself,buttheworldasitisreconceivedbyusinourconstructionoflanguage,preciselytobeacorrelateforlan-guage.Ifwestarttothinkofthis‘worldoflanguage’asinsomesensearealworld,aseparateentity,asitwere,fromtheworldasitisinitself,thenweseemtohavefoundsome-thingforwhicharealistviewisinappropriate:thenatureofthis‘worldoflanguage’willnotbealtogetherindependentofanythingtodowithanythoughtorrepresentationofit.ThissecondviewisrecognizablyKantian:itisrealistwithrespecttotheworldasitisinitself,andidealistwithrespecttothe‘worldoflanguage’.28Butwecannowimaginesomeonebeingscepticalaboutthepossibilityofdescribingtheworldasitisinitself,withinthisKantiansecondview.Iflanguagecanonlytalkaboutitemswhicharesuitablecor-relatesforitsgrammaticalcategories,howcanwetalkabouttheworldasitisinitself?Andifwecannoteventalkabouttheworldasitisinitself,howcanweevenformulatethisKantianposition?SowemaybeinclinedtoerasetheKantianworld-as-it-is-in-itselffromthepicture,leavingourselves\n98THELEGACYOFFREGEANDRUSSELLjustwiththe‘worldoflanguage’,whichnowbecomestheonlyworldwhichwecandescribeastheworld‘asitisinitself’.Butsince,onthisthirdpicture,theonlyworldwhichwecanthinkofastheworldasitisinitselfisstilljustthe‘worldoflanguage’,wenowseemtobecommittedtoastraightdenialof(R):thenatureoftheworldasitisinitselfisnotaltogetherindependentofanythingtodowithanythoughtorrepresentationofit.Onthecontrary:itsnatureisshapedbytheprojectionofourgrammar.29Wehaveherethreecompletelydifferentconceptionsoftherelationbetweenlanguageandtheworld.Buttheyhavethisincommon:theyareallcommittedto(CG),forallitsparadoxicality.(CG)itselfisneutralbetweenrealist,Kantian,andidealistapproachestolanguage.Whicheverwayweturnonthequestionofrealism,however,wehavetorecognizethatwholesentencesare,inacertainsense,basicinthenatureoflanguage.Ifthemeaningofwordshastoincludetheirgrammar,themeaningofwordsmustincludethewayinwhichtheyarecapableofcombin-ingwithotherwordstoformwholesentences,sincethereisnothingtothegrammarofwordsotherthantheircapacitytocombineincertainwayswithotherwordstoformwholesentences.Sothewholesentencehastobepresupposedinanyaccountofthemeaningofwords.ThisledFregetoinsistonhisfamous‘contextprinciple’.Heformulatesthisinvariousways.Hereisoneversion:[N]evertoaskforthemeaningofawordinisolation,butonlyinthecontextofaproposition[i.e.,sentence].30Andhereisanother:[It]isonlyinthecontextofaproposition[i.e.,sentence]thatwordshaveanymeaning.31It’snotentirelyclearwhatthisprincipleamountsto,orwhat,exactly,Fregeneedsforhisargumentstowork,32butitispossibletounderstandFregeaswantingtoinsistjustonthis:\nTHELEGACYOFFREGEANDRUSSELL99(CP)Thereisnomoretothemeaningofawordthanitscontributiontothemeaningsoflegitimatelyconstructedsentencesinwhichitmayoccur.Aswewillsee,WittgensteinunderstoodthebasicnessofthewholesentencemoreliterallyandmoreradicallythanFregehimselfdid.2GLOGICALFORMANDLOGICALCONSTANTSFregeandRussell,intheirdifferentways,acceptedver-sionsofthetwocoreassumptionsaboutlanguage,(Corr)and(Obj),whichIidentiﬁedinsection2A,andappliedthemtoeachofthethreekindsoflinguisticexpressionwhichitisnaturaltothinkarebasic,ontheFrege–Russelllogicalgrammar.Singulartermsarecorrelatedwithobjects(Russell’s‘things’),andpredicateswith‘concepts’(qualitiesandrela-tions,accordingtoRussell).Thecaseofsentencesisdiffer-ent,andmorecomplicated,butsurprisinglyanalogousclaimsareheldheretoo.Theyarecorrelatedwithtruth-values,accordingtoFrege,33orpropositions,accordingtotheearlyRussell.Andevenin1913,Russellseemstohavethoughtthattheworldcontainedwhatwemightthinkofascoun-terparts—ifnot,precisely,correlates—ofwholesentences:whenasentenceoftheform‘aRb’istrue,therewillexistacomplex,a-bearing-R-to-b,whichispropositionalinform.Butawholecategoryofexpressionsseemsheretohavebeenomittedfromconsideration.Thisisthecategoryofexpressionscommonlyreferredtoas‘logicalconstants’—suchexpressionsas‘itisnotthecasethat…’,‘either…or–‘,‘if…,then–‘,‘…and–‘.Anunderstandingoftheseexpressionsiscrucialtotheunderstandingoflogic,whichitselfwasacrucialconcernofbothFregeandRussell.Aretheseexpressionstowhich(Corr)applies?Aretheymeaningfulinvirtueofacorrelationwithsomethingextra-linguistic,someentityintheworld?OnFrege’smatureview,theseexpressionsaretreatedasbeingremarkablylikepredicates.Aswehaveseen,on\n100THELEGACYOFFREGEANDRUSSELLFrege’sview,themeaningfulnessofpredicatesdependsontheirbeingcorrelatedwithaspecialkindofitemintheworld—whathecallsconcepts.Theseareessentially‘unsaturated’orincompleteentities.Infact,theyareaspecialkindoffunction.Afunction,ingeneral,issomethingwhichtakesoneormoreobjectsasinput(orargument),andyieldsasingleobjectasoutput(orvalue).Differentkindsofexpres-sioncanrefertofunctionsofdifferentkinds.Thus‘thefatherofx’referstoafunction(ofbeingx’sfather):ifyoutakeaparticularobject(sayQueenElizabethII)asinput,orargument,yougetaparticularobject(KingGeorgeVI)asoutput,orvalue.Thefunctionreferredtobythepredicate‘xisamonarch’isofaparticularkind,onFrege’sview:ifyoutakeaparticularobjectasargument,yougetaveryspecialkindofobject—eithertheTrueortheFalse(accordingtowhethertheargumentisamonarchornot)—asvalue.The‘logicalconstants’ofFrege’slogic—theformalcounterpartstosuchexpressionsas‘itisnotthecasethat…’,‘either…or–‘,‘if…,then–‘,‘…and–‘—alsorefertofunctions,ofanotherspecialkind.Thesefunctionsarecalledtruth-functions:theytakethetruth-valuesofoneormoresen-tencesasarguments,toyieldthetruth-valueofacompoundsentenceastheirvalue.OnFrege’sview,function-expres-sionsingeneralaremeaningfulinvirtueofbeingcorrelatedwithaparticularkindofentity—anentitywhichis‘unsa-turated’orincomplete.Thesamewillthenbetrueofthe‘logicalconstants’:theywillbecorrelatedwithsimilarlyincompleteentities,thetruth-functions.ThiskindofviewisthedirectprovocationforsomeofWittgenstein’smostfundamentalthoughts(includingtheonewhichhehimselfcallshis‘fundamentalthought’:TLP:4.0312).Andithasdeeproots,withaverygeneralphilosophicalsigniﬁcance.Logicisnaturallythoughttobeanaprioridis-ciplineinthefollowingsense:wedonotﬁndoutbyexperi-mentorexperiencewhatfollowsfromwhat.Itistemptingtosupposethatthisepistemicpoint—whichconcernshowweknowaboutlogic—isunderpinnedbyametaphysicalclaim,whichwemightcallthethesisoftheworld-independence\nTHELEGACYOFFREGEANDRUSSELL101oflogic.Wemightformulatethatmetaphysicalthesisasfollows:(WIL)Logicdoesnotdependonanythinginparticularbeingthecase.(WIL)mightalsobethoughttoexplaintheapparentneces-sityoflogic:whatholdsinlogicholdsineverypossibleworld.Both(WIL)andtheclaimthatlogicisaprioriareconcernedwiththestatusofwhatwemightcalllogicaltruths:theyarenottruthsabouttheworld,andwedonotneedtoexperiencetheirtruthinordertoknowthattheyaretrue.Buttheseclaimsarenaturallythoughttorequireamoreradicalkindofindependencefromtheworld:theycannotdependonanykindofacquaintancewiththeworld.Theissuesherereachrightbackintothephilosophicaltradition:wewillbelookingatthoselinksfurtherinthenextsection.ButenoughhasalreadybeensaidtomakeFrege’sviewofthe‘logicalconstants’seempuzzling.Frege’sviewseemstomakelogicdependonsomethingintheworld:thespecialentitiesknownastruth-functions.Andourunderstandingoflogicseemsboundthentodependonsomekindofintuitionof,oracquaintancewith,theseentities.Russellwascertainlyexercisedovertheseissues.Heseemstobeadvocatingaversionoftheworld-independencethesis,andrejectingFrege’stheory,inthisremarkinhis1913TheoryofKnowledgemanuscript:Apropositionwhichmentionsanydefiniteentity,whetheruniversal[suchasaqualityorrelation]orparticular,isnotlogical:noonedefiniteentity,ofanysortorkind,iseveraconstituentofanytrulylogicalproposition.34Thisseemsclearlytodenythatthereareany‘logical’enti-ties.Whatarewetomakeoftheso-called‘logicalconstants’,then?HereiswhatRussellsays:‘Logicalconstants’,whichmightseemtobeentitiesoccurringinlogicalpropositions,arereallyconcernedwithpureform,andarenot\n102THELEGACYOFFREGEANDRUSSELLactuallyconstituentsofthepropositionsintheverbalexpressionofwhichtheirnamesoccur.35Wemightnoteacertainambivalencehere.‘Logicalcon-stants’arenotentities,arenotconstituentsofpropositions,butareneverthelessnamed.Wewillseethisambivalencerecurringlater.Whatisthis‘pureform’?Russellconsidersthefollowing‘purelogicalproposition’,derivedbyremovingthereferencetoitsconstituentsfrom‘ifSocratesishuman,andwhateverishumanismortal,thenSocratesismortal’:Whateverxandaandbmaybe,ifxisaandwhateverisaisb,thenxisb.Andhecomments:HerethereisnolongeranyconstituentcorrespondingtoSocratesandhumanityandmortality:theonlythingthathasbeenpreservedisthepureformoftheproposition,andtheformisnota‘thing’,notanotherconstituentalongwiththeobjectsthatwerepreviouslyrelatedinthatform.(Russell1984:98)Andhecontinuesafewsentenceslater:Itisobvious,infact,thatwhenalltheconstituentsofacomplexhavebeenenumerated,thereremainssomethingwhichmaybecalledthe‘form’ofthecomplex,whichisthewayinwhichtheconstituentsarecombinedinthecomplex.Itissuchpure‘forms’thatoccurinlogic.(Russell1984:98)Andhesuggestsapossiblewayofcharacterizingsuchpureforms:Take,forexample,theproposition‘SocratesprecedesPlato’.Thishastheformofadualcomplex:wemaynaturallysymbolizetheformby‘xRy’….Whenwehavereachedtheform‘xRy’,wehaveeffectedtheutmostgeneralizationwhichispossiblestartingfrom‘SocratesprecedesPlato’.Russell1984:98)\nTHELEGACYOFFREGEANDRUSSELL103Therearetwocrucialthingstonoteaboutthis.First,formsarenotentities,andarethereforenaturallyrepresentedbymeansofvariables(oneinplaceofeachsingularterm,andoneinplaceofeachpredicate:weshouldnote,though,theoddityofdescribingvariablesasinvolving‘generalization’).Second,formsareformsofcomplexes:thatistosay,theyareformsofthepropositionalentitieswhichare,insomesense,thecounterpartsofsentences.(Thecomplex,SocratesprecedingPlato,willbethecounterpartofthesentence‘SocratesprecedesPlato’,althoughitwillnotbethecorrelateofthesentence,inthewaythatobjectivepropositionswouldhavebeenonRussell’soriginalview—forreasonswhichweconsideredinsection2E.)Theideaseemstobetosecuretheworld-independenceoflogicbyclaimingthatlogiciscon-cernedwithformsofcomplexes,andnotwithentitiesofanykind.Unfortunately,Russellseemsnottohavebeenabletoholdontothisview.Whatcausedhimtroublewasacertainepistemologicalfact:weknow(totakethelatestexample)howSocrates,Plato,andprecedencecanbecombinedtoformacomplex.Russellthinksthatwecouldnotpossiblyknowthat,unlesswewereacquaintedwiththeformofthecom-plex(Russell1984:99).Russellacceptsthat‘acquaintance’mayherebebeingusedinan‘extendedsense’(Russell1984:99),butitisunclearthatthis‘extension’ofsenseisenoughtoremovethedifﬁcultywhichisbroughtinwiththeintro-ductionofthenotionofacquaintance.ThedifﬁcultyisthatforRussellacquaintanceistherelationwhichholdsbetweenaperson,ontheonehand,andtheobjectivecorrelateofsomefundamentalfeatureoflanguage,ontheother,invirtueofwhichthepersonisabletounderstandthemeaningofthefeatureoflanguage.Bysupposingthatweareacquainted,eveninan‘extendedsense’,withtheformsofcomplexes,Russellseemsforcedtotreattheseformsasakindofveryabstractobject.ItishardnottoreadRussell’sdescriptionoftheacquaintanceinvolvedhereasexpressinganawkwardhalf-consciousnessofthispoint.Whenhesaysthat‘acquaintance’\n104THELEGACYOFFREGEANDRUSSELLmaybebeingusedinan‘extendedsense’,theextensionseemstobeneededbecausewearedealingwith‘somethingasabstractasthepureform’—thatis,becauseoftheabstractnessoftheobjectofacquaintance,notitsnotreallybeinganobject.Andthefollowingremarkisalsorevealing:Asamatterofintrospection,itmayoftenbehardtodetectsuchacquaintance;butthereisnodoubtthat,especiallywhereveryabstractmattersareconcerned,weoftenhaveanacquaintancewhichwefinditdifficulttoisolateorbecomeacquaintedwith.(Russell1984:99)Thereisnohintherethattheobjectofthis‘extended’acquaintanceisanylessofanobjectthantheacquaintanceitselfis.ThispressureexertedbythenotionofacquaintanceisnaturallyunderstoodasthereasonforRussellchanginghiscanonicalwayofexpressingform.Whereasbefore,aswehaveseen,theformof‘SocratesprecedesPlato’isgivenbyanexpressioninvolvingvariables,‘xRy’,Russellsoonmakestheformafact—‘thefactthatthereareentitiesthatmakeupcomplexeshavingtheforminquestion’(Russell1984:114).Hisﬁnalexpressionoftheformnolongerinvolvesvariables,butquantiﬁers:insteadof‘xRy’wehave‘some-thinghassomerelationtosomething’(Russell1984:114).36WhatishereimplicitbecomesexplicitwhenRussellreturnstothenotionofformafewpageslater:Itwillberememberedthat,accordingtoourtheoryoftheunder-standingofpropositions,thepureformisalwaysaconstituentoftheunderstanding-complex,andisoneoftheobjectswithwhichwemustbeacquaintedinordertounderstandtheproposition….Sincewedesiredtogivethename‘form’togenuineobjectsratherthansymbolicfictions,wegavethenametothe‘fact’‘somethingissomehowrelatedtosomething’.Ifthereissuchathingasacquain-tancewithforms,asthereisgoodreasontobelievethatthereis,thenaformmustbeagenuineobject;ontheotherhand,suchabsolutelygeneral‘facts’as“somethingissomehowrelatedto\nTHELEGACYOFFREGEANDRUSSELL105something”havenoconstituents,areunanalyzable,andmustaccordinglybecalledsimple.(Russell1984:129)Here,unambiguously,formsareconstituentsonaparwiththeordinaryobjectsandrelationswhichweexpecttoﬁndinaRusselliananalysisofjudgement.AndRussellhimselfhasalreadyofferedwhatlooksadecisiveobjectiontoanysuchtheory:[Theform]cannotbeanewconstituent,forifitwere,therewouldhavetobeanewwayinwhichitandtheothertwoconstituentsareputtogether,andifwetakethiswayasagainaconstituent,wefindourselvesembarkedonanendlessregress.(Russell1984:98)RussellseemstohaveendedupinapredicamentnotwhollyunlikeFrege’spredicamentwithconceptsandobjects.Thecharacterofthenotionofacquaintance,whichRussellintroducestodealwithastrikingepistemicfact,seemstohaveforcedhimtotreatformsasobjects—eventhoughhehascompellingreasonnottothinkoftheminthatway.AndformsarenottheonlyobjectswhichRussellﬁndshimselfledtointroducebytherequirementsofthenotionofacquaintance,inordertomakesenseoflogic:Besidestheformsofatomiccomplexes,therearemanyotherlogicalobjectswhichareinvolvedintheformationofnon-atomiccomplexes.Suchwordsasor,not,all,some,plainlyinvolvelogicalnotions;andsincewecanusesuchwordsintelligently,wemustbeacquaintedwiththelogicalobjectsinvolved.(Russell1984:99)ThistreatmentbyRussellofthelogicalconstantscombinedwithhistreatmentof‘pureforms’toprovokeWittgensteintosomeofthemoststrikingandfundamentalclaimsoftheTractatus’conceptionoflanguage.37Hethoughtthatnokindofacquaintancewasneededforlogic,andthatthere\n106THELEGACYOFFREGEANDRUSSELLwereno‘logicalobjects’whichcorrespondedtothelogicalconstants.Thisisallpartofhiscommitmenttowhatwehavecalledthethesisoftheworld-independenceoflogic.38Thatthesisisalsoconnectedwiththeprojectinthephiloso-phyofmathematicswhichRusselltookoverfromFrege:indeed,itsmotivationcanbemoreclearlyshowninthatcontext.2HFREGEANDRUSSELLONMATHEMATICSRussell’streatmentoflogicalconstantsandforms—asobjectsofaspecialkindofacquaintance—is,infact,intensionwiththeapproachtothephilosophyofmathematicswhichhetookoverfromFrege.RussellandFregesharedacommitmenttologicismaboutmathematics—theviewthatmathematicsdependsonnothingbutlogic.Thisview,andthelargephilosophicalissueswithwhichitisconcerned,canbeseenastheoriginalrootofthegeneralphilosophicaloutlookpresentedintheTractatus.Indeed,itisnotunna-turaltothinkthattheproblemsarisingthroughthisapproachtomathematicsplayedasigniﬁcantroleeveninWittgenstein’sadoptionoftheconceptionoflanguagewhicheventuallycametoshapethebook.TheNotebooks,inwhichthethoughtswhichweretoﬁndexpressionintheTractatuswereﬁrstworkedout,beginnotwithanygeneralthoughtsaboutlanguage,butwiththisfamousremark:Logicmusttakecareofitself.(NB:2;TLP:5.473)Thisremarkcanbeseenasanexpressionbothoftheworld-independencethesis(WIL),whichweconsideredinthelastsection,andtheviewthatlogicisanaprioridiscipline,requiringnoexperienceoftheworld.Wittgenstein’sconcernwiththeseissuesarisesdirectlyfromthecontextofFrege’sandRussell’slogicismaboutmathematics.LogicismaboutmathematicsisthelinkbetweenWittgenstein’sconceptionoflogicandthewholephilosophicaltradition.\nTHELEGACYOFFREGEANDRUSSELL107ThesigniﬁcanceoflogicismaboutmathematicscanbetracedbacktoKant.Kantwasconcernedtodefendthepos-sibilityofmetaphysics,onacertainunderstandingofthatnotion.Onthisunderstanding,metaphysicsisthestudyofhowtheworldmustbe:thatis,itaimstoprovidetruthswhicharebothnecessaryandgenuinelyabouttheworld.Inordertobenecessary,Kantthoughttheyhadtobeapriori:presupposed,insomeway,inallthought.Butinordertobegenuinelyabouttheworld,theycouldnotbesimplytheproductoftheanalysisoftheconceptswhichwebringtotheworld:theycouldnot,thatis,beanalytic.SothepossibilityofmetaphysicsseemedtoKanttodependonthepossibilityoftherebeingtruthswhichwerebothsynthetic(notanaly-tic,notsimplytheresultofanalysingtheconceptsinvolved)andapriori.IninsistingontruthsofthiskindKantwasopposingHume,forwhomnecessarytruthssimplyreﬂectedourconcepts,andwere(whenseenfromanappropriatelyloftypointofview)ultimatelytrivial.ItwasnotjustontheoreticalgroundsthatKantthoughtthattherecouldbesyntheticaprioritruths:hethoughtthattherewereactualexamples.Hethoughtthatmathematicaltruthswereclearexamplesofsuchtruths,since,ontheonehand,theywerebothnecessaryandnotknownbyexperi-ment,and,ontheother,theybothhadclearapplicationtotherealworld(wecancountrealthings;wecanapplygeo-metrytoitemsinthespacearoundus),andwerenon-trivial.Kant’sphilosophyofmathematicswasthereforecentraltohisgeneralconceptionoftherelationbetweenthoughtandtheworld.OnKant’sview,mathematicaltruthsdependedonaco-operationbetweentwofaculties:thefacultyofsensibility,whichprovidesonewithakindofacquaintance(‘intuition’)oftheworld(evenifitisakindofpre-experientialaprioriintuition,andofnomorethantheworldasaspatio-temporalentity);andthefacultyofunderstanding,whichcontributesthelawsofthinking.Frege,inoppositiontoKant,aimedtoshowthatmathe-matics(orrather,arithmetic:hewasnotopposedtoKantongeometry)didnotdependonanykindofintuitionor\n108THELEGACYOFFREGEANDRUSSELLacquaintance:heclaimedthatitdependedonnothingbutlogic,withsomethinglikethethesisoftheworld-independenceoflogicbeingsimplyassumed.Fregetookhisviewtomeanthatarithmeticwasanalytic,ratherthansynthetic.Ofcourse,hisviewrequiredanenrichmentbothofthenotionoftheanalytic—itcannolongerbethoughtofasarealmofultimatelytrivialtruths—andoflogic.Fregedevelopedanewlogicalsystem,whichisnow,ineffect,modernlogic:heclaimedthatthislogicalonewasenoughtogenerateallofarithmetic.Arithmeticisbasedonasmallsetofaxioms.ThesewereﬁrstformalizedbyRichardDedekind,andalittlelaterbyGiuseppePeano,afterwhomtheyarenownamed.Hereisaninformalexpressionoftheversionoftheseaxiomswhichisnowgenerallyused:39(Pe1)0isanaturalnumber;(Pe2)Thesuccessorofanynaturalnumberisanaturalnumber;(Pe3)0isnotthesuccessorofanynaturalnumber;(Pe4)Nonaturalnumberisthesuccessorofmorethanonenaturalnumber;(Pe5)If0hasaproperty,andthesuccessorofanynaturalnumberwiththatpropertyalsohasit,thenallnaturalnumbershaveit.Therearetwobasicthingstonoteabouttheseaxioms.Theﬁrstisthatattheircoreisadescriptionoftheformalpre-suppositionsoftheprocedureofcounting(thenaturalnumbersarethecountingnumbers),whichbringswithitthenotionofasuccessor.Andthesecondisthat,intheformtheyhavehere(andweretakentohavebyFregeandRussell),theyimplyasimple(ifextensive)ontology:thenaturalnumbersaretakentobeobjects.Ifweacceptthesebasicpointsatfacevalue,showingthatarithmeticderivesfromlogicaloneisgoingtoinvolvethefollowingtask:wewillneedtoshowthattherearesomeobjects(thenaturalnumbers)whoseexistencedependsonlogicalone(whichwouldmakethem‘logicalobjects’40),andwhichhavethepropertiesnecessarytounderwritetheprocedureofcounting.\nTHELEGACYOFFREGEANDRUSSELL109Howcouldtherebeobjectswhichdependedonlogicalone,andwhichhadthecrucialpropertiesnecessarytounderwritearithmetic?Frege’sanswerdependsonthefollowingthought:attheheartoflogicisthenotionofpredication,andpredicationitselfisenoughtogenerateobjectsoftheappropriatekind.Theidea(inmodernterminology)isthateverypredicatedeﬁnesaclass:theclassofthingsofwhichthepredicateistrue(so,forexample,thepredicate‘xisapen’deﬁnestheclassofpens).Thisclassinturnisanobjecttowhichpredicatesapply.Sopredicationaloneisenoughtointroduceaspecialkindofobject,aclass;andthenotionofaclasscanbeusedtogeneratearithmetic.Intheﬁrstplace,itispossibletoconstructaseriesofclasseswithincreasingnumbersofmembers.Hereisoneway(closetoFrege’sown41),characterizedintuitively.Letusdeﬁneaclassastheclassofthoseobjectswhicharenotidenticalwiththem-selves,theclassofthoseobjectsofwhichthepredicate‘x6¼x’istrue;therearenosuchobjects,sothisclassisan(the)emptyclass.Importantly,thisclasscanberecognizedashavingnomemberswithoutrecoursetoexperience:itisamatteroflogicalonethatthattherecanbenothingwhichisnotidenticalwithitself.Oncewehavethisﬁrstclass,con-structed,apparently,fromlogicalone,wecanproceedwiththeconstructionofawholeseriesofclasses.Thatﬁrstclass,althoughempty,isitselfanobject;thereisapredicate‘xistheemptyclass’whichappliestoit.Thatpredicatecanbeusedtodeﬁneaclass,theclasswhosesolememberistheemptyclass.Wehavenowintroducedtwoclasses:theemptyclass,andaclasswithjustonemember.Thesetwoclassesthemselvesareobjects,andcanbecollectedtogethertoformathirdclass—aclasswithtwomembers.Itisintuitivelyclearthatthisseriescanbeextendedindeﬁnitely,witheachitemintheseriesbeingaclasswithonemorememberthantheitemwhichprecedesit.Suchaseriesprovidesuswithsomethingwhichatleastmirrorsthebasicarithmeticalnotionofsuccession,butitisnottheseriesofnumbersthemselves.Whatwewantisnottheclassitself,ateachstageintheseries,butthenumberof\n110THELEGACYOFFREGEANDRUSSELLitemsintheclass—whatwemightcallthenumberoftheclass.Inordertocapturethis,Fregeexploitsthenotionofequinumerousness,orsame-numberedness.Wecanaskoftwoclasseswhethertheyhavethesamenumberofmembersaseachother,orareequinumerous.Thenotionofequinu-merousnesscan,infact,bedeﬁnedwithouttalkingaboutnumbersatall:twoclassesareequinumerousifitispossibletopaireachmemberofoneclasswithexactlyonememberoftheother,andviceversa;andthisissomethingthatcanbeexplainedentirelyintermsofquantiﬁcationallogictoge-therwiththenotionofidentity.Ifwereturntoouroriginalseriesofclasseswithincreasingnumbersofmembers,wecanobviouslyassociatewiththatseriesaseriesofcollectionsofclasses—theclasseswhichareequinumerouswiththeclassesintheoriginalseries.Itis,ineffect,thislatterseries—theseriesofcollectionsofclasseswhichareequinumer-ouswiththeoriginalseries—thatFregeidentiﬁeswiththeseriesofnaturalnumbers.Thenumberofaclass,onFrege’sview,istheclassofclasseswhichareequinumerouswiththeappropriateclassintheoriginalseries.Sothenumber0istheclassofclasseswhichareequinumerouswiththeﬁrstclassinouroriginalseries(theclassofthingswhicharenotidenticalwiththemselves).Thenumber1istheclassofclasseswhichareequinumerouswiththesecondclassinouroriginalseries.Andsoon.Theseriesofnaturalnumbers,accordingtoFrege,isaseriesofclassesofclasses.BythismeansFregetookhimselftohavevindicatedtheclaimthatnumbersareobjects.First,hehasgivenameaningtophrasesoftheform‘thenumberof…’,soastoconformtothefollowingequivalence:(E)ThenumberofclassC1=thenumberofclassC2ifandonlyifclassC1isequinumerouswithclassC2.Phrasesoftheform‘thenumberof…’havethegrammarofsingularterms,onFrege’stheory.Sinceaproperlymeaningfulsingulartermmustrefertoanobject,theremustbeobjectsreferredtobyphrasesoftheform‘thenumber\nTHELEGACYOFFREGEANDRUSSELL111of…’;andtheseobjectsmustbenumbers.Second,hehasactuallyidentiﬁedarangeofobjectsfornumberstobe:itisarangeofclasses,withclassesbeingobjectswhoseexistencedependsonnothingmorethanthemeaningfulnessofthepredicateswhichdeﬁnethem.Whateveritsartiﬁciality(dowereallythinkthatnumbersareclasses?),Frege’sdeﬁnitionofnumberseemsenoughtoformthebasisofacompleteconstructionofarithmetic:wecanuseittoderivethePeanoaxioms.UnfortunatelyforFrege,attheverymomentwhenhislogicistprojectwascomingtoformalfruition,Russellpointedouttohimthathissystemwascontradictory(Frege1980:130–31).Theproblemwaswithoneofthekeyassumptionsdesignedtoshowthatthewholeconstructiondependsjustonlogic,theassumptionthatanypredicatecouldbeusedtodeﬁneaspe-cialkindofobject,aclass.TheproblemcomesfromthefactthatthereisnothinginFrege’ssystemtostopthepredicatewhichdeﬁnesaclassbeingappliedtothatclassitself,and,asRussellshowed,thisleadstoaparadox.Toseethis,considerﬁrstthepredicate‘isamemberofitself’.Ifweacceptthisasacoherentpredicate,itappliestrulytoclasseswhicharemembersofthemselves—theclassofthingswhicharenotpens,forexample(sincethatclassisnotitselfapen)—andfalselytoeverythingelse.Thoseotherthingsseemtobepickedoutbyadifferentpredicate—thepredicate‘isnotamemberofitself’.Nowsupposethislastpredicatedeﬁnesaclass:theclassofthings(classes)whicharenotmembersofthemselves.CallthisclassS.Letusask:isSamemberofitself?Thatis:doesthepredicate‘isamemberofitself’applytrulyorfalselytotheclassS?Suppose,ﬁrst,thatSisamemberofitself:sincetobeamemberofitselfitmustmeettheconditionimposedbythepredicate‘isnotamemberofitself’,itmustthennotbeamemberofitself.Soifitisamemberofitselfitisnotamemberofitself.Sosuppose,instead,thatSisnotanotamemberofitself.Butnotbeingamemberofitselfisenoughtomeettheconditionimposedbythepredicate‘isnotamemberofitself’,whichmeansthatSqualiﬁesasamemberofitself.SoifSisnota\n112THELEGACYOFFREGEANDRUSSELLmemberofitself,thenitisamemberofitself.Wehaveacontradiction.Itseemsthatthemomentweallowourselvestoformulateapredicatesuchas‘isnotamemberofitself’,andallowsuchapredicatetodeﬁneaclass,wearegoingtobeintrouble.Russellhimselfdidnotabandoneitherthelogicistprojectingeneral,or,inparticular,theattempttogroundmathe-maticsinthetheoryofclasses:insteadhetriedtodealwiththeparadoxbyrestrictingthemannerofconstructionofclasses,andtherangeofadmissiblepredicates.Morespeciﬁ-cally,hetookclassestobeconstructedinahierarchy:atthebasewereindividuals;atthenextstagewereclassesofindi-viduals;atthenextstage,classesofclassesofindividuals,andsoon.Classescouldonlyhavemembersfromlowerstagesinthehierarchy,sotheideaofaclasseitherbeingornotbeingamemberofitselfbecamesimplyunintelligible.Correlatively(sinceexactlysimilarparadoxesarisewiththenotionofapropertyofnotbeingpossessedbyitself,orwiththenotionofapredicatesuchas‘xdoesnotapplytoitself’),predicatescouldonlybemeaningfullyappliedtoobjectsatlowerlevelsinahierarchyofobjects;sothepredicate‘xdoesnotapplytoitself’iscountedassimplymeaningless.Thistheory—Russell’s‘theoryoftypes’—mayhaveavoidedtheparadoxes,butithadtheresultthatfeaturescommontodifferentlevelsofthehierarchybecameuncapturable(sinceanyattempttocapturethemwouldinvolveapredicatewhichdisobeyedthehierarchyrestrictions).Anditalsomeantthatextraaxioms,ofuncertainstatus,hadtobeintroducedtogenerateallofarithmetic.42Theseextraaxiomsarenotobviouslyamatterjustoflogic;sotheﬁnalstatusoftheconstruction,asadefenceoflogicismaboutmathematics,iscorrespondinglyunclear.Wittgensteinwasclearlyconvincedofthecentraltenetoflogicismaboutmathematics:thatmathematicsdependedonnointuitionoforacquaintancewiththeworld,howevergeneralorabstractsuchanintuitionmightbe;andconse-quentlythatmathematicaltruthswerenotsynthetic,inKant’ssense.Thisisanapplicationtothecaseof\nTHELEGACYOFFREGEANDRUSSELL113mathematicsofthegeneralviewofnecessitywhichunderliesthethesisoftheworld-independenceoflogic.Buthewasnotimpressedbytheattempttoconstructapseudo-worldof‘logicalobjects’,whichseemedtoprovideonewithsome-thingwhichonlyintuitioncouldoffer,thoughwithoutappealingtointuition.Hisrejectionoftheclass-theoreticconstructionofarithmeticwasatleastparalleltohisrejec-tionoftheideaofspeciallogicalobjectsofacquaintancewhichwerecounterpartstothefamiliarlogicalconstants.IfwethinkoftheTractatusasbeingmotivatedinpartbyadesiretomaintainsomeformofthelogicismwhichheinheritedfromFregeandRussell,andwithitarejectionoftheideaofmathematicsasarealmofsyntheticaprioritruth,wecanseealarger,andmoregenerallyphilosophicalpurposetothework.JustasKanttriedtomakesenseofmetaphysics,ingeneral,asrequiringsyntheticaprioritruths,sowecanseetheTractatusasanattempttomakesenseofwhatisnecessarilytrueoftheworld—ingeneral,andnotjustinthemathematicalcase—withoutappealingtosyntheticaprioritruths.Ifwepursuethislineofthought,theTractatusbeginstolooklikeaworkwhoseconcerniswiththesameﬁeldofproblems,broadlyspeaking,asKant’sworkis,althoughitoffersaradicallydifferentsolutiontothem.\n3THEGENERALTHEORYOFREPRESENTATION3AWITTGENSTEIN’SSTARTINGPOINTThegrandmetaphysicaltheorywithwhichtheTractatusbeginsisnothingbutwhatisrequired,onWittgenstein’sview,bytheverypossibilityoflanguage.Butwhat,exactly,doesthatrequire?InthelightoftheworkofFregeandRussell,Wittgensteinwillhavefoundhimselfwithtwofundamentalassumptionsandapairofproblems.Thetwofundamentalassumptionsarethecorrelationassumptionandtheobjectivityassumptionwhichwereidentiﬁedinthepreviouschapter:(Corr)Languagesdependfortheirmeaningfulnessoncorrelationsbetweencertainlinguisticitems,ontheonehand,andextra-linguisticitems,ontheother.(Obj)Theextra-linguisticitemswithwhichthoselinguisticitemshavetobecorrelatedforlanguagestobemeaningfulareitemsintheworld(objects).\nTHEGENERALTHEORYOFREPRESENTATION115(Corr),orsomethingveryclosetoit,seemsjustobvious:1itiswhatunderliestheclaim,whichhasbeenacceptedalmostwithoutquestionatleastsinceAristotle,thatlanguagesaresystemsofsigns.And(Obj)seemsforcedonusonceweacceptthegeneralorientationtowardstheworldwhichcomeswithFrege’srejectionofpsychologism:itiscorrela-tionswithitemsintheworldwhichmakelanguagesmean-ingful,notassociationswiththingsinspeakers’minds.AndthetwoproblemswhichWittgensteinfacedarethese:(P1)Whichlinguisticitemsneedtobecorrelatedwiththingsintheworldforlanguagestobemeaningful?(P2)Howistheunityofthesentencetobeexplained?Theseproblemsneedalittleexplanation.Inthecaseof(P1),anissuearisesforeachofthethreebasickindsofexpressioninaFregeangrammar:singularterms,predicates,andsen-tences.Singulartermsarenaturallyjustdeﬁnedtobetermswhosemeaningfulnessdependsontheirbeingcorrelatedwithparticular,individualobjects.Thequestiontheniswhich,ifany,expressionsofordinarylanguage(andothersymbolsystems)shouldbecountedassingularterms.Fregehadbeengenerousinhisinclusionofordinaryexpressions:inparticular,hecountedordinarypropernamesanddeﬁnitedescriptionsassingularterms.Theproblem,then,wastounderstandhowanexpressionofthiskindcouldhavemeaning,iftherewasnorealobjectwithwhichitwascor-related.Frege’suseofhistechnicalnotionof‘sense’providedasolutiontotheproblemwhosemeritswere,atbest,unclear.Withhistheoryofdescriptions,Russellfoundawaytobemoresparinginwhathecountedasasingularterm.Infact,neitherdeﬁnitedescriptionsnorordinarypropernameswereincluded.Thecategoryofsingularterms—whatRussellhimselfwouldcall‘logicallypropernames’—wasrestrictedtothosetermswhicharecorrelatedwithitemswithwhichweareacquainted.Thesewillbeitemsaboutwhoseexistencewecannotbemistaken,soanexpressionwillonlybecountedasasingulartermwhenwe\n116THEGENERALTHEORYOFREPRESENTATIONcanbesurethattherereallyisanobjectwithwhichitiscorrelated.TheproblemwiththecaseofpredicatesisclearfromFrege’sdifﬁcultywiththeconcepthorse,togetherwiththedifﬁcultieswhichseemtofaceRussell’salternativeapproach.Predicatesarenaturallyunderstoodtobeinsomesenseincomplete,tocontaininthemagapwhereasingulartermmaybeplaced.Thisthoughtreﬂectsthefactthatthepre-dicateinFrege’sgrammarcontainsthecopula,ortheverb,whichhastraditionallybeenseentobewhatisresponsibleforthebindingtogetherofthepartsofasentencetoformasingleunity.Thedifﬁcultycanbeseenifweconsiderwhe-ther,ifpredicatesaremeaningfulinvirtueofbeingcorre-latedwithsomeentityintheworld,theentityinquestionitselfincorporatessomecounterparttothesentence-unifyinggrammarwhichpredicatesaretraditionallyunderstoodtohave.Ifitdoes—iftheworldlycounterparttoapredicateisitselfanincompleteentity—wehaveFrege’sproblemwiththeconcepthorse:itwill,atbest,beimpossibletosaywhatthepredicaterefersto,byactuallyusingtheconceptofreference,sinceeveryattempttodothatwillinevitablytreattheworldlycounterparttothepredicateasacompleteentity.2If,ontheotherhand,weadoptRussell’ssolution,andtreattheworldlycounterpartsofpredicatesasbeingnodifferentatthelevelofthemostfundamentallogicalcate-goryfromtheworldlycounterpartsofsingularterms—theywillalljustbeobjects(Russell’s‘terms’)—thenweseemunabletomakesenseofthegrammarofpredicates:howdotheselinguisticitemshavethesentence-unifyinggrammarwhichtheyseemtohave?Itlooks,onthefaceofit,asifanywayofcorrelatingpredicateswithitemsintheworldwillleadtoseriousproblems,solongaswecontinuetothinkthatpredicatesaretheagentsoftheuniﬁcationofsentences.Asforsentencesthemselves,thedifferingviewsofFregeandRussellagainserveasawarning.FregeandRussellbothatsomepointtookthemeaningfulnessofsentencestorequirecorrelationswithentitiesintheworld.3InFrege’s\nTHEGENERALTHEORYOFREPRESENTATION117case,theentitieswereoddinthemselves—theTrueandtheFalse—andprovidednodistinctioninmeaningamongallthetruesentences,ontheonehand,orallthefalsesen-tences,ontheother.Inhisearlytheory,Russelltooksen-tencestobecorrelatedwith‘propositions’—sentence-likeworldlycounterpartsofsentences.Butthisfacedthedifﬁ-cultythatitwashardtomakesenseoftherereallybeingsuchsentence-likecounterpartsoffalsesentences.4Inresponsetothis,Russellmovedtohis‘multiple-relation’theoryofjudgement,therebyabandoningthethoughtthatsentencesneedtobecorrelatedwithentitiesintheworld—andhethenfaceddifﬁcultiesmakingsenseoftheunityofsentences.Inadditiontotheversionsofproblem(P1)whichariseinthecaseofsingularterms,predicates,andsentences,thereisanotherclassofexpressionswhichiscrucialtoFrege’ssystem,butaboutwhichneitherFregenorRussellhadany-thingverysigniﬁcanttosay.Whatarewetomakeofthelogicalconstants—theformalcounterpartsofsuchexpres-sionsas‘if’,‘not’,‘and’,and‘or’—orthequantiﬁers(whichcorrespondto‘all’and‘some’)?IntheTheoryofKnowledgemanuscript,Russellatleastacknowledgedthatsomeexpla-nationneededtobegivenofthemeaningoftheseexpres-sions,andquickly(ifrathervaguely)assumedthattheremustbe‘logicalobjects’withwhichtheyarecorrelated.Butthisisproblematic,forreasonswhichwillbeconsideredinsomedetailinChapter5.Somuchforthevariousformsofproblem(P1).Problem(P2)—overtheexplanationoftheunityofthesentence—isnotwhollyunconnectedwiththem.Iflanguagesaremeaningfulinvirtueofacorrelationbetweenlinguisticitemsandsomethingextra-linguistic,itisnaturaltothinkthatthedistinctiveunityandcompletenessofsentencesmustmirrorsomeextra-linguisticunity(eveniftheextra-linguisticunityisitselfnomorethanaprojectionofalin-guisticunity).5Butwhereisthatextra-linguisticunitytobefound?Itseemsthatitcannotbesomethingcreatedbyanactofjudgement—asLocke,andtheRussellofthe\n118THEGENERALTHEORYOFREPRESENTATION‘multiple-relation’theoryheld—sincethatlooksincompa-tiblewiththegenerallyworld-directedconceptionoflan-guageenshrinedin(Obj).Anditisnotimmediatelyobvioushowitcanbeanythingintheworld,sinceitishardtoseehowtherecouldbeanyappropriateextra-linguisticunitiesinthecaseoffalsesentences.Infact,itseemsthatthisproblemliesbehindtheformofproblem(P1)whicharisesinthecaseofpredicates.Findingacounterpartintheworldtothesentence-unifyinggrammarwhichistraditionallyassignedtopre-dicatesbelongswiththeearlyRussell’ssolutiontotheproblemofexplainingtheunityofthesentence—andthereforeseemstorequirethepostulationofobjectivesententialcounterpartseventofalsesentences.Ontheotherhand,supposingthattheworldlycorrelatesofpredicateshavenothinginthemwhichcorrespondstothedistinctivegram-marofpredicatesseems—onthefaceofit,atleast—toforceustoadopttheLockean,act-of-judgementaccountoftheunityofsentences.WecantakeitthatWittgensteinadopted(Corr)and(Obj)astheonlythingtothinkaboutlanguage,andthat,asaresult,hefacedproblems(P1)and(P2)intheseuncomfor-tableforms.ThetheoryoflanguageoftheTractatuscanthenbeseenashissolutiontothem.Thattheoryistheapplicationtolanguageofageneraltheoryofrepresentation.Therestofthischapterwillbeconcernedwiththegeneraltheory;wewilldealwiththeapplicationofthegeneraltheorytothecaseoflanguageinthenextchapter.3BTHEPARISCOURTROOMMODELThecoreofWittgenstein’snewtheoryoflanguageispre-sentedinthisfamousremarkinthenotebookhewaswritinginSeptember1914:Inthepropositionaworldisasitwereputtogetherexperimentally.(Aswheninthelaw-courtinParisamotor-caraccidentisrepresentedbymeansofdolls,etc.)(NB:7)\nTHEGENERALTHEORYOFREPRESENTATION119ThereferenceintheparenthesisisapparentlytosomethingwhichWittgensteinreadaboutinamagazine.ThiscourtroommodelseemstohavebeentheinspirationforwhathascometobeknownasWittgenstein’s‘picture’theoryoflanguage.Buttheterm‘picture’herecanbemis-leading.IttranslatestheGerman‘Bild’,whichdoesnotmeanquitethesame.‘Bild’,like‘picture’,isappliedprimarilytovisualrepresentations,butitgetstherebyadifferentroute:‘picture’islinkedetymologicallywithpainting,while‘Bild’isconnectedwiththemoregeneralnotionsofcompositionandformation.Thismeansthat‘Bild’isnaturallyappliedtomodels,which‘picture’isnot.And,indeed,Wittgensteinisquitehappytousetheword‘model’(German‘Modell’)inpresentingthe‘picture’theory(TLP:2.12).IndescribingWittgenstein’stheory,Iwillmostlytalkof‘picturesormodels’,inordertopreventtooeasyanassimilationbetweentheGermanword‘Bild’andtheEnglishword‘picture’.Infact,ifwearetounderstandwhatWittgensteinispro-posing,itiscrucialtoseethathisaccountoflanguageisreallyrootedinthoughtaboutmodels—likethemodelinthePariscourtroom.Hewasnotstruckbytheso-called‘picture’theoryaftergoingtoanartgallery,orlookingatabookofsketches.ItissigniﬁcantthatinhispresentationofthetheoryoflanguageintheTractatushesaysthis:3.1431Theessentialnatureofthepropositionalsignbecomesveryclearwhenweimagineitmadeupofspatialobjects(suchastables,chairs,books)insteadofwrittensigns.InunderstandingWittgenstein’stheory,weshouldnotbelookingforanalogiesbetweenpaintingsorphotographs,ontheonehand,andsentencesontheother.Weshouldbetryingtounderstandwhatisimportantaboutthekindofmodelinwhichwemightbenaturallydescribedas‘puttingaworldtogetherexperimentally’.SowhatexactlywasitthatsuddenlystruckWittgensteinwhenhereadaboutthecourtroommodel?6Wellwhatmightstrikeus?Letusimaginethemodelinalittledetail.Wecan\n120THEGENERALTHEORYOFREPRESENTATIONsupposethatitmightincludesomethinglikeamaporplanofthelayoutofthestreets,paintedonalargeboard;perhaps,even,someblocks(ofwood,say)mightbeincludedtoshowthelocationofbuildings,ifthesearerelevanttowhathap-penedintheaccident.Allthisis,asitwere,theﬁxedpartofthebackground.Nowsupposethattheaccidentinvolvedthreevehiclesandtwopedestrians.Wewillwantsomekindofmodelforeachofthevehicles,andalittledoll,orsomeotherﬁgureofanappropriatescale,foreachofthepedestrians.Thesemodelsare,asitwere,loose:theirpositionisnotﬁxedinadvance.Whatwedoisputtheminappropriateplacesonthemodelstreetsandmodelpavements,inordertoindicatewheretherealcarsandtherealpedestrianswerelocatedontherealstreetsandpavementsatthetimeoftheaccident.Whenweconsidersuchamodelinthiskindofdetail,themostobviousthingaboutitisthatthemodelcarsandpeoplearemovable:wecanputthemindifferentplacesonthemodelstreetsandpavements.Nowofcoursethewaywemovethem—byliftingthemupwithourhandsandput-tingthemdownsomewhereelse—isquitedifferentfromthewayinwhichtherealcarsandpeoplecanmove.Butthepositionstheycanendupinarenotsodifferent,onceweallowforscale.Themodelcarsandpeoplearesolid,spatialobjects,describablebythegeometryandgeneralphysicsappropriatetosuchthings;andsoaretherealcarsandpeople.Therangeofpositionsonthebaseboardinwhichthemodelcarsandpeoplecanendupisexactlythesame—allowingforacertainlossofdetailduetothechangeofscale—astherangeofpositionsontherealstreetsandpave-mentsinwhichtherealcarsandpeoplecouldhaveendedup.Thepossibilitiesofarrangementofthemovablebitsofthemodelareexactlythesameasthepossibilitiesofarrange-mentofthemovablethings—therealcarsandpeople—inreality.Thismakesitpossibleforustousethemodeltoconstruct,experimentally,awayinwhichtherealthingsmighthavebeenarranged.ThisisthecoreofWittgenstein’sobservation.Themodeliscomposedofanumberofmovablethingsarrangedina\nTHEGENERALTHEORYOFREPRESENTATION121certainway.Eachofthemovablethingsinsomesensestandsfor,orrepresents,amovablethingintherealworld.Andtherangeofwaysinwhichthemovablethingsinthemodelmightbearrangedisexactlythesame—allowingforscale—astherangeofwaysinwhichthemovablethingsintherealworldmightbearranged.Movabilityisjustpossibilitymadevivid:whatismovablecanactuallybedifferentlylocated.Andthisvividnessiswhataccountsfortheinspirationprovidedbythecourtroommodel.Buttherearealternativepossibilitiesevenforwhatisﬁxedinamodel:evenwhatisﬁxedcouldhavebeendifferentlylocated.Sotheactuallocationoftheﬁxedpartsofthecourt-roommodel—thelayoutofthemodelstreetsandbuildings—couldhavebeenotherwise.Andthesamemorals,broadlyspeaking,applytotheﬁxedpartsofthemodelastothemovingparts.Eachoftheﬁxedpartsofthemodelstandsfor,orrepresents,aﬁxedthingintherealworld.Andtherangeofwaysinwhichtheﬁxedpartscouldhavebeenarrangedisthesame—allowingforconsiderationsofscale—asthewaysinwhichtheﬁxedthingsintheworldcouldhavebeenarranged.Atthispoint,wecanseethatwhatholdsmostobviouslyformodelswithmovablecomponentsmightalsobethoughttoapplytoaverybroadclassofrepresentations—includingpicturesasthosearestandardlyunderstood.Apaintingfromlife,forexample,maybecomposedofmarksmadewithcolouredpaintonasheetofcanvas.Eachofthosemarks,thoughnotmovablenow,couldhavebeenplaceddif-ferentlyonthecanvas.Anditisatleastnotabsurdtosup-posethateachmark(ofacertainsize,atanyrate)standsfor,orrepresents,somethingintherealworld.Andthentherangeofwaysinwhichthemarkscouldhavebeenarranged,whilestillcountingasrepresentingthesamethingsintheworld,mightbethoughttobethesameastherangeofwaysinwhichtherelevantthingsintheworldcouldhavebeenarranged.This,Isuggest,isexactlythereasoningwhichledWittgensteintothetheoryoflanguagewhichisusuallyreferredtoasthe‘picturetheory’,butwhichIprefertodescribeasthetheorythatsentencesaremodels.TheParis\n122THEGENERALTHEORYOFREPRESENTATIONcourtroommodelisnaturallytakentobecapableofrepre-sentingordepictingthetrafﬁcaccidentinvirtueofthefollowingthreefacts:(PM1)Themodelhasmovablecomponents,andtherealsituationinvolvesmovableobjects;(PM2)Themovablecomponentsofthemodelcanbecorrelatedwiththemovableobjectsoftherealsituation;(PM3)Therangeofwaysinwhichthemovablecomponentsofthemodelcanbepositionedisthesameastherangeofwaysinwhichthemovableobjectsinrealityarecapableofbeingpositioned.Ifwegeneralizefrommovabilitytothemoregeneralnotionofpossibility,thissuggeststhefollowinggeneralconceptionofmodels:(M1)Amodelhascomponentswhichcouldhavebeenarrangedotherwise,andrealsituationsinvolveobjectswhichcouldhavebeenarrangedotherwise;(M2)Thecomponentsofamodelcanbecorrelatedwithobjectsinreality;(M3)Therangeofwaysinwhichthecomponentsofamodelcouldhavebeenarrangedisthesameastherangeofwaysinwhichthecorrelatedobjectsinrealitycouldhavebeenarranged.7AndthisgeneralconceptionofmodelsisthentakenbyWittgensteintoapplytoallkindsofrepresentation,includingrepresentationbywhatweordinarilythinkofaspictures.ThisisthecoreofWittgenstein’sview.ButitisaswelltonoteonepeculiarityofWittgenstein’suseoflanguageinthepresentationofhistheory,whichwillhavesomesigniﬁcancewhenweconsiderthecaseoflanguageinthenextchapter.SofarwehaveratherlooselycharacterizedWittgenstein’sviewbyusingamore-or-lesseverydaynotionof‘repre-sentation’.ButWittgensteinhimselfusestwodistinctrangesofwordsin(broadly)systematicallydifferentways.OntheonehandarewordslinkedwiththeGerman‘Darstellung’:\nTHEGENERALTHEORYOFREPRESENTATION123thesearenaturallytranslatedbymeansofsomeformoftheEnglish‘represent’.Ontheotherhand,therearewordslinkedwiththeGerman‘Bild’(picture,model).WhatisthepointofWittgenstein’sdifferenceofuse?Putsimply,thepointisthis.Therelationshipbetweenapictureormodel(Bild)andrealityisgenerallydescribedbymeansofacognateoftheword‘Bild’itself,andismostnaturallytranslatedinEnglishbymeansofsomecognateof‘picture’(forexample,‘pictorial’,‘depict’).Intheseterms,therelationshipbetweenamodelandrealityispictorial;themodeldepictsreality—anditmaydepictrealitycorrectlyorincorrectly.Ontheotherhand,cognatesoftheword‘Darstellung’areusedtodescribethewayamodeldepictsrealityasbeing.Ifweusesomecognateoftheword‘repre-sent’forthisnotion,wewillsaythatamodelrepresentsthatthingsareacertainway.8Onthisuseofthenotionofrepresentation,nopictureormodelcanrepresentsomethingincorrectly:rather,whatitrepresentsmaybecorrectorincorrectabouttherealitywhichthemodeldepicts.Wittgensteinisgenerally(thoughnotalways)carefultousethetworangesofGermanwordsinthesesystematicallydifferentways(anexceptioncanbefoundat2.173,andthereareothersat4.04and4.12),butOgdendoesnotobservethedifferenceinhistranslation(onthispointthePearsandMcGuinnessispreferable).InquotationsfromthetextIwillcontinuetousetheOgdentranslation,althoughIwillreformulateit(inthespiritofthePearsandMcGuinnessversion)totakeaccountoftheactualGermanwordsinvolved,recordinginthenoteswhenIhavedoneso.Thepointisnotcrucialforthepurposesofthischapter,butwilltakeonsomeimportancewhenweconsidertheapplicationofthegeneraltheoryofrepresentationtolanguage,inthenextchapter(seeChapter4,section4C).3CTHEGENERALTHEORYOFREPRESENTATIONThe2.1sand2.2spresentWittgenstein’sgeneraltheoryofrepresentation—thatistosay,theypresenttheapplication\n124THEGENERALTHEORYOFREPRESENTATIONoftheinsightsgainedfromthePariscourtroommodeltothegeneralcategoryofrepresentationsor‘pictures’.Theyseem,then,tobebroachinganewsubject,somethingdifferentfromthegrandmetaphysicaltheorywhichoccupiesthe1sandearly2s.But,ofcourse,thenumberingoftheseremarks—thefactthattheyareinthe2satall—indicatesthatinWittgenstein’smindtheybelongwiththegeneralelabora-tionofthenatureoffactswhichistheprimarybusinessofthesesections.Thisissomethingweneedtoexplain.2.1presentsuswithasummarystatementofourrelationtotheworld.Itwillbehelpfultopresentthisremarkinbothofthetwoclassictranslations.Ogdenputsitlikethis:Wemaketoourselvespicturesoffacts.WhereasPearsandMcGuinnessputitlikethis:Wepicturefactstoourselves.Asisoftenthecase,Ogden’stranslationisword-for-wordliteral,whilePearsandMcGuinnessgivemoreofthecollo-quialﬂavouroftheoriginal.TheGermanexpressionwhichOgdentranslatessoliterallyhasacolloquialforcewhichismuchmorenearlycapturedbyPearsandMcGuinness:itisaperfectlyordinarywayofsayingthatwevisualizefacts—even,perhaps,justthatwehavefactsinview.9Assuchitseemsundeniable,oncewehaveacceptedthattheworlditselfconsistsoffacts.WhattheOgdentranslationbringsoutisthat,ifwetakeitliterally,theeverydayGermanwayofdescribingthisalmostundeniablethingactuallysuggeststhatweconstructsomething—something—whenweviewtheworld.TheeverydayGermansuggeststhatviewingtheworldisamatterofconstructingpicturesormodels.WegettherealforceofwhatWittgensteinisclaimingherewhenweputtogetherwhatwegatherfromthesetwotranslations.Ifweoncegrantthattheworldconsistsoffacts—which,afterall,hasbeenoneofthecentralassertionsofthe1sandearly2s—itseemsundeniablethat,insome\nTHEGENERALTHEORYOFREPRESENTATION125sense,wepicturefactstoourselves.Thisisjusttosaythatwehaveaccesstotheworld.ButtheeverydayGermanwayofdescribingthissuggeststhatourhavingaccesstotheworldinvolvesusconstructingsomething,apictureormodeloftheworld.Wittgenstein’spointisjustthatthislit-eralimplicationoftheeverydayGermanisentirelycorrect:ouraccesstotheworlddoesinvolveourconstructingpic-turesormodelsofit.10Whatthiswillmeanisthatthecon-ceptionofrepresentationderivedfromthePariscourtroommodel—theconceptionenshrinedin(M1)–(M3)—appliestoourmostfundamentalengagementswiththeworld.11Thebulkoftheremarksbetween2.11and2.174canbeseenaselaborationsofthemodelconceptionofrepresenta-tion,buttheyalsodrawoutsomeconsequencesofthatconceptionwhicharecrucialbothforWittgenstein’sresponsetothedifﬁcultieshefoundinFregeandRussellandforthestatusoftheTractatusasawhole.Sections2.13and2.131areexpressionsof(M2).Section2.14presupposesatleasthalfof(M1):thefactthattheelementsofapicturearecombinedinadeﬁnite(particular,determinate)waypre-supposesthattheycouldhavebeencombinedotherwise.Moreover,thisphraseechoes2.031,whereitisclaimedthatinanatomicfactobjectsarecombinedinadeﬁnite(particular,determinate)way:andthatgivesustheotherhalfof(M1).WhatWittgensteinsaysabouttheformofapicturegivesus(M3).Recall,ﬁrst,theintroductionofthenotionofforminrelationtoobjects(theultimateconstituentsoffacts):2.0141Thepossibilityofitsoccurrenceinatomicfactsistheformoftheobject.Thatistosay:theformofanobjectistherangeofwaysinwhichthatobjectcancombinewithotherobjectstoformatomicfacts.Nextconsidertheapplicationofthenotionofformtoatomicfacts:2.032Thewayinwhichobjectshangtogetherintheatomicfactisthestructureoftheatomicfact.\n126THEGENERALTHEORYOFREPRESENTATION2.033Theformisthepossibilityofthestructure.Theformofanatomicfactisitsbeingpossibleforitscon-stituentobjectstobearrangedinthewaysinwhichtheycanbearranged.Itis,asitwere,theformofallofthecon-stituentobjectstakentogether,seenfromthepointofviewoftheatomicfactofwhichtheyareconstituents.Thenotionofformisthenappliedtopicturesinawaywhichispreciselyparalleltothis:Thisconnexionoftheelementsofthepictureiscalleditsstructure,andthepossibilityofthisstructureiscalledtheformofdepictionofthepicture.12(2.15)Andthisisthebasisofwhatis,ineffect,anassertionof(M3),theclaimthattherangeofwaysinwhichthecomponentsofamodelcouldhavebeenarrangedisthesameastherangeofwaysinwhichthecorrelatedobjectsinrea-litycouldhavebeenarranged.HereishowWittgensteinputsitﬁrst:2.151Theformofdepictionisthepossibilitythatthethingsarecom-binedwithoneanotherasaretheelementsofthepicture.13Theword‘as’here(‘so…wie’inGerman)means:inthesamewayas.Themodelconceptionrequiressomethingtobethesame—therangesofpossibilitiesofarrangementofthecomponentsofbothmodelandrealitymustbethesame,accordingto(M3).Wittgensteinexpressesthepointintermsofform,whichwehaveseenisjustthenotionofpossibilitiesofarrangement:2.161Inthepictureandthepicturedtheremustbesomethingiden-ticalinorderthattheonecanbeapictureoftheotheratall.2.17Whatthepicturemusthaveincommonwithrealityinordertobeabletorepresentitafteritsmanner—rightlyorfalsely—isitsformofdepiction.14\nTHEGENERALTHEORYOFREPRESENTATION127Thisisreallyjust(M3),expressedintermsofform.Wittgensteinmakesthreeimportantfurtherclaimsaboutrepresentationingeneralinthesesections(the2.1sand2.2s):twoofthemtakeontheirfullsigniﬁcanceonlywhenthisgeneraltheoryisappliedtolanguage,whiletheﬁnalramiﬁcationsofthethirdarenotrealizeduntiltheveryendofthewholebook.Theﬁrstclaimisexpressedinthesetworemarks:2.14Thepictureconsistsinthefactthatitselementsarecombinedwithoneanotherinadefiniteway.2.141Thepictureisafact.Strictlyspeaking,2.14isover-translatedhere:thereisnowordinthisGermansentencecorrespondingtotheEnglish‘fact’.TheGermanjustmeans‘Thepictureconsistsinthis,thatitselements…’.Butthisdoesnotmakethiswayofputtingtheclaimaltogetherwrong:afterall,afactispreciselyathat—athatthingsarearrangedinacertainway.Andtheclaimis,ofcourse,summarizedinpreciselythemannerofOgden’stranslationinthefollowingremark(2.141doescontainaGermanwordcorrespondingto‘fact’—thefamiliar‘Tatsache’).Theclaimisastrikingone.Wenaturallythinkofapictureoramodelasacomplexobject:anobjectwithcomponentparts—movablepartsinthecaseofthePariscourtroommodel.Wittgensteinheredeniesthis:apictureoramodelisnotanobjectatall,andwhatweusuallythinkofasitscomponentpartsarenotrelatedtothepictureormodelaspartstoawhole.Rather,apictureormodelisathat,andwhatwethinkofaspartsarereallyjust‘elements’.Insteadofbeinganobjectwithparts,apictureormodelisathatcertainelementsarearrangedinacertainway.Thatpicturesormodelsarefactsisrequiredby(M3),ifpicturesormodelsaretobecapableofrepresentingfacts;(M3)requiresthatthecomponentsofthemodelandthecomponentsofthecorrespondingrealityshouldbecapableofbeingarrangedinthesameways.Iftherelevantrealityisafactwhoseconstituentsarecombinedintheways\n128THEGENERALTHEORYOFREPRESENTATIONappropriatetofacts,thenanyrepresentationwhichiscapableofrepresentingthatfactmustalsobeafact.HenceWittgensteinwrites:Thattheelementsofthepicturearecombinedwithoneanotherinadefiniteway,representsthatthethingsaresocombinedwithoneanother.(2.15;myemphasis)Atthispointtheclaimthatpicturesormodelsarefactshasnotbeenjustiﬁed.Indeed,Wittgensteinnevergivesanyexplicitjustiﬁcationforit.Butajustiﬁcationcanbeofferedonhisbehalf,onceweseethesigniﬁcanceoftheclaimforthephilosophyoflanguage.AtthatpointwewillseehowitisthebasisofWittgenstein’ssolutiontoproblem(P2),thedifﬁcultyofexplainingtheunityofthesentence(seeChapter4,section4G,below).ThesecondimportantclaimthatWittgensteinmakesaboutpicturesormodels—whosefullsigniﬁcanceagaincanonlybeseenoncethetheoryisappliedtothecaseoflanguage—isembeddedintheseremarks:2.1511Thusthepictureislinkedwithreality;itreachesuptoit.2.1512Itislikeascaleappliedtoreality.2.15121Onlytheoutermostpointsofthedividinglinestouchtheobjecttobemeasured.2.1514Thedepictingrelationconsistsoftheco-ordinationsoftheelementsofthepictureandthethings.152.1515Theseco-ordinationsareasitwerethefeelersofitselementswithwhichthepicturetouchesreality.Thebasicviewexpressedhereisthis:apictureormodelgetstobeapictureormodelinvirtueofitselementsbeingco-ordinatedwiththecomponentsoftherealitywhichitrepresents.Theideaisthatitisthecorrelationswhosepos-sibilityisdeclaredby(M2)whichmakeapictureapicture.InthecaseofthePariscourtroommodel,themodelgetstobeadepictionofthetrafﬁcaccidentinvirtueofthemodel\nTHEGENERALTHEORYOFREPRESENTATION129carsandpeoplebeingcorrelatedwith—takeninsomewaytostandfor—therealcarsandpeoplewhichwereinvolvedintheaccident.AsWittgensteincomments:2.1513Accordingtothisviewthedepictingrelationwhichmakesitapicture,alsobelongstothepicture.16ThecrucialclaimWittgensteinismakingisthatthecorrela-tionsbetweenpictureandrealityneedonlybecorrelationsbetweenelementsofthepictureandthingsinreality:itisnotalsorequiredthattherebeacorrespondencebetweenthepictureasawhole—thefactthattheelementsarearrangedinaparticularway—andafactinreality—thefactthatthethingsinrealityarearrangedinaparticularway.Thismeansthattherecanberepresentationswhichdepictthingsincorrectly,orfalsely—whichrepresentthingsasbeingotherwisethantheyactuallyare.Thiswillhaveanobvioussigniﬁcancewhenthetheoryisappliedtolanguage.ItmeansthatWittgensteinistakingaparticularstandontheissuesraisedbyproblem(P1),theproblemofdecidingwhichlin-guisticitemsneedtobecorrelatedwithitemsintheworldforlanguagestobemeaningful.HeisgoingagainsttheviewofFregeandtheearlyRussell,anddenyingthatthemean-ingfulnessofsentencesrequiresthemtobecorrelatedwithanythingintheworld.Heisclaimingthatwedonotneedtomakepeculiarobjectsoftruth-values,asFregedid;nordoweneedtoposit‘objectivefalsehoods’—falsefacts,asitwere—astheearlyRusselldid.AccordingtoWittgenstein,theonlycorrelationswhicharerequiredarebetweenelementsofthepicture(eventually:thesentence)andthingsinreality,notbetweenthewholepicture(sentence)andsomethinginrealitywhichmightbetakentobethecorrelateofapicture(sentence).Itisworthpausingforamomenthereoverthepictur-esqueimageof2.1512and2.15121.Theimageisofanordinaryrulerormeasure,markedoutwithlinesatintervals(millimetresandcentimetresinametricsystem;quarter-inches,half-inches,andinchesinanimperialsystem):these\n130THEGENERALTHEORYOFREPRESENTATIONarethe‘dividinglines’Wittgensteinspeaksof.Wittgensteinsaysthatitisonlytheendsoftheselines—theendsbytheedgeofthemeasure—whichtouchtheobjecttobemea-sured.Whatpointisbeingmadehere?Itmaybethatthepointistheonewehavejustexplained:thereonlyneedtobecorrelationsbetweentheelementsofapictureandthethingsinreality,notbetweenapictureasawholeandsomethingcorrespondingtoitinreality.Buttheimageoftherulerfallsapartonthisreading.WhatWittgensteinsaysisthattherestofthedividingline—thepartwhichrunsawayfromtheedgeofthemeasure—doesnottouchrea-lity.Thesuggestedreadinghastosupposethatthewholepictureisherelikenedtothewholedividingline.Butthedifﬁcultyisthatthepictureconsistsinthefactthatitsele-mentsarearrangedinacertainway;inthetermsofourimage,theseelementsarethedividinglines;andthatmeansthatthefactwhichconstitutesthepicturehastobeafactaboutallthedividinglinesonthemeasure(whichareeachcorrelatedwithsomethinginreality),andnotafactabouttherelationbetweenthedifferentpartsofeachdividingline.Soitishardtoseehowthisimagecanbemakingthepointthatthereneedbenocorrelateinrealitytothewholepicture—evenifthatisapointwhichWittgensteinwantstomake.Wegetamoresatisfyinginterpretationoftheimageifweconsider2.1512and2.15121intheircontext.ThecontextisWittgenstein’sversionofclaim(M3),hisclaimthatarepre-sentationmusthavethesameformastherealityitdepicts.Theclaimof2.15121thenbecomessomethinglikethis:nothingmattersabouttheelementsofapictureormodelotherthanthattheyhavethesamerangesofpossibilitiesofcombinationastheitemsinrealitywithwhichtheyarecorrelated.Nofurthersimilarityisrequired.Andthisamounts,ineffect,totheclaimthattheelementsofapictureormodelarearbitrarysigns:whateverrepresentationalworktheelementsofapicturemaydo,itcanbedonebyquitedifferentthings,providedthatthosedifferentthingshavethesamepos-sibilitiesofcombinationwithotherthings.Thepointoftheremark,onthisinterpretation,istoinsistthatrepresentation\nTHEGENERALTHEORYOFREPRESENTATION131onlyrequiresaveryabstractkindofsimilaritybetweenrepresentationandreality:nothingmorethansamenessofform.17Ifthisisright,theclearconnectionbetween2.15121and2.1515—theybothcontaintheideaoftheelementsofapicturetouchingreality—makesafurtherpoint.2.15121,ontheinterpretationwhichIhavesuggested,claimsthatallthatisrequiredforapicturetobeapictureisthattheformofthepicturebethesameastheformofreality;and2.1515claimsthatwhatisrequiredisfortheelementsofapicturetobecorrelatedwiththingsinreality.Puttingthetwotogetherseemstoamounttomakingthefollowingclaim:itisonlypossiblefortheelementsofapicturetobecorrelatedwiththingsinreality,iftheitemsoneachsideofsuchacorrelationcanbecombinedinthesamewayswithotheritems.Thatistosay,theclaimwhichisbeingmadehereisthatwhatisassertedby(M2)—thepossibilityofcorrelation—requireswhatisassertedby(M3)—samenessofform.Itisnotthatwemightcorrelateelementsofamodelwithitemsinreality,andthendecidehowtheelementsofthemodelcanbemovedaround:itisonlyiftheelementsofthemodelalready,orthereby,18havethesamerangesofpossi-bilityofcombinationastheitemsinrealitythatthecorrelationcanhavebeensetupintheﬁrstplace.3DTHEIMPOSSIBILITYOFDEPICTINGFORMThethirdimportantclaimaboutrepresentations,whichWittgensteintakestofollowfromhisoverallaccount,emergesinthesesections:2.172Thepicture,however,cannotdepictitsformofdepiction;itshowsitforth.192.173Thepicturerepresentsitsobjectfromwithout(itsstandpointisitsformofrepresentation),thereforethepicturerepresentsitsobjectrightlyorfalsely.202.174Butthepicturecannotplaceitselfoutsideofitsformofrepresentation.21\n132THEGENERALTHEORYOFREPRESENTATIONTheclaimof2.172willturnouttohaveabsolutelyfunda-mentalsigniﬁcanceforthewholeTractatus:thisclaimentailsthattheTractatusitselfismeaningless,onitsownterms.Andhere,in2.173and2.174,wegetWittgenstein’sargu-mentforthatclaim.Acasecanbemadeforsayingthatthesetwoshortsectionsarethepivotalsectionsofthewholework.Unfortunately,theargumentisnotcompletelyclear.Thecrucialstepsseemtobethese:(1)Apicturecanonlydepictsomething(its‘object’)ifitcandepictitcorrectlyorincorrectly;(2)Apicturecanonlydepictsomethingcorrectlyorincorrectlyfromapositionoutsidewhatitdepicts;(3)Apicturecannotoccupyapositionoutsideitsownform;so(4)Apicturecannotdepictitsownform.Tobeginwith,weneedtobeclearthatwhenhetalksaboutthepicture’s‘object’in2.173,Wittgensteinisnottalkingabouttheobjectswhicharethefundamentalconstituentsoffacts,andhence,intheend,oftheworld.Histermforobjectinthatsense(thenecessaryexistentswhoseformistheformoftheworld)is‘Gegenstand’;butherethetermis‘Objekt’.Theobjectofarepresentationinthissense(the‘Objekt’sense)iswhatisdepicted:thatis,accordingtoWittgenstein,acertainsituationinreality.(PearsandMcGuinnessactuallytranslate‘Objekt’hereassubject.)Asweknow,theformofarepresentationisitsbeingpossiblefortheelementsoftherepresentationtobecom-binedinthewaytheyare:forexample,itsbeingpossibleforthemodelcarsandpeopleinthePariscourtroommodeltobearrangedinthewaytheyare.Theclaimof2.172is,then,thatapicturewhichrepresentsthatthingsareacertainwaycannotrepresentthatitispossibleforitsownelementstobethesameway.Thereasonis,apparently,thatapicturecannot‘placeitselfoutside’itsownformofrepresentation.Sotheargumentclearlyturnsonwhatitisforapicturetobe‘outside’whatitrepresents.Aslightlylatersectionsuggestsanaturalinterpretation:\nTHEGENERALTHEORYOFREPRESENTATION1332.22Thepicturerepresentswhatitrepresents,independentlyofitstruthorfalsehood,throughitsformofdepiction.22Isuggestthatforapicturetobeoccupyingaplace‘outside’whatitrepresentsisforitsbeingapicture(and,indeed,itsbeingthepictureitis)tobeindependentofwhetheritrepresentsthingscorrectlyorincorrectly.Ifweadoptthisinterpretation,thenwecanrewritethewholeargumentasfollows:(1*)Apicturecanonlyrepresentthatp(foragiven‘p’)ifitcanrepresentthatpcorrectlyorincorrectly;(2*)Apicturecanonlyrepresentthatpcorrectlyorincorrectly,ifitsbeingapictureisindependentofwhetherornotitistruethatp;(3*)Apicture’sbeingapicturecannotbeindependentofwhetheritispossibleforitsownelementstobearrangedastheyarearranged(orthatitispossiblethatthingsinrealityaresoarranged);so(4*)Apicturecannotrepresentthatitispossibleforitsownele-mentstobearrangedastheyarearranged(orthatitispos-siblethatthingsinrealityaresoarranged).Premise(3*)heremustbeacceptedonceweacceptthecen-tralclaimofWittgenstein’sconceptionofrepresentation:thatis,onceweaccept(M3).Butwhatisgoingonin(1*)and(2*)?ItissometimessuggestedthatWittgenstein’srea-soningintheTractatusturnsfundamentallyonaprincipleknownasthePrincipleofBipolarity.Accordingtothisprinciple,initsmostgeneralform,everymeaningfulsen-tencemustbecapablebothofbeingtrue,andofbeingfalse.Itisnotenoughmerelythateverysentencemustbeeithertrueorfalse:thatistheprincipleknownasthePrincipleofBivalence.ThePrincipleofBipolaritydemands,notmerelythateachpropositionmustfallintooneofthetwocate-gories,butthatbothcategoriesmustbe,asitwere,liveoptionsforeveryproposition.IfwethinkthatBipolarityisthebasicassumptionoftheargumentof2.173and2.174,we\n134THEGENERALTHEORYOFREPRESENTATIONmaybetemptedtoreadthatprincipleexplicitlyinto2.173,andhenceintopremise(1*):theconditiononapicture’srepresentingthatpwillbethatbothcorrectlyrepresentingthatpandincorrectlyrepresentingthatpmustbeliveoptions.ThePrincipleofBipolarityiscertainlysomethingwhichWittgensteinacceptedatsomepointsduringthecompositionoftheTractatus(NL,pp.98–99,101–02).ButalthoughIthinkthatsomethinglikethePrincipleofBipolarity—atleastinaqualiﬁedform—isinvolvedintheargument,Ithinkthatthisprincipleitselfdoesnothavethefundamentalrolewhichthiskindofreasoningascribestoit,anditarisesin2.173inaslightlydifferentwayfromthatwhichthisreasoningsuggests.Ifwetakethephrase‘canrepresentthatpcorrectlyorincorrectly’(orthephrase‘representsitsobjectrightlyorfalsely’in2.173)asbeingitselfanexpressionofthePrincipleofBipolarity,itwillmean,ineffect:iscapablebothofbeingcorrectandofbeingincorrectinrepresentingthatp.Premise(1*)willthenbethesubstantialclaim,andpremise(2*)willbetriviallytrue.Butthissurelymis-representstheshapeoftheargument(andof2.173),whichrequires(2*)tobethesubstantialclaim,with(1*)being,onreﬂection,undeniable,evenifnotquitetrivial.Isuggestthatthebasicreasonforaccepting(2*)canbeapproachedasfollows.Consideragainthecourtroommodel.Supposethatitmisrepresentstherealtrafﬁcaccidentverybadly:themodelcarsandpeopleareinaltogetherthewrongplaces.Andnowimaginesomeonesaying,‘Still,themodelhasgotsomethingright.’Wewonderwhatthismightbe.‘Well,it’srightaboutitsowngeometry,atleast,’comesthereply.Thisreplyissurelyabsurd,anditsabsurdityisthebasisof2.173.Whatisabsurdaboutthisreply?Itseemstobesomethinglikethis.Thewholebusinessofrepresentationistoportraysomethingwhichisindependentoftherepresentationitself.Thishasalwaysbeenthepointofrepresentation.Whatisitforsomethingtobeindependentofarepresentation?Thenaturalsuggestionisthis:somethingisindependentofarepresentation,intherelevantsense,iftherepresentationmightbewrongaboutit.Puttingthisalltogether,wereachthethoughtthat\nTHEGENERALTHEORYOFREPRESENTATION135arepresentationcanonlydepictsomethingwhichitmightbewrongabout.Andthatmeansthatnorepresentationcandepictsomethingwhichispresupposedinitsbeingtherepre-sentationitis.Sincenorepresentationcanbetherepresenta-tionitiswithoutitsownexistencebeingatleastpossible,norepresentationcancountaseitherrepresentingordepictingitsownpossibility,whichmeansthatnorepresentationcanrepresentordepictitsownform,inWittgenstein’ssense.IfthisisthecoreofWittgenstein’sreasoning,thenitdoesinvolvesomethinglikethePrincipleofBipolarity—thoughinaratherdifferentform—butthatprincipleisnotthemostfundamentalthingaboutthereasoning.Themostfundamentalthingisthesimplethoughtaboutrepresentation,thatrepresentationisessentiallyrepresentationordepictionofsomethingindependentoftherepresentation.AndtheformofthePrincipleofBipolaritywhichfollowsfromthisisbothmoregeneralandmorerestrictedthantheoriginalstatementsuggested.Theoriginalformulationinvolvedtheclaimthateverymeaningfulsentencemustbecapablebothofbeingcorrectandofbeingincorrect.TheprinciplewhichWittgensteiniscommittedto(effectively(2*))ismoregen-eralthanthis,inthatitappliestorepresentationswhicharenotsentences.Butitalsoseems,onthefaceofit,tobemorerestricted,since,amongsentences,itappliesonlytothosewhicharerepresentations,anditisnotobviousthatWittgensteinassumesthatallsentencesarerepresentations.23Wittgenstein’sargumenthereseemstohaveaverysig-niﬁcantconsequenceforissuesofpossibilityandnecessity.Heseemstobecommittedtothisclaim:(NF)Norepresentationcanbenecessarilycorrectornecessarilyincorrectjustinvirtueofitsform.Forifarepresentationwerenecessarilycorrectorincorrectjustinvirtueofitsform,thenitwouldbecorrectorincorrectjustinvirtuebeingtherepresentationitis;whichcontradicts(2*).And(2*)alsoseemstobethebasisforthefollowingremarks:\n136THEGENERALTHEORYOFREPRESENTATION2.224Itcannotbediscoveredfromthepicturealonewhetheritistrueorfalse.2.225Thereisnopicturewhichisaprioritrue.Alloftheseclaimswillhaveconsiderablesigniﬁcancewhenweturntothestatusofphilosophy.Thereisanotherextremelyimportantpointabouttheclaimof2.172.Althoughitclaimsthatnorepresentationcandepictitsownform,itdoesnotclaimthattheformofrepresentationisinvisible.Itis,rather,visibleinadifferentway:arepresentationdoesnotdepictitsownform,butit‘showsitforth’(or,asPearsandMcGuinnessputit,it‘dis-playsit’).WeseeheretheﬁrstappearanceofacontrastwhichiscentraltotheTractatus,andtoitsviewofthestatusofphilosophy:betweenwhatcanberepresented(ultimately,whatcanbesaid),ontheonehand,andwhatcanonlybeshown,ontheother.Weseeherethatwhatisdepictedisalwaysathat—thatsomethingisthecase(thatthingsarearrangedinacertainway);whereas(inthiscaseatleast)whatisshownisform—thepossibilitiesofcombinationofthings.3ETHOUGHTSANDLOGICALFORMWittgensteinoffersusageneralconceptionofrepresenta-tion.Itscentralthesisisthatrepresentationrequiresanidentityofform—anidentityofpossibilitiesofcombinationofcomponents—betweenarepresentationandtherealitywhichitdepicts.Thisgeneralconceptionofrepresentationisappliedtothecaseofsentences,inparticular,bywayoftwocrucialnotions:thenotionsoflogicalform,andofthought.Iwillclosethischapterbyconsideringthesenotions.Thenotionoflogicalformisintroducedinsection2.18:Whateverypicture,ofwhateverform,musthaveincommonwithrealityinordertobeabletorepresentitatall—rightlyorfalsely—isthelogicalform,thatis,theformofreality.\nTHEGENERALTHEORYOFREPRESENTATION137Andthepointiselaboratedtwosectionslater:2.182Everypictureisalsoalogicalpicture.(Ontheotherhand,forexample,noteverypictureisspatial.)Anumberofclaimsarebeingmadehere,bothinthechar-acterizationoflogicalform,andinthedescriptionofitas,precisely,logicalform.Intheﬁrstplace,logicalformisthemostgeneralformwhichmaybecommonbetweenarepresentationandwhatitrepresents.Thispointismostnaturallyexplainedintermsofpossibilitiesofcombinationorarrangement(whichare,afterall,whatWittgenstein’snotionofformisabout).Theremaybepossibilitiesofspatialarrangement.Theremaybepossi-bilitiesoftemporalarrangement.Theremaybepossibilitiesofarrangementintermsofpitch,oronaspectrum.Eachofthesekindsofpossibilityofarrangementisdifferentfromtheothers,buttheyareall,accordingtoWittgenstein,pos-sibilitiesoflogicalarrangement.Thesigniﬁcanceofthispointwillbeclearlater,whenweconsiderthefollowingstrikingclaimwhichWittgensteinmakestowardstheendoftheTractatus:24Thereisonlylogicalnecessity.(6.37)Theuniversalityoflogicalformcanbeexpressedintermsofthenotionofaspace.Wecanthinkofaspaceasdeﬁnedbywhatispossibleandwhatimpossiblewithinit.SowecanimagineaEuclideanspaceandanon-Euclideanspace,whilestillremainingwithintheboundsofgeometry.Wecantalkofthespaceofcolours,orthespaceoftonality.Ifweexpresstheuniversalityoflogicalformintheseterms,wewillsaythatallthesespacesarepartof,orliewithin,logicalspace.HenceWittgensteinisabletosay:2.202Thepicture[i.e.,everypicture]representsapossiblestateofaffairsinlogicalspace.\n138THEGENERALTHEORYOFREPRESENTATIONAndthis,ofcourse,recallsthefollowingremark,madeveryearlyonintheTractatus:1.13Thefactsinlogicalspacearetheworld.Theﬁrstpointaboutlogicalform,then,isthatlogicalformisthemostgeneralformwhicharepresentationmaysharewithreality.Thesecondpointisclearlyconnectedwiththis,althoughitmightseemtorunbeyondit:itisthatlogicalformistheformofreality(2.18).Thereasonwhythismightseemtorunbeyondtheﬁrstpointisthatitmightseemthatthefollowingclaim(oftheunrepresentabilityofsomeaspectsofreality)couldbetrue:(UR)Thereareaspectsofrealitywhichcannotberepresented.Clearly,if(UR)weretrue,thiswouldmeanthattherewerewaysinwhichobjectscanbecombinedwhichoutrunwhatanyrepresentationcouldmatch.Therewould,then,bepos-sibilitieswhichcouldnotbereﬂectedinanyrepresentation.SinceWittgensteininsistshere(2.18)thatthemostgen-eralformwhicharepresentationmaysharewithrealityisjusttheformofreality,hecannotbeaccepting(UR).Here,though,itisimportanttodistinguishbetweentwodifferentwaysofnotaccepting(UR):(i)Onemightthinkthat(UR)wasfalse—thatis,thattherearenoaspectsofrealitywhichcannotberepresented;(ii)Onemightjustdeclinetoaccept(UR),withoutassertingthattherearenoaspectsofrealitywhichcannotberepresented.Itisimportanttodistinguishbetween(i)and(ii),becausethereisatleastthesmellofathreatofparadoxabout(i):itlooksasif,inevencontemplatingthepossibilityofaspectsofrealitywhichcannotberepresented(inordertodenythatpossibility),weneed,atleast,togettowardsrepresentingthem(asthoseaspectswhichcannotberepresented).Itmaybethatthereisnorealparadoxhere,butweshouldatleast\nTHEGENERALTHEORYOFREPRESENTATION139beawareofthepossibilityofalesscommittalpositionthan(i);weshouldbeawarethatsomeonemightsimplydeclinetocountenancearealitywhichcontainedaspectswhichcannotberepresented.Itistemptingtothinkthatanyviewwhichrefrainsfromaccepting(UR)mustbeanti-realist,insomeway.InChapter1(section1F)Iofferedthisstatementofrealism:(R)Realityasitisinitselfisaltogetherindependentofanythingtodowithanywayofrepresentingit.Wemightthinkthat(R)wouldmakethedenialof(UR)lookunmotivated,andhencethatitwouldbeoddforarealisttodeny(UR):surelyifrealityasitisinitselfisaltogetherindependentofanythingtodowithanywayofrepresentingit,weshouldexpecttheretobeaspectsofrealitywhicharenotrepresentable?Infact,thereisnosuchobviousconnec-tionbetween(UR)andanti-realism.TheseareissueswewilllookatinsomedetailinChapter6.Somuch,then,forWittgenstein’spositiveclaimsaboutlogicalform.ButwhatisthesigniﬁcanceofWittgenstein’sdecisiontousetheterm‘logicalform’todescribethemostgeneralformwhichcanbecommontorepresentationsandreality,theformofrealityitself?TheﬁrstandmostobviousreasonforthischoiceoftermisthatWittgensteinwilllaterbeusingthismostfundamentalformoftheworldaspartofhisaccountofthenatureoflogic,andofthewayinwhichtheso-called‘logicalconstants’(whicharenormallyexpres-sedby‘onlyif’,‘not’,‘and’,‘or’,andsoon)functioninsentences.Wittgenstein’saccountoflogicandthelogicalconstantswillbeexplainedinChapter5.Butthedescriptionoftheformofrealityaslogicalformhasafurtherpoint.Logicisthestudyofvalidity.Validityisthepropertyanargumenthaswhenitsconclusionreallyfollowsfromitspremises.Andthepremisesandconclusionsofargumentsarethingsthatcanbeexpressedinsentences.Ifformisconcernedwithpossibilitiesofarrangement,logicalformmustbeconcernedwithpossibilitiesofarrangement\n140THEGENERALTHEORYOFREPRESENTATIONwithinandbetweensentences.Thatistosay,theidentiﬁcationoftheformofrealityaslogicalformisalreadytheidentiﬁ-cationoftheformofrealityastheformofwhatcanbeexpressedorrepresentedinsentences.Ineffect,tosaythattheformofrealityislogicalformistosaythatthereisnothinginrea-litywhichisnotdescribable,inthewordsofsomelanguage.ThestageisthussetfortheapplicationofWittgenstein’sgeneraltheoryofrepresentationtotheapparentlyspecialcaseoflanguage,throughthesuggestionthatlanguageisnotsomuchaspecialcaseasthegeneralcase.Buttheactualapplicationisindirect:3Thelogicalpictureofthefactsisthethought.WittgensteinishereclearlydistancinghimselffromFrege’sconceptionofthought.ForFrege,aswehaveseen,athoughtiswhatsomeonethinks:itistheobjectofthinking,some-thinggraspedinthinking.Onhisaccountofmeaning,itisthe‘sense’ofasentence(inhistechnicalsenseof‘sense’).ForWittgenstein,ontheotherhand,athoughtisarepre-sentation,anarrangementofpictorialelementswhicharecorrelatedwithitemsintheworld.Itisnotanobjectofthinking,somethinggraspedinthinking,butsomethingproducedinthinking.Wittgensteinappliesthepointintheverynextremark,whichOgdentranslatesasfollows:3.001‘Anatomicfactisthinkable’—means:wecanimagineit.ThisisararecasewheretheOgdentranslationprefersthecolloquialtotheliteral,withsomelossofsigniﬁcance.25Amoreliteraltranslation,followingOgden’sownexamplefromtheparallelsection2.1,wouldreadasfollows:‘Anatomicfactisthinkable’means:wecanmaketoourselvesapictureofit.Thepointseemstobethis.Everythingwhichcanberepre-sentedatallcanberepresentedinapicturewemaketo\nTHEGENERALTHEORYOFREPRESENTATION141ourselves:andapicturewhichwemaketoourselvesiswhatWittgensteincallsathought.3.001hasastrikingconsequence,givenWittgenstein’sgeneralconceptionofrepresentationasmodelling:Whatisthinkableisalsopossible.(3.02)Ifwecanthinkthatsomethingisthecase,wecanformapictureormodelwhichrepresentsthatitisthecase.Butapictureormodelcanonlyrepresentthatsomethingisthecaseinvirtueofhavingitselementsarrangedinawayinwhichthecorrespondingitemsinrealitycouldbearranged.Butiftheitemsinrealitycouldbearrangedlikethat,thenwhatthepictureormodelrepresentsasactuallybeingthecasemustatleastbepossible;whichiswhatWittgensteinclaimsat3.02.Thismeansthatwecannotrepresentanimpossiblestateofaffairs,awaythingsinrealitycouldnotbearranged.Wecannotevendothatinordertosaythatthingscouldnotbearrangedlikethat.Itseems,then,thatwecannottrulysay:(5)Itisimpossiblethatp.Forif(5)istrue,the‘p’herewillhavetorepresentanimpossiblestateofaffairs.26Andthatmakesitlookasifitwillbeequallyimpossibleforustosaytruly:(6)Itisimpossiblethatnot-p.Butthislatterisequivalentto‘Itisnecessarythatp’.Thatmeansthatwecansaytrulyneitherthatitisimpossiblethatp,northatitisnecessarythatp.Ifwecansaytrulyneitherthatitimpossiblethatp,northatitisnecessarythatp,wemightwonderwhetherwecouldtrulysayeventhis:(7)Itispossiblethatp.\n142THEGENERALTHEORYOFREPRESENTATIONAfterall,thereisasenseinwhichwecannotberulingoutanythingsubstantiveinsayingthat:thereisnosubstantive—imaginable,picturable,modellable—alternativewhichwearerulingoutwhenwesaythatitispossiblethatp.Andifwearerulingoutnothingsubstantive,itmaybehardtoseehowwecanbeassertinganythinginusing(7).Wittgensteindoes,indeed,seemtohavethoughtthatwecannottrulysaythatsomestateofaffairsisevenpossible.TheissuewillbediscussedinsomedetailinChapter6.Butinordertoseewhyhethinksthis,weﬁrstneedtoseehowhisgeneraltheoryofrepresentationisappliedtolanguage;andthatisthetopicofthenextchapter.\n4SENTENCESASMODELS4APRELIMINARYEXPOSITIONTheTractatus’stheoryoflanguageisatbasetheapplicationtolanguageofthegeneraltheoryofrepresentationwhichwasexaminedinChapter3—thetheorythatrepresenta-tionsrepresentinthesamewayasthePariscourtroommodel.Accordingly,thebasicclaimofthetheoryoflanguageoftheTractatusiswhatisstatedat4.01:Thepropositionisapictureofreality.Thepropositionisamodeloftherealityaswethinkitis.But‘propositions’areﬁrstmentionedat3.1:whathasbeengoingoninthesectionsfrom3.1to4.0031?Veryroughly,theseinterveningsectionsdotwothings:theyjustifytheveryideathatpropositionsmightbemodelsofreality;andtheydevelopthatideainsuchawayastojustifythemeta-physicsofthe1sandearly2s(themetaphysicswhichwasoutlinedinChapter1).Thesectionswhichfollow4.03ela-boratesomeoftheconsequencesforphilosophyoftheclaim\n144SENTENCESASMODELSthatpropositionsaremodels,andintroducethetheoryoflogic.(IwillbeconsideringthetheoryoflogicinChapter5,andtheaccountofphilosophyinChapter7.)Languageisintroducedwiththisremark:3.1Inthepropositionthethoughtisexpressedperceptiblythroughthesenses.ThepointisalittleclearerinthePearsandMcGuinnessversion:Inapropositionathoughtfindsanexpressionthatcanbeperceivedbythesenses.Thisremarkraisestwoquestionsimmediately.First,whatisa‘proposition’?ThewordisatranslationoftheGerman‘Satz’.Itisnotentirelyclearhowweshouldunderstandit,however.Itismostnaturallyunderstoodasbeingusedtorefertoasentence—or,rather,aparticularkindofsen-tence:adeclarativesentence,onewhichisgrammaticallysuitedtosaysomethingtrueorfalse.ButeventosaythataSatzisadeclarativesentencedoesnotsettlemattersﬁnally:afterall,whatisasentence?Wittgensteinseemsmostlytousetheword‘Satz’torefertoasentencewithameaning(asin3.12),butthereareplaceswherehecannotmeanthat(6.54,forexample).ThisisapointwhichIwillreturnto(insection4Cbelow):forthemoment,itisenoughjusttobeawareoftheissue.Theotherquestionraisedimmediatelyby3.1isexactlywhatclaimWittgensteinmeanstobemakinghere.Hemightbetakentobemakingeitherorbothofthefollowingclaims:(i)Everysentenceisanexpressionofathought;(ii)Everythoughtisexpressed(i.e.,expressible)inasentence.IsuggestthatWittgensteinisactuallyconcernedtoassertboth(i)and(ii).Itis(ii)whichiscrucialtothesequenceofthoughtofthefollowingremarks:\nSENTENCESASMODELS1453Thelogicalpictureofthefactsisthethought.3.1Inthepropositionthethoughtisexpressedperceptiblythroughthesenses.3.2Inpropositionsthoughtscanbesoexpressedthattotheobjectsofthethoughtscorrespondtheelementsofthepropositionalsign.Itisonlyif3.1includestheassertionof(ii)thatwehaveanyreasontothinkthateverythoughtcanbeexpressedinanotationwhichrevealsitstrueform(whichiswhat3.2claims).Ontheotherhand,itisonlyif3.1includestheassertionof(i),thattheTractatus’sgeneraltheoryofrepresentationcanbeappliedtolanguageingeneral,andhence,inparticular,toattemptstosaysomethingphi-losophical(whosesigniﬁcancewillbeclearinChapter7below).Tobeginwith,IwillpresentjustanoutlineofWittgenstein’sapplicationtosentencesofhisgeneraltheoryofrepresenta-tion.Butthereisonethingtobeclearaboutfromthestart:theapplicationismeanttobecompletelyliteral.Wittgensteinisnotclaimingthatsentencesaresomehowlikepicturesormodels;norishisclaimthatsentencesarepic-turesmetaphorical.Hisclaimisthattheanalysisofmodelswhichheprovidesinthe2.1sand2.2sappliescompletelystraightforwardlyandliterallytosentences—or,atleast,tocertainbasicsentences.Sentencesjustaremodels,strictlyandliterally.Recallthecorecommitmentsofthegeneraltheoryofrepresentation:(M1)Amodelhascomponentswhichcouldhavebeenarrangedotherwise,andrealsituationsinvolveobjectswhichcouldhavebeenarrangedotherwise.(M2)Thecomponentsofamodelcanbecorrelatedwithobjectsinreality.(M3)Therangeofwaysinwhichthecomponentsofamodelcouldhavebeenarrangedisthesameastherangeofwaysinwhichthecorrelatedobjectsinrealitycouldhavebeenarranged.\n146SENTENCESASMODELSIfsentencesaretobepicturesormodels,itfollowsfrom(M1)and(M2)thattheymusthaveelements;accordingly,Wittgensteinsays:Thepropositionisapictureofitsstateofaffairs,onlyinsofarasitislogicallyarticulated.(4.032)And,giventhis,(M3)requiresthis:14.04Inthepropositiontheremustbeexactlyasmanythingsdis-tinguishableasthereareinthestateofaffairs,whichitrepresents.Theymustbothpossessthesamelogical(mathematical)multiplicity(cf.Hertz’sMechanics,onDynamicModels).2Afterall,differentnumbersofcomponentscannothavepreciselythesamepossibilitiesofcombination.Butasentenceisnotjustamixtureofthewordswhichareitspictorialelements.Inaformulationwhichechoes2.14,Wittgensteinsays:Thepropositionalsignconsistsinthefactthatitselements,thewords,arecombinedinitinadefiniteway.(3.14)Thatis,justaspicturesormodelsingeneralarefacts(2.141),soaresentences:Thepropositionalsignisafact.(3.14)AsWittgensteinrecognizes,wedonotreadilythinkofsen-tencesasfacts:instead,weareinclinedtothinkofthemascomplexobjects.Itakeitthatthisisoneofthekey‘mis-understanding[s]ofthelogicofourlanguage’whichlieattheheartoftheproblemsofphilosophy,accordingtothePreface(TLP,p.27).3ButWittgensteinthinksthatthetrue\nSENTENCESASMODELS147natureofsentencesbecomesclearerifweimaginethemhavingsomethingotherthanawrittenform:3.1431Theessentialnatureofthepropositionalsignbecomesveryclearwhenweimagineitmadeupofspatialobjects(suchastables,chairs,books)insteadofwrittensigns.Themutualspatialpositionofthesethingsthenexpressesthesenseoftheproposition.Hereweseeasentencetakingontheexplicitappearanceofamodel,likethePariscourtroommodel.Andlateronheusesexactlythelanguageheusedwhenheﬁrst(inNB7)referredtothecourtroommodel:Inthepropositionastateofaffairsis,asitwere,puttogetherforthesakeofexperiment.(4.031)Ofcourse,ifweinsistthatsentencesarefacts,andnotcomplexobjects,thatmakesadifferencetohowwecantalkaboutthem.Thatispartofthepointofthefollowingremark:3.1432Wemustnotsay,‘Thecomplexsign“aRb”says“astandsinrelationRtob”’;butwemustsay,‘That“a”standsinacertainrelationto“b”saysthataRb’.(Thoughthisremarkisimportantinotherways,towhichIwillreturninsection4F.)Infact,ifsentencesarefacts,andnotcomplexobjects,therewillbesomedifﬁcultyintalkingaboutthematall:Statesofaffairscanbedescribedbutnotnamed.(3.144)Thislastpointisofcrucialimportanceinthegeneralmoti-vationforthetheorythatsentencesarepicturesormodels.Wittgensteinheremakesaradicaldistinctionbetweenthe\n148SENTENCESASMODELSrelationwhichholdsbetweenanameandtheobjectforwhichitstands,ontheonehand,andtherelationbetweenasentenceandthefactwhichobtainsifthesentenceistrue,ontheother.Asentenceisnotanykindofname:tosupposethatitiswouldbetotreatsentences—which,likeallpic-turesormodels,arefacts—ascomplexobjects.Thatdif-ferenceisreﬂectedinmanywaysinlanguage,butamongthemostimportantisthis.Itisafundamentalfactaboutlanguagethateverylanguagecontainsanindeﬁnitenumberofsentenceswhichanycompetentspeakerofthatlanguagecanunderstandwithouthavingpreviouslyencounteredthem.Wittgensteinseemstohavetakenthisfundamentalfacttoprovethatsentencesarepicturesormodels:4.02This[i.e.,thatthepropositionisapictureofreality:4.01]weseefromthefactthatweunderstandthesenseofthepropositionalsign,withouthavinghaditexplainedtous.Wittgensteincertainlyhasacasehere,thoughIthinkheisoverstatingit.Whatiscorrectisthatthetheorythatsen-tencesarepicturesormodelscanexplainhowitispossibleforsomeonetounderstandasentencewhichshehasnotpreviouslyencountered,withouthavinghaditexplainedtoher.Thereasonisthis.Aswesawinthelastchapter,amodel’sbeingthemodelitiscannot,accordingtoWittgenstein,dependonitsbeingcorrect.Ifsentencesarepicturesormodelsinthesameway,thenthemeaningfulnessofasen-tence—or,atleast,ofasentencewhichisarepresentation—mustbeindependentofwhetheritistrue.Wittgensteinholdsthefollowingviewofwhatitistounderstandasentence:Tounderstandapropositionmeanstoknowwhatisthecase,ifitistrue.(4.024)Andheconcludes,correctly:Onecanthereforeunderstanditwithoutknowingwhetheritistrueornot.(4.024)\nSENTENCESASMODELS149Wecanhavethisunderstandingbecausethefollowingistrue:Oneunderstands[theproposition]ifoneunderstandsitsconstituentparts.(4.024)Thisfallsdirectlyoutoftheclaimthatsentencesarepicturesormodels,onthegeneralconceptionofrepresentationwhichweconsideredinthepreviouschapter.Foronthatconcep-tion,sentencesarenotmeaningfulbecauseofanycorrelationbetweenthesentencesthemselvesandanyfactsintheworld:ifwearenottofollowtheearlyRusselldownthepathtoobjectivefalsehoods(falsefacts),thatwouldmakethemeaningfulnessofasentence—itsbeingtherepresentationitis—dependonitsbeingtrue(seeChapter2,section2D).Instead,sentences,likeallpicturesormodels,aremeaningfulinvirtueoftheirelementsbeingcorrelatedwithitemsintheworld.Consequently,alloneneedsinordertounderstandthemeaningfulnessofasentenceistoknowwhichitemsinrealityitselementsarecorrelatedwith.ThewayinwhichIthinkWittgensteinoverstateshiscasein4.02amountstothis.Whatheoffersisaplausible—onemightthinkcompelling—caseforthinkingthattheviewthatsentencesarepicturesormodelsprovidesagood(per-hapseventhebest)explanationofthefactthatwecanunderstandsentenceswehavenotencountered.Buteventhatfallsshortofprovingthatsentencesaremodels,givenjustthefactthatwecanunderstandsentenceswehavenotcomeacrossbefore,whichiswhat4.02seemstoclaim.Ingeneral,inferencestothebestexplanationmakeitrationaltobelievesomething:theydonotprovethatthingtobetrue.Theimportantﬁnalpointoftheapplicationtosentencesofthegeneralaccountofpicturesormodelsisthis.Sentences,likepicturesormodelsgenerally,havethefollowinglimita-tion:whateverelsetheymayrepresentordepict,theycannotrepresentordepicttheirownform.Inthegeneralaccountofrepresentation,Wittgensteinexplainsthispointintermsoftheimpossibilityofapicturestanding‘outside’\n150SENTENCESASMODELS(‘ausserhalb’)itsownform—outsidethepossibilityofitscomponentsbeingarrangedinthewaytheyare(2.173,2.174).Thatspatialmetaphorisre-usedinthetheoryofsentencesinconnectionwiththemathematicalmultiplicitywhichmodelandrealitymustshare:4.041Thismathematicalmultiplicitynaturallycannotinitsturnbedepicted.Onecannotgetoutside[‘heraus’]itinthedepiction.4Anditreturnsin4.12,inaclearechoof2.172–2.174:Propositionscanrepresentthewholereality,buttheycannotrepre-sentwhattheymusthaveincommonwithrealityinordertobeabletorepresentit—thelogicalform.Tobeabletorepresentthelogicalform,weshouldhavetobeabletoputourselveswiththepropositionsoutside[‘ausserhalb’]logic,thatisoutsidetheworld.5Wesawearlierthatacertainnotionof‘showingforth’or‘displaying’isusedinconnectionwithforminthegeneralcaseofrepresentations:2.172Thepicture,however,cannotdepictitsformofdepiction;itshowsitforth[‘weistsieauf’].Asimilarnotionisnowusedinconnectionwiththesenseofasentence:4.022Thepropositionshows[‘zeigt’]itssense.Thepropositionshows[‘zeigt’]howthingsstand,ifitistrue.Anditsays,thattheydosostand.Anditisusedquiteexplicitlyinremarksaboutformwhicharepreciselyparalleltothosemadeinthegeneraltheoryofrepresentation:Propositionscannotrepresentthelogicalform:thismirrorsitselfinlanguage.\nSENTENCESASMODELS151Thepropositionsshow[‘zeigt’]thelogicalformofreality.Theyshowitforth[‘weistsieauf’].6(4.121)Anevenmoredramaticconclusion,however,isdrawnherethanwasdrawnexplicitlyforthegeneralcaseofrepresentations:4.1212Whatcanbeshowncannotbesaid.Thisismoredramatic,becauseoftheimplicitclaimitmakesabouttheformofeachsentence.Whatthegeneraltheoryofrepresentationtellsusisthatnorepresentationcanrepresentitsownform;butthatseemstoleaveitopenfortheformofonerepresentationtoberepresentedbyanotherrepresenta-tion.Accordingly,wemightthinkthat,althoughnosentencecouldrepresentitsownform—stateitsownsense—itmightbepossiblefortheformofonesentencetoberepre-sentedbyanother.Butthispossibilityiswhatisexplicitlyruledoutby4.1212:nosentencecanstatetheformofanysentence.Thisclaimisonlylegitimateifeverysentencehasthesameform.Wewillconsiderwhatthatmeansinalittlemoredepthinsection4Ebelow,andagainwhenweconsiderthetheoryoflogicinChapter5.Wethereforeseeherethegeneraltheoryofrepresentationappliedexplicitly,literally,andincarefuldetailtothecaseofsentences.Sentences,likepicturesormodelsgenerally,representinvirtueofhavingelementswhichcanbecorre-latedwithitemsinreality,andinvirtueofthoseelementshavingthesamerangesofpossiblecombinationasthecor-respondingelementsofreality—thatistosay,thesameformasreality.Butthisbringswithitanecessarylimitation,withsentencesaswithpicturesormodelsingeneral:nosentencecanrepresentordepictitsownform.SomuchfortheoutlineofWittgenstein’saccountofsentencesasmodelsofreality.Nowweneedtolookatitinabitmoredetail,inordertounderstandhowitanswerstheproblemsaboutlan-guagewhichWittgensteininheritedfromFregeandRussell,andhowitgeneratesthemetaphysicsofthe1sand2.1s.\n152SENTENCESASMODELS4BSAMENESSOFFORMANDRULESOFTRANSLATIONThecentralclaimoftheTractatus’sviewoflanguageisthatsentenceshavethesameformastherealitytheydepict.Aswehaveseen,thisclaimaboutformisreallyjustaclaimaboutpossibilitiesofarrangement.Thecrucialclaimofsamenessofforminthecaseofsentencesisthisvariantofthegeneralclaimaboutmodels,(M3):(SM3)Therangeofwaysinwhichthecomponentsofasentencecouldhavebeenarrangedisthesameastherangeofwaysinwhichthecorrelatedobjectsinrealitycouldhavebeenarranged.Thismaystrikeusasastrangeclaim:ifweconsiderthearrangementofwordsinasentence,ontheonehand,andthearrangement(forexample)offurnitureinaroom,ontheother,itmightseemtousthatthereisnosimilarityatallinthepossibilitieswhichareavailable.Wittgensteinclearlyfeltthistoo:4.011Atthefirstglancetheproposition—sayasitstandsprintedonpaper—doesnotseemtobeapictureoftherealityofwhichittreats.Butnordoesthemusicalscoreappearatfirstsighttobeapictureofmusicalpiece;nordoesourphoneticspelling(let-ters)seemtobeapictureofourspokenlanguage.Andyetthesesymbolismsprovetobepictures—evenintheordinarysenseoftheword—ofwhattheyrepresent.7AndyetinsomecasesWittgensteinthoughtthat(SM3)wasobvious:4.012ItisobviousthatweperceiveapropositionoftheformaRbasapicture.Herethesignisobviouslyalikenessofthesignified.Thismightseemsheerbravado,butinmanycasesofsen-tencesinvolvingtwo-placepredicates,(SM3)isindeedquiteintuitive.Considerthissentence,forexample:\nSENTENCESASMODELS153JohnhatesMary.ItishardnottothinkofthissentenceinthekindofwayWittgensteindoes:weimagineJohnontheoneside,andMaryontheother,andashootingofdaggerlooksfromonetotheotherexpressedbytheword‘hates’.ThedifﬁcultyistoseehowthepossibilitiesofarrangementofthewordsonthepagecanstrictlybethesameasthepossibilitiesofinterrelationbetweenJohnandMarywithrespecttodaggerlooks.Ithinkthesolutionisthatjustasthebaldstatement‘JohnhatesMary’doesnotcaptureeverythingabouttherelation-shipbetweenJohnandMary,evenifitistrue,sothepos-sibilitiesofarrangementofthewordsonthepagedonothavetoencompassallthepossibilitiesofinterrelationbetweenJohnandMarywithrespecttodaggerlooks—sinceevendaggerlooksarericherininformationthanthesimpleword‘hates’.WehaveallthatWittgensteinneedsfor(SM3)ifthepossibilitiesofarrangementofwordsarethesameassomeofthepossibilitiesofarrangementofthecorrespondingitemsinreality.ThatthissolutionisWittgenstein’sownissuggestedbyhisuseofthegeometricalimageofprojectiontoexplaintherelationbetweenlanguageandreality(3.11–3.13;4.0141).Inageometricalprojection(forexample,ofathree-dimensionalobjectontoatwo-dimensionalscreen),weexpectsomepropertiesoftheobjectprojectedtobelostandotherstobetransformed—aswithperspective—butsomewillbepre-served.Oftenwhatremainsinvariantwillbeextremelyabstract.Wittgenstein’sthoughtseemstobethatifweﬁndourselvesthinkingthatthereisnosimilarityofformbetweenarepresentationandwhatitdepicts,wearesimplylookingfortoowholesaleandtooconcreteasimilarity.Wittgenstein’sviewoftheissuesisexpressedinthisreactiontocaseswheretherelevantsimilarityisnotobvious.4.0141Inthefactthatthereisageneralrulebywhichthemusicianisabletoreadthesymphonyoutofthescore,andthatthereisarulebywhichonecouldreconstructthesymphonyfromthe\n154SENTENCESASMODELSlineonagramophonerecordandfromthisagain—bymeansofthefirstrule—constructthescore,hereinliestheinternalsimilaritybetweenthesethingswhichatfirstsightseemtobeentirelydifferent.Andtheruleisthelawofprojectionwhichprojectsthesymphonyintothelanguageofthemusicalscore.Itistheruleoftranslationofthislanguageintothelanguageofthegramophonerecord.Theclaimbeingmadehereisastrongone:itisnotthattheexistenceofacertainkindofruleoftranslationisevidenceofsamenessofform;northattheexistenceofsucharulesomehowexpressesanunderlyingsamenessofform.Theclaimisthatsamenessofformbetweenamodelandrealityisnothingbuttherebeingaruleoftranslationbetweenthetwo.Thisis,ineffect,amaximallyabstractconceptionofsimilarity.Atranslationofatextfromonelanguagetoanotherproducessomethingwhichisinacertainwayequivalentinthesecondlanguagetowhattheoriginaltextwasintheﬁrst.Suchanotionofequivalenceiswhatthedemandofsamenessofformeventuallyamountsto:asen-tencehasthesameformaswhatitdepictsifitis,inthelanguage,equivalenttoitinacertainrespect;whichistosaythatwhatisdepictedcanberecoveredfromit,asthesymphonycanberecoveredfromthescore.Theimportantthingaboutthenotionoftranslationinplayhereisthatitdoesnotinvolvepiecemealtranslation,ofasingletextorsentenceofonelanguageintoanotherlanguage:itistheideaofonewholelanguagebeingtranslatedintoanother:Thetranslationofonelanguageintoanotherisnotaprocessoftranslatingeachpropositionoftheoneintoapropositionoftheother,butonlytheconstituentpartsofthepropositionaretranslated.(4.025)Onthisconception,theconstituentpartsarecorrelatedwitheachother,justastheconstituentsofsentencesingeneralarecorrelatedwiththeconstituentsoffactsinreality.Itisbecausethenotionoftranslationinvolvedhereisfundamentally\nSENTENCESASMODELS155concernedwiththetranslationofconstituentsofproposi-tionsthatitisplausibletosaythatsamenessofformessen-tiallyconsistsinthepresenceofaruleoftranslation:samenessofformissamenessofpossibilitiesofcombination,andthatrequiresacertainequivalenceamongconstituents.Furthermore,thenotionoftranslationalsoprovidesaplausibleelaborationofthemetaphorofsamenessofform.‘Form’literallymeansshape:tosaythatlanguagehasthesameformastheworldistosaythatlanguagehasthesameshapeastheworld.Thisisevidentlyametaphoricalclaim:howwouldwenaturallyunderstandit?Whatmightitbeforsentencestohavetheshapeoftheworld?Hereisanaturalthought:forsentencesinalanguagetohavethesameshapeastheworldisforittobepossibleforsomeone,whowasacquaintedwiththeworldbutdidnotyetunderstandthelanguage,tocometounderstandthelanguagesimplyonthebasisofanexperienceoftheworldwhichisavailablewith-outunderstandingthelanguage,togetherwiththeuseofreason—atleast,insofarasthelanguageisintelligibleatall.Thismakessenseoftheideaofamappingoftheworldbyalanguage:suchamappingpresupposesthattheworldisintelligibleindependentlyofthelanguageinquestion,inso-farasitisintelligibleatall,andthatthelanguageisthenintelligible(insofarasitisintelligibleatall)justonthebasisofunderstandingthemappingrelation.8Thisconceptionoftherelationbetweenlanguageandtheworldismostnaturallyunderstoodinarealistway.RecallthatIformulatedrealismastheacceptanceofthisclaim:(R)Thenatureoftheworldasitisinitselfisaltogetherindependentofanythingtodowithanythoughtorrepresentationofit.Anysubstantialdenialofthatclaimcountsasaformofidealism.Thenatural,realistwayofreadingtherule-of-translationconceptionofsamenessofformseemstobefoundinWittgensteinhimself.Thusinnotestakenoflectureswhichhegavein1930,soonafterhisreturntophilosophy,weﬁndtheseremarks:9\n156SENTENCESASMODELSButgrammarisnotentirelyamatterofarbitrarychoice.Itmustenableustoexpressthemultiplicityoffacts,giveusthesamedegreeoffreedomasdothefacts.(WLC8)Grammarisamirrorofreality.(WLC9)Theﬁrstoftheseremarkssuggeststhatobjectivepossibilityconstrainsgrammar,whichsuggeststhatobjectivepossibi-lityisindependentofgrammar;thisalsoissuggestedbythe‘mirror’image.Ofcourse,theseremarksareratherlaterthantheTractatusitself,andWittgensteinmightbythistimehaveforgottensomeofthephilosophywhichoriginallymoti-vatedhim.Butinanycase,althoughtheyarenaturallyunderstoodinarealistway,theycanbemadecompatiblewithaformofidealism.Thekeyistonotethatinmyela-borationoftherule-of-translationconceptionofsamenessofform,itbecamenaturaltotalkabout‘alanguage’—ratherthanjustlanguage.Whenwetalkabouttranslation,wehaveinmindtranslationbetweenonelanguageandanother,andnotsometranslationbetweenlanguageingeneralandtheworldasitisinitself,takenneat.10Oncewetakeproperaccountofthis,anon-realistunderstandingoftherule-of-translationconceptionofsamenessofformbecomesavailable—and,indeed,naturalasaninterpreta-tionoftheTractatus.Supposethatsomeoneisabletothinkabouttheworld.OntheaccountofthoughtwhichispresentedintheTractatus,thismeansthatsheisabletoformforherselfpicturesormodelsoftheworld.Someonecouldbeinthispositionwithoutyethavingtheabilitytospeakaparticularlan-guage(EnglishorGerman,say),ortouseacertainnota-tion.Butherabilitytoformpicturesormodelsforherselfcanitselfbecountedasknowledgeofakindoflanguage.NotewhatWittgensteinsaysinresponsetoaquestionfromRussell:\nSENTENCESASMODELS157DoesaGedanke[thought]consistofwords?No!Butofpsychicalconstituentsthathavethesamesortofrelationtorealityaswords.(CL125)Oursubject’spositionis,then,thatshecanoperatewithakindoflanguage—whichuseswhatwemaycallthesymbolsofthought—whilenotyetbeingabletouseanyfamiliar,everydaylanguageornotation.Nowsupposethatweunderstandtherelationbetweenthisthought-languageandtheworldinanidealistway.Thatis,weimagineoursubjectasprojectingthestructureofherthought-languageontotheworld,sothatitsgrammarisvisibleinthenatureoftheobjectswhicharereﬂectedback,asitwere,toher.(Forthisidea,recallthediscussionofrea-lismandidealisminChapter2,section2F,above.)Theworldwhichisapropercorrelateofherthought-languageisnowunderstoodtobedependent,inpart,onthewayinwhichitisrepresentedinherthought-language.Ofcourse,oursub-jectnowhasakindofaccesstotheworldwhichisindepen-dentofunderstandinganyfamiliarlanguage(suchasEnglishorGerman),oranyfamiliarnotation.Theconceptionoflanguagewhichisenshrinedintherule-of-translationunderstandingofsamenessofform(whichunderlies4.0141)sayssimplythatthereissomekindofruleoftranslationwhichcantakesomeonefromthisthought-languageaccesstotheworldintounderstandinganyfamiliarlanguageornotation.Andwecanreadtheremarksfrom1930inthesameway:grammarwillpresentitselfas‘notentirelyamatterofarbitrarychoice’tosomeonewhoalreadyhassomeconceptionoftheworld—theconceptionprovidedbyherownthought-language.Eventheseremarksdonotrequirearealistreading.Whatthismeansisthateventherule-of-translationcon-ceptionofsamenessofform,whichseemsatﬁrstsighttorequiresomeformofrealism,isinfactcompatiblewithanidealistviewofthefundamentalrelationbetweenlanguageorrepresentation,ontheonehand,andtheworld,ontheother.\n158SENTENCESASMODELS4CSAMENESSOFFORM,SENSE,ANDNONSENSEForalltheabstractnessoftheconceptionofsamenessofformwhichWittgensteinembraces,thereisafurtherreasonwhyitmightseemthattheworldcouldnothavethesameformaslanguage.Formisamatterofpossibilitiesofcom-bination,onWittgenstein’sview.Butitmightseemthatthenotionofcombinationwhichappliesinthecaseoflanguagewasquitedifferentfromtheonewhichappliesinthecaseoftheworld.Inthecaseoflanguage,itmightseemthatthecrucialnotionwearereallyinterestedinisessentiallynor-mative:weareconcernedwithgrammaticalcombinations,combinationswhicharelegitimate,whichresultinawell-formedratherthananill-formedstring,whichgeneratepropersentences.Thereareotherpossiblecombinations,weareinclinedtothink—combinationswhichareillegitimateorungrammatical,whichdonotresultinpropersentences.Inthecaseoftheworld,ontheotherhand,thereisnosuchnormativityinvolvedinthenotionofcombinationofelements:thereisnocontrastbetweenlegitimateandillegitimatecombinations—therearejustthepossiblecombinations.How,then,canwesaythatthepossibilitiesofcombinationinlanguagearethesameasthepossibilitiesofcombinationinreality,withoutinvolvingourselvesinanuglyequivocationoverthenotionofpossibilityofcombination?Wittgensteinsolvesthisproblembysimplyblockinganydistinctionbetweennormativeandnon-normativeconceptionsofpossiblecombinationinthecaseoflanguage:5.4733Fregesays:Everylegitimatelyconstructedpropositionmusthaveasense;andIsay:Everypossiblepropositionislegiti-matelyconstructed,andifithasnosensethiscanonlybebecausewehavegivennomeaningtosomeofitsconstituentparts.(Evenifwebelievethatwehavedoneso.)Thus‘Socratesisidentical’saysnothing,becausewehavegivennomeaningtotheword‘identical’asadjective.Forwhen\nSENTENCESASMODELS159itoccursasthesignofequalityitsymbolizesinanentirelydif-ferentway—thesymbolizingrelationisanother—thereforethesymbolisinthetwocasesentirelydifferent;thetwosymbolshavethesignincommonwithoneanotheronlybyaccident.WewillreturntothecontrastwithFregeinthenextsection.ThepointwhichWittgensteinismakingin5.4733turnsonacontrastbetweensignsandsymbols.Thenotionofasymbolisintroduced,alongwiththatofanexpression,inthisremark:EverypartofapropositionwhichcharacterizesitssenseIcallanexpression(asymbol).(3.31)Butthisisstillquiteobscure,becauseitisnotobviouswhat‘characterizes’meanshere.Ourbestbetistolookmorepar-ticularlyatthemeaningof‘proposition’,andatWittgenstein’sconceptionofsense.Thenotionofsense—inrelationtopicturesingeneral—isintroducedinthefollowingremark:2.221Whatapicturerepresentsisitssense.Understandingthisremarkdependsonrecallingthecontrastbetweentheterms‘represent’(‘darstellen’)and‘depict’(‘abbilden’),astheyaregenerallyusedbyWittgenstein.11Whatisdepictedisreality—nothinglessthanwhatisactuallythecase.Whatisrepresented,ontheotherhand(asWittgensteingenerallyusestheterm),isawayrealitymightbe.Considerthesentence‘JohnhatesMary’,andsupposethat,infact,JohndoesnothateMary.Theactualfact,therealstateofrelationsbetweenJohnandMary,isdepictedbythesentence;butwhatthesentencerepresentsisjustthatJohnhatesMary;andthis—thatJohnhatesMary—iswhatWittgensteincountsasthesenseofthesentence.ThisuseofthenotionofsenseisquitedifferentfromFrege’s.12OnFrege’sview,everymeaningfullinguisticexpressionhasasense(asheusestheterm):thesenseofan\n160SENTENCESASMODELSexpressionisjustamatterofthewayinwhichthereferent—theentitywhosecorrelationwiththeexpressionmakesitmeaningful—ispresented.OnWittgenstein’suse,bycon-trast,onlywholesentencescanhavesense,andthesenseofasentenceisjustthepossiblefactwhichitrepresents.WittgensteinhasnousefortheFregeanideaofsenseasanextradimensionofmeaning—alayerofcognitivesigniﬁcanceoverandaboveanexpression’sreference.Wittgenstein’scontrastbetweensenseandreferenceisnotbetweendiffer-entdimensionsofmeaningwhichthesameexpressionmighthave:ratheritisbetweenthedifferentkindsofmeaningwhichdifferentkindsofexpressionmayhave.Nameshavereference,butsentenceshavesense.13Thepointofchoosingdifferentwordsistoemphasizetheradicaldif-ferenceinkindbetweennamesandsentences,adifferencewhichFrege’stheoryobscures.Withthisinmind,wecangoontoconsiderthewayinwhichWittgensteincharacterizespropositions:3.11Weusethesensiblyperceptiblesign(soundorwrittensign,etc.)ofthepropositionasaprojectionofthepossiblestateofaffairs.Themethodofprojectionisthethinkingofthesense3.12ThesignthroughwhichweexpressthethoughtIcallthepropo-sitionalsign.Andthepropositionisthepropositionalsigninitsprojectiverelationtotheworld.3.13Tothepropositionbelongseverythingwhichbelongstothepro-jection;butnotwhatisprojected.Thereforethepossibilityofwhatisprojectedbutnotthisitself.Intheproposition,therefore,itssenseisnotcontained,butthepossibilityofexpressingit.(“Thecontentoftheproposition”meansthecontentofthesig-nificantproposition.)Inthepropositiontheformofitssenseiscontained,butnotitscontent.Theseremarksarenotwithoutinternaltension,butthemainthoughtseemstobethis.Themeresoundsorwrittenmarks(thesigns,onWittgenstein’saccount)donot\nSENTENCESASMODELS161themselvesdeterminegrammar—whatwethinkof,ante-cedently,asthelegitimateorderingofwords.Thatistosay,themeresignsdonotdeterminetherangeofwaysinwhichgrammaticalcombinationscanbemade.Butitisonlyoncetherangeofgrammaticalcombinationsisﬁxedthatwecaneventhinkofsettingupcorrelationswiththeworld.Thepropositioniswhatwehavewhenwehaveastringofsignswiththerangeofpossiblegrammaticalcombinationsﬁxed.Itis,therefore,onlytheconstituentsofaproposition—ratherthanamerepropositionalsign—whichcanbecor-relatedwithitemsinreality.Ineffect,apropositionisacertainkindofsignwiththesyntaxﬁxed.Contrarytosomemodernuses,14syntaxbringsinmorethanwhatwearegivenwiththemeresigns:wecanhavetwoexamplesofthesamesign,whichhavedifferentsyntax;syntaxprovidesuswiththerangeofcombinations.Asymbolisapartofapropositioninthissense:itisasignwhichhasasyntax.Justasapropositionalsignis‘sen-siblyperceptible’(3.11),so‘Asignisthepartofthesymbolperceptiblebythesenses’(3.32).Andjustassigns,ingen-eral,arenotenoughforsyntax—3.321Twodifferentsymbolscanthereforehavethesign(thewrittensignorthesoundsign)incommon—theycansignifyindif-ferentways.Fortwosymbolstosignifyindifferentways(seealso3.322)isjustforthemtohavedifferentsyntax—thatis,tobedifferentsymbols.AndWittgensteinmakesitclearthatthisismorethanjusthavingdifferentmeanings:Intheproposition“Greenisgreen”—wherethefirstwordisapropernameandthelastanadjective—thesewordshavenotmerelydifferentmeaningsbuttheyaredifferentsymbols.(3.323)Butthereisstillsomeuncertaintyoverwhatthenotionofasymbolinvolves;andthesameappliestothenotionofa\n162SENTENCESASMODELSproposition.Thisisworthconsideringinalittlemoredetail,sinceithassomeimportancefortheinterpretationoftheTractatusasawhole,aswellasfor5.4733itself.Wehavealreadyseenthatthepointofintroducingthenotionofasymbolistofocusonthesyntaxofanexpression:thepointof3.323isthatthepropernameandtheadjectivedifferinsyntax,andnotjustinmeaning(notjustintheobjectsassignedtothem).Anditisnaturaltotakethisaspresupposingthattherecanbeexpressionswiththesamesyntax,butwithdifferentmeanings(justastherecanapparentlybedifferentobjectswiththesameform—see2.0233).Buttherearetwoquestionswhicharestillnotﬁnallyresolvedhere.First,couldtherebeanexpressionwhichhadasyntaxbutnomeaning—withnoobjecthavingbeenassignedtoit?(Orisitonlyingivingmeaningtoasignthatweﬁxitssyntax?)And,second,whereexactlydothenotionsofsymbolandpropositionﬁtinhere?Thatis,evenifitispossibleforsyntaxtobeﬁxedindependentlyofmeaning,isﬁxingthesyntaxenoughtogiveusasymbolorproposition,ordoweonlyhaveasymbolorpropositiononcethemeaningisgiven,aswellasthesyntax?Letusdealwiththeﬁrstquestionﬁrst.Ifasymbolisacomponentofaproposition,3.13stronglysuggeststhatthesyntaxofasymbolcanbeﬁxedwithoutgivingitameaning,withoutassigninganobjecttoit.ForWittgensteinsaystherethatthepropositioncontains‘theformofitssense,butnotitscontent’—thatis,surely,itssyntax,butnotwhatisactuallyrepresented.Andagain,thepropositionissaidtoinclude‘everythingwhichbelongstotheprojection’—thatis,thepossibilitiesofcombination,thesyntax—‘butnotwhatisprojected’—thatis,nottheparticularaspectsoftheworldwhicharedepictedinapropositionwhichhasmean-ing.Andthepointseemstobeputbeyonddoubtbythisremarkfromalittlelateron:3.33Inlogicalsyntaxthemeaningofasignoughtnevertoplayarôle;itmustadmitofbeingestablishedwithoutmentionbeingthereby\nSENTENCESASMODELS163madeofthemeaningofthesign;itoughttopresupposeonlythedescriptionoftheexpressions.3.33looksunambiguoushere.ItseemsclearlytopresenttheofﬁcialviewoftheTractatusonourﬁrstquestion—thequestionwhethersyntaxcanbeﬁxedwithoutﬁxingmean-ing.15Inprinciple—andideally—syntaxcanbeﬁxedinadvanceofassigningmeaning.Thiswillbedonesimplybyﬁxingtherulesforcombiningsignswithothersignsinwholesentences—which,ofcourse,willthenmakesymbolsofthosesigns.Thereasonforthinkingthatthisistheofﬁcialviewofthebookisthatthisiswhatisrequirediftheaccountofsentencesasmodelsisstrictlytofollowtheexamplesetbythegeneralaccountofrepresentationasmodelling,forwhichthePariscourtroommodeldoesindeedprovideaclearandusefulparadigm.Thegeneralaccountofrepresentationimaginestwoparallelsystems—therepresentationalsystem,ontheonehand,andreality,ontheother—whicharebothsubjecttothesamenecessities,andwhichthereforepermitthesamepossibilitiesofarrangement.Ifthetwosystemsareparallel,eachmustbe,tosomedegree,independentoftheother.Anditisimportanttoinsistonthisliteralunderstandingoftheviewthatsentencesaremodels,becauseitmakesallthedifferencetothekindofanswerwhichtheTractatuspro-videstotheKantianquestionofhowmetaphysicsispossible.IsketchedoutwhatItakeWittgenstein’sanswertobeinsection5oftheIntroduction.IwillreturntoitinChapter5,section5E,below.Theideathatlanguageandrealitycon-stitutetwosystemswhichareparallelbutsubjecttothesamenecessitiesseemstorequirethatsyntaxbe,inprinciple,independentofcorrelationsbetweenlanguageandtheworld.Isuspectthattheprincipalreasonforresistingthisinter-pretationisthethoughtthatitinvolvesacommitmenttorealism,16asIhavedeﬁneditearlier—thatis,asacceptanceofthefollowingclaim:(R)Thenatureoftheworldasitisinitselfisaltogetherindependentofanythingtodowithanythoughtorrepresentationofit.\n164SENTENCESASMODELSAnditisreasonabletodoubtthatWittgensteinwasarealist.(ThisisanissuewhichwillbeconsideredproperlyinChapter6.)ButIhavebeeninterpretingtheconceptionofsentencesasmodelsallalongasinvolvingparallelsystemssubjecttothesamenecessities,andIhavealreadyarguedthatcommitmenttosuchaparallelismisnotenoughinitselftocommitWittgensteintorealism(seesection4B,above;aswellassection2FofChapter2).Weseemtohaveaclearanswertoourﬁrstquestion,whethersyntaxcanbeﬁxedwithoutﬁxingmeaning.Butthisstillleavesopenoursecondquestion:whetherﬁxingthesyntaxisenoughtogiveusasymboloraproposition.Onthisquestion,itlooksasiftheevidenceisnotdecisive—indeed,itiscontradictory.Aswehavealreadyseen,3.13seemsclearlytosaythatpropositionsaredeﬁnedbysyntax,independentlyofmeaning.Butthereisthisapparentlycon-tradictorystatement:3.326Inordertorecognizethesymbolinthesignwemustconsiderthesignificant[sinnvollen]use.Andthehistoryofthislaststatementmakestheappear-anceofcontradictionhereevenstarker.Thethoughtof3.326ﬁrstappearsinarelativelyearlyremarkintheNotebooks:Inordertorecognizethesigninthesignwehavetoattendtotheuse.(NB:18)TherearejusttwodifferencesbetweenthesetwoversionsintheGerman.17TheﬁrstisthatWittgensteinhasintroducedthenew,technicalnotionofsymbolbythetimeoftheTractatus.18Thesecondisthat‘sinnvollen’—senseful,sig-niﬁcant,meaningful—isinsertedtoqualify‘Gebrauch’(use).WhyshouldWittgensteinhavebotheredtoinsertthat,iftherecouldbesymbols(includingpropositions,sentences)withnomeaning?Moreover,lateronWittgensteinsays(aswehaveseen):\nSENTENCESASMODELS165Tounderstandapropositionmeanstoknowwhatisthecase,ifitistrue.(4.024)Anditishardtoseehowwecouldunderstandsomethingwhichhadnomeaning.3.326isaremarkwhosetranslationWittgensteincom-mentedexplicitlyon,inalettertoOgden.Hiscommentisnotaltogetherunambiguous,however.Hereitisinfull:Ithink‘significant’isal[l]righthere.Themeaningofthisprop[osition]is:thatinordertorecognizethesymbolinasignwemustlookathowthissignisusedsignificantlyinpropositions.I.e.,wemustobservehowthesignisusedinaccordancewiththelawsoflogicalsyntax.Thus‘significant’heremeansasmuchas‘syntacticallycorrect’.(LO:59)Wemighttakethelastsentenceheretobeassertingthatin3.326‘signiﬁcant’(‘sinnvollen’)meansjustsyntacticallycorrect.Butthisisitselfproblematic:thatisjustnotwhat‘sinnvollen’means.Thetermmeanssensefulorhavingsense,andbeing‘sinnvollen’contrastswithhavingnosense(whichistheverynotionwhichisatissuein5.4733).And,aswewillseeinamoment,itisusedin3.14tomean,precisely,senseful,meaningful.ThisactuallymakesitquitetemptingtointerpretWittgenstein’scommenttoOgdenon3.326asanattempttorewrite3.326inawaywhichmakesitmoreobviouslyconsistentwith3.14.Seeninthislight,thecommentasawholewouldlookasifitisagradualmassagingofthetextof3.326towardstheviewof3.14.But,infact,theappearanceofcontradictionbetween3.326and3.14needbenomorethananappearanceanyway.Althoughinprinciple,andideally,asymbolcanbeintro-ducedinadvanceofanyassignmentofmeaning,inpracticebothtaskswilloftenbedoneatonce,andwhatweareusuallyconfrontedwitharesymbolswhichalreadyhavesomemeaningassignedtothem.Andwecantake3.326tobeconcernedjustwiththislastkindofcase.Itiseasytobe\n166SENTENCESASMODELSmisledaboutthesyntaxofexpressionsinactualuse(3.324).Inparticular,whenthesamesign—thesametypeofmarkorsound—isused,itiseasytosupposethatwehavethesamesyntax(thisistheworryof3.323).Toavoidthat,weoughtideallytosetupanunambiguoussymbolism(3.325).Butforthewordswealreadyhave,thekeyistoattendproperlytothewaytheyareused(3.326).Inpractice,thiswillbetheonlywayofgettingclearabouttheirsyntax(hencethe‘must’in3.326).Asfor4.024,itlooksasifWittgensteinhasalreadyanticipatedthetemptationtothinkofapropositionassomethingwhichhasameaning,inthefollowingremarkwhichisaddedasaparenthesisin3.13:‘Thecontentoftheproposition’meansthecontentofthesignificant[sinnvollen]proposition.Inthecontextof3.13,whichseemsconcernedtosaythatapropositionisamerelysyntacticentity,thishastobeunderstoodassayingthat‘thecontentoftheproposition’meansthecontentofthepropositiononceameaninghasbeenassignedtoitsparts.Accordingly,IthinktheofﬁcialviewoftheTractatusisthatsymbolsingeneral,andthereforepropositions(sen-tences),inparticular,aredeﬁnedbytheirsyntax,indepen-dentlyoftheirmeaning,butlesshangsonthisanswertooursecondquestionthanhangsontheanswertoourﬁrst.Italsoseemstomethattakingsymbols—andthereforepropositions—tobedeﬁnedbytheirsyntaxmakesthemostnaturalsenseofthepassagewesetouttoaddressatthebeginningofthissection:5.4733,whereWittgensteindrawsacontrastbetweenhisownviewofnonsenseandtheoneheﬁndsinFrege.19Recallthatitisherethatheblocksthepossibilityofadistinctionbetweennormativeandnon-normativeconceptionsofthepossibilityoflinguisticcombi-nation,andtherebyallowsthepossibilitiesofcombinationinlanguagetobethesameasthepossibilitiesofcombinationinreality.Wittgensteinputshispointasfollows:\nSENTENCESASMODELS167Everypossiblepropositionislegitimatelyconstructed,andifithasnosensethiscanonlybebecausewehavegivennomeaningtosomeofitsconstituentparts.(5.4733)(WemightnotethatonceagainWittgensteinseemsexplicitlytoendorsetheviewthatsyntaxisindependentofmeaning.Whatheseemstocountenanceissomethingwhichis‘legitimatelyconstructed’—thatis,‘syntacticallycorrect’(LO:59)—whichhasnosense,becausenomeaninghasbeengiventosomeofitsparts.)Thetwodifferentconceptionsofpropositions—asbeingdeﬁnedbysyntaxalone,orashavingtheirmeaningessentially—givedifferentconstrualsoftheﬁrstclausehere.Onthemerelysyntacticconceptionofpropositions,thatclausejustsaysthis:Therecannotbeillegitimatelyconstructedpropositions.Therestoftheremarkthenallowsthattherecanbepropo-sitionswithnomeaning.Onthesyntax-plus-meaningcon-ceptionofpropositions,ontheotherhand,theﬁrstclausemeanssomethinglikethis:Nothingwhichisillegitimatelyconstructedcanbeanentityofthecategorypossibleproposition.Andtherestoftheremarkallowsmerelythattherecanbepossiblepropositionswithnomeaning(thatistosay,theyarenotactualpropositions).Theﬁrstreadingstrikesmeasmuchthemostnatural.Wittgenstein’spointin5.4733canbeexplainedasfollows,inlinewiththatﬁrstreading(itiseasyenoughtovarythisfortheotherreading).Thegeneraltheoryofpropo-sitions(sentences)asmodelsrequiresthattheelementsofanypossiblesentencemustbecapableofbeingcombinedinexactlythesamewaysasthoseinwhichthecorre-spondingelementsofrealitycanbecombined.Supposewe\n168SENTENCESASMODELSallowedthattherecanbeungrammaticalsentences—syn-tacticallyillegitimatecombinationsofsententialcomponents.Thatwouldmeanthatthepossiblewaysofcombiningsen-tentialcomponentswouldincludeboththelegitimateandtheillegitimatecombinations.Ifwearestilltomaintainthatsentencesaremodels,wewouldthereforehavetosupposethatitwasthislargerrangeofpossibilities—includingtheillegitimateaswellasthelegitimateones—whichcoincidedwiththerangeofpossiblecombinationsofobjectsintheworld.Butthatwouldmakethecapacityofsentencestobemodelsofrealityentirelyindependentoftheirsyntax:syntaxwouldnowbeirrelevanttotherepresentationalcapacityofsentences.Sentenceswouldbe,ineffect,akindofnaturalentity.Ontheotherhand,ifweallowthatsyntaxisrelevantatalltotherepresentationalcapacityofsentences,wecannotallowthepossibilityofungrammatical,syntacticallyillegiti-matesentences.Foriftherewereillegitimatesentences,theywouldhavetorepresentimpossiblecombinationsofobjects,andifweallowedthatasentencecouldrepresentanimpos-siblecombinationofobjects,wewouldbeallowingthatthecomponentsofsentencescanbecombinedinwaysinwhichthecorrespondingelementsofrealitycannotbecombined—whichcontradictsthethesisthatsentencesaremodels.Accordingly,whatwemightantecedentlyhavethoughtofasillegitimatecombinationsofsymbolscanreallybenomorethanstringsofmarksorsounds.Weonlyhaveaproposition,inthesenseof5.4733,onwhatIthinkisitsnaturalreading—somethingcapableofrepresentingtheworld,ratherthanamerestringofmarksorsounds—ifwehavesomethingwhichisasyntacticallypossiblecom-binationofsymbols:thatis,somethingwhichislegiti-matelyconstructed.Suchathing,obviously,cannotbemeaningless—nonsense—invirtueofbeingungramma-tical.Consequently,itcanonlybemeaninglessif,despiteitsbeingingoodordersyntactically,noobjectshavebeenassignedasthemeaningofsomeofitsparts.Andthatistheclaimof5.4733.\nSENTENCESASMODELS1695.4733hasalargesigniﬁcanceforanimportantaspectoftheinterpretationoftheTractatusasawhole—anissuewewillreturntoinChapter7.WeseehereWittgensteinclearlyadvocatingpartofwhathasbeencalledan‘austere’concep-tionofnonsense(Conant2000:176).The‘austere’conceptionconsistsoftwocentralclaims:20(Au1)Whatisnonsensefailstohaveanysense;itdoesnothaveanincoherentkindofsense;(Au2)Whatfailstohavesensefailstohavesensebecausemeaninghasnotbeenassignedtoitortosomepartofit.Section5.4733isanexplicitstatementof(Au2):WittgensteinherecontrastshisviewwithaviewwhichheascribestoFrege,whichwouldallowthatapropositioncouldfailtohavesensethroughbeingillegitimatelyconstructed.ItseemsclearthatthereasonwhyWittgensteinadopts(Au2)isthatthisiswhatheneedstodo,ifheistomaintainthesame-formthesis,(SM3),whichisattheheartofhisaccountoflanguage,withoutdependingonanawkwardequivocationbetweennormativeandnon-normativeconceptionsofpossi-blecombination.Andthesamesame-formthesis,(SM3),alsogeneratesacommitmenttoaformof(Au1):itrulesouttheideaofanonsensepropositionsomehowrepresentinganimpossiblestateofaffairs—aswesawattheendofChapter3.4DTHECONTEXTPRINCIPLEANDTHEGENERALFORMOFTHESENTENCETheconceptionofnonsenseexpressedin5.4733islinkedwithWittgenstein’sunderstandingofafamousprincipleofFrege’s—theContextPrinciple.ThisprincipleisenunciatedinvariouswaysinFrege’searlywork,TheFoundationsofArithmetic.Herearetwoformulations:(CP1)nevertoaskforthemeaningofawordinisolation,butonlyinthecontextofaproposition.(Frege1884:x)\n170SENTENCESASMODELS(CP2)itisonlyinthecontextofapropositionthatwordshaveanymeaning.(Frege1884:§62)ThegeneralpointofFrege’sinsistenceonthisprinciple,asheﬁrstintroducesit,istoenablehimtorejectdecisivelyanysuggestionthatmeaningmightbesomethingpsychological—thatthemeaningofwordsmightbeamatterof‘ideas’inthemindsofspeakers,forexample.TheminimalclaimoftheContextPrincipleisthatthemeaningofwordsmustalwayseitherincludeordependontheirgrammar,sothatwordswithquitedifferentsyntaxmusthavedifferentkindsofmeaning.AswesawinChapter2(section2D)thisisessen-tialifwearetoaccommodatetheunityofsentenceswithoutmakingmeaningpsychological.Ifwesupposethatthegrammarofwordsisirrelevanttotheirmeaning,theunityandcompletenesswhichisthedistinctivemarkofsentencescannotbethoughttoarisenaturallyoutofthecomponentsofsentences—ithastobeimposedonthem.Andifitisimposedonthem,theunityofsentenceshastobethepro-ductofanactofthemind;andiftheunityofsentencesisaproductofanactofthemind,itlooksasiftheunitywhichiscreatedhastobeaunityinthemind;atwhichpointitishardtoseehowmeaningcouldbenon-psychological.ButwhatexactlydoesFregeneedforthispoint?Itisarguablethatheneedsnomorethanthis:(CP)Thereisnomoretothemeaningofawordthanitscontributiontothemeaningsoflegitimatelyconstructedpropositionsinwhichitmayoccur.ThisseemstobethereadingofFregewhichWittgensteinexpressesat5.4733,and,certainly,the(CP1)formulationrequiresnomorethanthis(althoughitcanalsobereadasanexpressionofthesamethoughtasappearsin(CP2)).Itisimportanttobeclearthat,althoughthissuggests—justbyseemingtoopenaspaceforillegitimatelyconstructedpro-positions—aconceptionofnonsensewhichisatoddswith\nSENTENCESASMODELS171clause(Au2)ofthe‘austere’viewofnonsenseconsideredinthelastsection,evenonthatreadingitdoesnotleadtoanyviolationof(Au1).Afterall,itisnaturaltoascribetoFrege,aswellassomeformoftheContextPrinciple,aprinciplewhichwemightcallthePrincipleofCompositionality:(PC)Thereisnomoretothemeaningofapropositionthanisdeterminedbythemeaningofitsparts,togetherwiththeirmodeofcombination.Itwouldfollowfromthis,incombinationwith(CP),thatanillegitimatecombinationofwordswouldhavenomeaningatall—notsomekindofincoherentmeaning;itisthusentirelyinlinewithclause(Au1)ofthe‘austere’conceptionofnonsense.AlthoughaversionoftheContextPrincipleinlinewith(CP)wouldseemtobeenoughforthepurposeswhichFregeusestojustifytheprinciple’sintroduction,21itwillnotdoforWittgenstein’s.Aswehaveseen,Wittgenstein’sinsis-tenceonsamenessofform—samenessofpossibilitiesofcombination—betweenlanguageandtheworldrequireshimtoremoveanyspaceforacontrastbetweenlegitimateandillegitimatecombinationsofwords.Hehastoholdthatthereareonlylegitimatecombinations:theputativeillegiti-matecombinationsarenotreallycombinationsofthosewordsatall—theyaremerelyassemblagesofmarksorsounds.Consequently,heseemstoendorsethe(CP2)for-mulationonitsstrongest(mostliteral)interpretation:3.3Onlythepropositionhassense;onlyinthecontextofaproposi-tionhasanamemeaning.TheﬁrstclausehereexpressesWittgenstein’sdivergencefromFregeoverthenotionofsense(whichwesawearlier,insection4C):senseisthekindofmeaningwholesentenceshave—itisnotadimensionofmeaning,asitwasforFrege.ThesecondclauseexpressesthestrongversionoftheContextPrinciple.\n172SENTENCESASMODELSWhydoesWittgensteininsistonthisversion?Therea-soningmightbethis.Whathecannotallowisthattheremightbeillegitimatecombinationsofwords.Butitisplau-siblethatifwordscouldappearinisolation—notinlegit-imatepropositionalcombinations—thentheycouldappearinillegitimatecombinations.Afterall,whatisanillegitimatecombinationofwordsotherthanastringofisolatedoccurrencesofthosewords?SoitisplausibletothinkthatWittgensteinhastodenythatwordscanoccurinisolation.Thismightseemabsurd:surelywordscanoccurinisola-tion—justontheirown?Inparticular,itmightseemthatsuchisolatedusesarepresupposedbytheveryfactthatgivestheunityofthesentenceitspoint.Whatmattersaboutsentences,assuch,isthattheyaredistinctfrommerelistsofwords:theyhaveacompletenessandunitywhichamerelistdoesnot.Buttosaythatseemstopresupposethattherecanbeoccurrencesofwordswhicharenotinsentences—aswordsinalist,inparticular.Andisn’titjustobviousthatwordscanoccurinlists,andthereforenotinwholesentences?Thisisapowerfulpoint,butitlooksasifthereissome-thingwhichWittgensteincansayagainstit.HereiswhatWittgensteinsaysaboutexpressions(words,symbols):3.311Anexpressionpresupposestheformsofallpropositionsinwhichitcanoccur.Itisthecommoncharacteristicmarkofaclassofpropositions.3.312Itisthereforerepresentedbythegeneralformofthepropositionswhichitcharacterizes.Andinthisformtheexpressionisconstantandeverythingelseisvariable.Wittgensteinhereenunciatesaconceptionoftherelationshipbetweenwordsandsentenceswhichisdistinctfromtheonewhichispresupposedintheobjection.AccordingtoWittgenstein,wordsarenotingredientsinsentences:theyarecommoncharacteristicmarksofclassesofsentences.Awordisnotsomethingwhichistakenfromelsewhereand\nSENTENCESASMODELS173combinedwithothersuchthingstoformasentence:itisalwaysjustsomethingwhicharangeofsentenceshaveincommon.Ifthisiswhatawordis,thenwhenawordoccursinalist,itdoesnotoccuroutsideasentence:rather,thewritingofawordinalistisawayofgatheringtogetherallthesentencesinwhichthewordoccurs.AsWittgensteinputsit:Anexpressionisthuspresentedbyavariable,whosevaluesarethepropositionswhichcontaintheexpression.(3.313)Onthisaccount,whenweseejusttheexpressionsinalist,weareinclinedtomisunderstandwhatweareseeing:reallyweareseeingonlypartofwhatisbeingpresentedtous—thepartwhichiscommontoallthesentencesofwhichtheexpressioncanbeapart,andnotthefactthattherearealwaystheotherpartsofthosesentences.Tomakethisexplicit,wemightusetheformofexpression‘…E…’asawayofindicatinganysentenceofwhichtheexpression‘E’mayformapart.Inthatcase,wheneverwecomeacrosstheexpression‘E’apparentlyinisolation(asinalist),whatwereallyhaveissomethingoftheform‘…E…’.Consider,then,thelistofwordswhichmightnormallybewrittenasfollows:‘Socrates’‘is’‘identical’.Ifthatlistreallyisalistofwords(expressionsorsymbols,asWittgensteinunderstandsthesenotions),itisthesamelistaswouldbewritteninournewnotationlikethis:‘…Socrates…’‘…is…’‘…identical…’.Ifwethinkoflistsofwordsinthisway,theyarenotexamplesofplaceswherewordsappearinisolation,outside\n174SENTENCESASMODELSthecontextofsentences.Rather,listingwordsisjustawayoflistingrangesofsentences.Itisworthpausingforamomentonthenotionof‘con-text’inplayin3.3.WhenFregewritesthat‘itisonlyinthecontextofapropositionthatawordhasanymeaning’,thewordtranslated‘context’hereis‘Zusammenhange’,whichmeans,literally,hangingtogether.AndWittgensteinusesthesamewordinhisformulationoftheContextPrinciplein3.3.Wittgensteinisattentivetotheetymologyhere.Recallthatinhisaccountoftherelationshipbetweenobjectsandatomicfacts,inthebasicstructureoftheworld,Wittgensteinwrites:2.03Intheatomicfactobjectshang[‘hängen’]inoneanother,likethelinksofachain[‘Kette’].Andwhenhegetstothelinguisticcounterpartofatomicfacts—so-calledelementarysentences—hewrites:4.22Theelementarypropositionconsistsofnames.Itisahangingtogether[‘Zusammenhang’],alinkinginachain[‘Verkettung’],ofnames.22WehavejustseenthatWittgensteinthinksthatallexpres-sionscanbepresentedasvariables:thatistosay,eachexpressioniswhatiscommon,orconstant,acrossarangeofsentences,therestofwhichisvariable.Everyexpressioncanthereforebepresentedasapropositionalvariable—wherethevariableindicatestherangeofsentences(‘propositions’)whichhavethatexpressionincommon(3.313–3.314).(NotethatWittgenstein’suseofthenotionof‘propositionalvari-able’differsfromthecontemporaryone.Wenowusethetermforarangeofletterswhichwehavesetasidetoreplacewholesentencesinformalizationsofarguments—standardly‘p’,‘q’,and‘r’.Wittgenstein,however,thinkseveryordinaryexpressionisitselfa‘propositionalvariable’(3.313).)Consider,forexample,thename‘Socrates’.Thisnamecanoccurincombinationwithaone-placepredicate(examples\nSENTENCESASMODELS175mightbe‘isugly’,‘iswise’,‘iswaspish’)toformasimplekindofsentence.23Wecanindicatethewholerangeofsuchsentences—allthesentenceswhichcombinethename‘Socrates’withaone-placepredicate—byusingavariableinplaceoftheone-placepredicates.Wemightthenindicatethatwholerangewiththeexpression‘fSocrates’:thiswholeexpressionisapropositionalvariable.Thevaluesofthisvariableareallthesentencesinwhichthename‘Socrates’occursincombinationwithaone-placepredicate.Obviously,wecouldalsoreplacethename‘Socrates’herewithavari-able—whosefunctionwillbetorepresent,asitwere,thewholerangeofnames.Wemightwritetheresultingexpression‘fx’.Thiswholeexpressionisonceagainapro-positionalvariable:itindicatesthewholerangeofsentenceswhichconsistofasinglenameincombinationwithaone-placepredicate.Allthesentencesinthatrangearethevaluesofthisvariable.Thisisthekindofprocesswhichisdescribedinthefollowingremark:3.315Ifwechangeaconstituentpartofapropositionintoavariable,thereisaclassofpropositionswhichareallthevaluesoftheresultingvariableproposition.Thisclassingeneralstilldependsonwhat,byarbitraryagreement,wemeanbypartsofthatpro-position.Butifwechangeallthosesigns,whosemeaningwasarbitrarilydetermined,intovariables,therealwaysremainssuchaclass.Butthisisnolongerdependentonanyagreement;itdependsonlyonthenatureoftheproposition.Itcorrespondstoalogicalform,toalogicalprototype[‘Urbild’:pre-model].24Allofthesentenceswhicharevaluesofapropositionalvariableofthiskindaresentencesofspeciﬁctype:forexample,sentencesconsistingofaone-placepredicateincombinationwithaname,orsentencesconsistingofatwo-placepredicateincombinationwithtwonames,orsentencesconsistingoftwosentencesjoinedby‘and’—andsoon.Butitseemsthatweoughttobeabletospecifysomethingmoregeneralthanthis—somethingwhichiscommontoall\n176SENTENCESASMODELSsentences.Withoutthis,wemightbedoubtfulaboutthecoherenceoftheveryideaofasentence,justassuch.25Thiswouldbethegeneralformofthesentence.ThatthereissuchageneralformofthesentenceisofcentralimportancetotheTractatus.Wittgensteindiscussestheissueinthecontextofhisaccountoflogic,andwewillconsideritinthatcontextinthenextchapter.Butitisworthanticipatingthatdiscussionalittle,inordertolinkitbacktotheremarksaboutthecontextprinciplewhichintroducetheideaofapropositionalvariable.Inthatlaterdiscussion,Wittgensteinsaysthefollowingthings:(G1)Thegeneralformof[the]propositionis:Suchandsuchisthecase.(4.5)(G2)Thegeneralpropositionalformisavariable.(4.53)(G2)isanexpressionofthesamepointastheonewhichWittgensteinmakesaboutexpressionsingeneral,in3.311–3.316.Thegeneralpropositionalform—thegeneralformofthesentence—iswhatiscommontoeverysentence.Andwhatiscommontoeverysentencecanberepresentedbyavariablewhichcanbereplacedbyanysentence.Inthiscontext,itisworthremarkingonthedifferencebetweenOgden’stranslationof(G1)andthisalternative,providedbyPearsandMcGuinness:Thegeneralformofapropositionis:Thisishowthingsstand.Ogden’stranslationisclearlypreferablehere:its‘suchandsuch’isaclosetranslationoftheGerman‘soundso’,andgivespreciselytheideaofavariable.26‘Suchandsuch’(liketheGerman‘soundso’)isanexpressionwhichismeanttobereplacedbyamoreprecisespeciﬁcation:itisanordinary-languagevariable.27Wittgensteinoffersanargumentfortheclaimthatthereisageneralformofthesentence(at4.5).Itisanargumentwhichappearstobedistinctfromthesimplethoughtthatwithoutsuchageneralformtheideaofthesentence,in\nSENTENCESASMODELS177general,wouldbeincomprehensible.Anditseemstodependonthepreciseclaimshemakesaboutlogic,sowewillcon-sideritindetailinthatcontext.Butsomethingofthesig-niﬁcanceoftheclaimcanbeseeninthecontextoftheTractatus’sgeneraltheoryoflanguage—thetheorythatsentencesaremodels.Forifthereisageneralformofthesentence—aformwhichiscommontoallsentences—thenthatwillbesomethingwhichnosentencecandepict,since,ingeneral,nopicturecandepictitsownform.Similarly,itwillfollowfromthegeneralaccountoflanguagethatnoth-ingwhichcanonlybedescribedbydescribingthegeneralformofthesentencewillbedescribable.ThiswilltakeonafundamentalimportancewhenWittgensteinturnstothestatusofphilosophy.4EANALYSISANDELEMENTARYSENTENCESThecentralclaimoftheTractatus’sconceptionoflanguageisthatsentencesaremodels,likethePariscourtroommodel.Thismeans,inparticular,thattheelementsofsentencesmusthavethesamepossibilitiesofcombinationasthecor-respondingitemsinreality.ButisWittgensteinreallyclaimingthatallsentencesaremodels?Anddoeshethinkthateverypartofeverysentenceiscorrelatedwithsome-thinginrealitywhichsharesthesamepossibilitiesofcombination?TheanswertobothquestionsisNo.Hisclaimthatsen-tencesarepicturesormodels(at4.01,forexample)shouldbecomparedwithhisclaim(at1.21)thatanyfactcaneitherbethecaseornot,whileeverythingelseremainsthesame.Theclaimat1.21seemstoapplyunrestrictedlytoeverykindoffact;butreallyWittgensteinonlytakesittoholdforatomicfacts:itwasjustthatthemoregeneralnotionoffacthadtobeusedintheﬁrstinstance.Inthesameway,althoughtheapparentlyunrestrictedclaimthatsentencesarepicturesormodelsmightseemtoapplytoeverysentence,reallyWittgensteindoesnotneedittoholdforeverykindofsen-tence,andIthinkitisclearthathedoesnotholdit.He\n178SENTENCESASMODELSreallyneedsittohold—andmeansittohold—justforaverylimitedclassofsentences,thosewhichhecallselemen-tarysentences.Formostpurposes,wecantreatthe‘picturetheory’—thetheoryofsentencesasmodels—strictlyspeaking,asatheoryonlyofelementarysentences.Thisexplainsthefollowingsequenceofremarks:3.2Inpropositionsthoughtscanbesoexpressedthattotheobjectsofthethoughtscorrespondtheelementsofthepropositionalsign.3.201TheseelementsIcall‘simplesigns’andtheproposition‘com-pletelyanalysed’.3.21Totheconfigurationofthesimplesignsinthepropositionalsigncorrespondstheconfigurationoftheobjectsinthestateofaffairs.3.21is,ineffect,astatementofthecrucialsameness-of-formassumption(SM3);thecontextmakesitclearthatitisonlysupposedtoapplytosentenceswhichconsistsolelyof‘simplesigns’.3.201alsoindicatesthatnotallofthesinglewordsinasentencewillcountas‘simplesigns’:forsomesentences,itseems,willnotbe‘completelyanalysed’,andthesewillcontaincomponentswhichstandinneedofana-lysis.Thatistosay,someofthesinglewordsinanunana-lysedsentencewillnotcountas‘simplesigns’.Wittgensteinclaimsherethatitispossibleinprinciplefortheretobesentenceswhichconsistwhollyof‘simplesigns’.Onlythesesentenceswillbemodelsinthestrictsense,althoughthepossibilityofdescribingtheworldinlanguageatallwilldependonthepossibility,inprinciple,ofanalysingfamiliarsentencesintermsofthesebasic,elementarysen-tenceswhichconsistjustof‘simplesigns’.Butwhatisa‘simplesign’?Theanswertothisquestioniscontainedinthefollowingtwosections:3.23Thepostulateofthepossibilityofthesimplesignsisthepostulateofthedeterminatenessofthesense.3.24Apropositionaboutacomplexstandsininternalrelationtothepropositionaboutitsconstituentpart.\nSENTENCESASMODELS179Acomplexcanonlybegivenbyitsdescription,andthiswillbeeitherrightorwrong.Thepropositioninwhichthereismentionofacom-plex,ifthisdoesnotexist,becomesnotnonsensebutsimplyfalse.Thatapropositionalelementsignifiesacomplexcanbeseenfromanindeterminatenessinthepropositionsinwhichitoccurs.Weknowthateverythingisnotyetdeterminedbythisproposition.(Thenotationforgeneralitycontainsaprototype.)Thecombinationofthesymbolsofacomplexinasimplesymbolcanbeexpressedbyadefinition.HereweseeWittgensteincommittinghimselftothefollowingclaims:(i)Sensemustbedeterminate.(ii)Sensecanonlybedeterminateiftherearesimplesigns.(iii)Sentenceswhichcontainsignswhichstandforcomplexesareevidentlyindeterminate.Therearethreethingswhicharenotquiteclearaboutthis,however.First,itisnotimmediatelyclearwhatthe‘deter-minateness’whichWittgensteinspeaksofis.Second,itisnotquiteobviouswhat‘complexes’are.And,third,thecharacteroftheargumentinvolvedinclaims(i)–(iii)isnotcompletelyclear.ThekindofindeterminacywhichisWittgenstein’scon-cernherecanbediscoveredbyreﬂectingontheremarkinparentheses:‘Thenotationforgeneralitycontainsaproto-type’.Theobviousnessofthis—indicatedbytheemphasison‘contains’here—isclearlysupposedtounderlinetheobviousnessoftheindeterminacyofsentenceswhichcontainsignsforcomplexes.Sinceweconsidered3.315inthelastsection(strictlyspeaking,outoforder),wehavealreadycomeacrossthenotionofa‘prototype’,orpre-model(‘Urbild’).Aprototypeinthissenseissomethinglike‘xiswise’or‘fx’,whichresultsfromreplacingsomeorallofthedifferentpartsofasentencewithvariables.Thestandard(logical)notationforgeneralitydoesindeedcontainaproto-typeinthissense.Forexample,‘EverythingisF’isrendered\n180SENTENCESASMODELS‘8xFx’(or‘(x)Fx’);and‘SomethingisF’isrendered‘9xFx’.Theprototypesinvolvedhereareindeterminateinthesenseofbeingunspeciﬁc:‘xiswise’doesnotsaywho,inparti-cular,iswise’;‘fx’doesnotsaywhatparticularobjecthaswhatparticularquality.Itis,infact,thisunspeciﬁcitywhichensuresthatsentencesinvolvinggeneralityarenotliterallypicturesormodels:theydonotconsistofelementswhicharecorrelatedwithitemsinreality(nor,aswewillseeinChapter5,section5C,aretheysimplycompounds—con-junctionsoralternations—ofsentenceswhichconsistofelementswhicharecorrelatedwithobjectsinreality).Claim(i),then,mustbetheclaimthatsensecannotbeunspeciﬁcinthewayinwhich‘prototypes’,inWittgenstein’ssense,are.Butwhatmightthatmean?Thenaturalinter-pretationisthatitmeansthatusesofsuchunspeciﬁcproto-types—forexample,inexpressionsofgenerality—canonlyhavesenseinvirtueofthoseprototypesbeingvariableswhichcaninprinciplebereplacedbyspeciﬁcsentences.Thatistosay,theuseoftheseprototypesisonlyreallyawayofindicatingarangeofspeciﬁcsentences.Thisroughlycoin-cideswiththemoreeverydaythoughtthatgeneralclaimslike‘EverythingisF’or‘SomethingisF’canonlyreallybetrueinvirtueofmorespeciﬁcclaimsoftheform‘aisF’.Wittgensteinseemstothinkthattheobviouslackofspe-ciﬁcityofexpressionsofgeneralityshowsthatsentenceswhich‘mention’complexeslackspeciﬁcityinthesameway.Thisseemstorequirethatsentenceswhich‘mention’com-plexesmustthemselvesinvolveexpressionsofgenerality.Andthishasonlyonenaturalinterpretation,inthehistor-icalcontextoftheTractatus.Anexpressionwhichmentionsacomplexmustbebeingtreatedinasimilarwaytoadeﬁ-nitedescription,somethingoftheform‘TheF’(where‘F’issingular).Fregetreatedsuchexpressionsassingularterms—thatistosay,asexpressionswhichareonlymeaningfulinvirtueofbeingcorrelatedwithsomethingintheworld.ButRussell,inhistheoryofdescriptions,treatedthemasinvolvingquantiﬁerexpressions;thatistosay,asinvolvinggenerality(seeChapter2,section2C,above).28Hetreatedan\nSENTENCESASMODELS181expressionoftheform‘TheF’asequivalentinmeaningto‘ThereisexactlyonethingwhichisF,andthatthing…’.ItisafeatureofRussell’stheorythatwhenthereisnothingwhichsatisﬁesthedescription—whenthereisnoF—thesentencewhichcontainsthephraseisnotmeaningless—asitwouldhavebeenonFrege’sview(leavingasidethenotionofFregean‘sense’)—butfalse(becausetherejustisnotexactlyonethingwhichisF).ThiscoincidespreciselywithwhatWittgensteinsayshere:Thepropositioninwhichthereismentionofacomplex,ifthisdoesnotexist,becomesnotnonsensebutsimplyfalse.(3.24)AndtheconnectionwithRussellismadeevenclearerlaterinthebook:5.526Onecandescribetheworldcompletelybycompletelygeneral-izedpropositions,i.e.withoutfromtheoutsetco-ordinatinganynamewithadefiniteobject.Inorderthentoarriveatthecustomarywayofexpressionweneedsimplytosayafteranexpression‘thereisoneandonlyonex,which…’:andthisxisa.SoWittgensteinseemssimplytoassumethatexpressionswhichappeartostandforcomplexesareproperlytreatedasRusselltreatsdeﬁnitedescriptions—thoughperhapswithaslightqualiﬁcation.ThequaliﬁcationisthatWittgensteinisunlikelytohavebeenhappytoregarda‘complex’asathingatall.Itseemsmoreplausibletoattributetohimtheviewthatwherethelaypersonmightseea‘complex’,Wittgensteinseesonlythecomponentsandfactsabouttheirarrangement—orrather:onlythattherearesomecomponentsarrangedincertainways.Thushesays:2.0201Everystatementaboutcomplexescanbeanalysedintoastatementabouttheirconstituentparts,andintothosepro-positionswhichcompletelydescribethecomplexes.\n182SENTENCESASMODELSWittgensteinseems,then,toassumewithoutargumentthatsentencesabout‘complexes’needtobeanalysedbymeansofsomeuseofgenerality.Becausethenotationforgeneralityalwaysinvolvestheinspeciﬁcityof‘prototypes’,andtheinspe-ciﬁcityof‘prototypes’isitselfanindicationofthepossibilityoftheirbeingreplacedbyspeciﬁcexpressions,thefactthatexpressionswhichstandforcomplexesaretobeanalysedbymeansofgeneralityistakentoshowthattheremustbe‘simplesigns’.Andsince‘simplesigns’areherecontrastedwithexpressionswhichstandforcomplexes,‘simplesigns’mustbeexpressionswhichstandforsimpleentities—thatistosay,objects.Ifthisisright,thereisnoargumentherefortheexistenceofsimpleentities—theobjectsintroducedintheearly2s.Theargumentwehavehereseemstopresupposeacontrastbetween‘complexes’andsimpleentities,andthentobeconcernedtoshow,merely,thatitmustbepossibleinprin-ciplefortheretobesignsforthesimpleentities:thatis,thenamesfromwhichfullyanalysedsentencesareconstructed.Thatmeansthattheargumentfortheexistenceofobjects,inthesenseoftheearly2s,mustdependjustongeneralfea-turesoftheTractatus’stheoryoflanguage—inparticular,ontheassumptionthatlanguageandtheworldmustshareacommonform.And,infact,onmyinterpretationtheargu-mentforsubstancein2.02andthefollowingsectionsdoesindeeddependjustongeneralfeaturesoftheTractatus’stheoryoflanguage.(SeeChapter1,section1D.)Sections3.23–3.24mustthenbeconcernedtoaddressadifferentworry.Anditisnothardtoseewhatthatworrymustbe.Itistheworrythatthewordsofourordinarysentencessimplydonotstandforitemsintheworldwhichhavethesamerangesofpossiblecombinationasthewordsdo,andwhoserangesofpossiblecombinationconstitutetheformoftheworlditself—thatistosay,theultimatepos-sibilitiesofcombinationofthings.Infact,wehaveverylittleideaoftheobjectswithwhichwordswouldhavetobecor-relatedfortheretobethiskindofmatch.Thepointof3.23–3.24is,then,simplytoclaimthatthefailureofthesurface\nSENTENCESASMODELS183grammarofoureverydaylanguagetomeetthedemandsofthetheorythatsentencesaremodelsisnoobjectiontothetheoryitself—orindeedtothemeaningfulnessofoureverydaylanguage.Infact,Wittgensteinthinksthatoureverydaylanguageisperfectlymeaningful:29Allpropositionsofourcolloquiallanguageareactually,justastheyare,logicallycompletelyinorder.(5.5563)Insteadofgivingupthetheoryofsentencesasmodels,ordoubtingthemeaningfulnessofoureverydaylanguage,Wittgensteinthinksthatweneedtounderstandoureverydaywordsasinvolvingimplicitgeneralizations,whoseinstances,ultimately,willconsistentirelyofsignsforsimpleobjects,hanginginoneanotherlikethelinksofachain.Wittgensteinsummarizeshisapproachtoeverydaylanguagesinthisremark:4.002Manpossessesthecapacityofconstructinglanguages,inwhicheverysensecanbeexpressed,withouthavinganideahowandwhateachwordmeans—justasonespeakswithoutknowinghowthesinglesoundsareproduced.Colloquiallanguageisapartofthehumanorganismandisnotlesscomplicatedthanit.Fromititishumanlyimpossibletogatherimmediatelythelogicoflanguage.Languagedisguisesthethought;sothatfromtheexternalformoftheclothesonecannotinfertheformofthethoughttheyclothe,becausetheexternalformoftheclothesisconstructedwithquiteanotherobjectthantolettheformofthebodyberecognized.Thesilentadjustmentstounderstandcolloquiallanguageareenormouslycomplicated.4FPREDICATESANDRELATIONSWearenowinapositiontounderstandWittgenstein’sgen-eraltheorymoreclearly.Languageiscapableofrepresentingrealityinvirtueofthepossibilityoftherebeingsentenceswhichconsistwhollyofsimplesigns—names—ofthe\n184SENTENCESASMODELSobjectswhosepossibilitiesofarrangementconstitutetheultimatepossibilitiesoftheworld.Wittgensteinscornfullydismissesquestionsaboutthenatureoftheseobjects—beyondwhathistheoryrequires—butthereisonequestionwhichmightseemtobepressingforhim,andonwhichthereissomedoubtwhetherhehadasettledview.DoWittgenstein’sobjectsincludequalitiesandrelations?Inthetermsofanancientdebate,wasWittgensteina‘realist’ora‘nominalist’aboutqualitiesandrelations?30(Inthetradi-tionaldebateonthisissue,arealistholdsthat‘universals’—qualitiesandrelations—exist,inthesenseofbeingthings—objects—whereasanominalistdeniesthis,hopingtoexplainlanguagewhichseemedtorefertouniversalsasinvolvingnothingmorethanacomplicatedwayofdealingwiththeuseoflinguisticexpressions.Notethatthisuseoftheterm‘realism’isonlytangentiallyconnectedwiththeuseoftheterminwhichitcontrastswith‘idealism’,asinChapter1,section1F,forexample.)Wittgenstein’sviewsonthisissuemightappearatﬁrstsighttobeconfusedandinconsistent.ThedifﬁcultyisrevealedbywhathesaysintextsoutsidetheTractatus,whichareneverthelessclearlyrelevanttoit.In1913hewrote:(a)Ihavechangedmyviewson‘atomic’complexes:Inowthinkthatqualities,relations(likelove)etc.areallcopulae!(CL:24)Andagain:(b)Indefinablesareoftwosorts:namesandforms.Propositionscannotconsistofnamesalone,theycannotbeclassesofnames.(NL:96)Butin1915hewrote:(c)Relationsandproperties,etc.areobjectstoo.(NB:61)\nSENTENCESASMODELS185Andsoonafterhereturnedtophilosophy(sometimein1930–31),heisrecordedassayingthisinexplanationofTractatus2.01(‘Astateofaffairs(astateofthings)isacombinationofobjects(things)’):(d)Objectsetc.ishereusedforsuchthingsasacolour,apointinvisualspaceetc.….‘Objects’alsoincluderelations;apropositionisnottwothingsconnectedbyarelation.‘Thing’and‘relation’areonthesamelevel.Theobjectshangasitwereinachain.31(WLC:120)Thepuzzleisthis.Astexts(a)and(b)show,in1913heseemstohavethoughtthatqualitiesandrelationswerenotobjects,andthatsomethingotherthannameswasneededfortheretobewholesentences.Butin1915,andagainlongafterthewritingoftheTractatus,heseemstohavedecidedthatqualitiesandrelationsareobjects.Thiscouldbeputdowntoasimplechangeofmind,wereitnotforacrucialtextinthemiddleoftheTractatusitself:3.1432Wemustnotsay,‘Thecomplexsign“aRb”says“astandsinrelationRtob”’;butwemustsay,‘That“a”standsinacertainrelationto“b”saysthataRb’.Thisseemstoexpress(amongotherthings)exactlythedoctrineoftext(b):itseemsthatthesymbol‘R’doesnotfunctionasanameofarelation,butasawayinwhichthetwonames‘a’and‘b’canberelated—somethingwhichthetwonamescanbewritteneachsideof.And,indeed,3.1432isverballyveryclosetothisremarkof1913,fromwhichitseemsultimatelytoderive:In‘aRb’,‘R’lookslikeasubstantive,butisnotone.Whatsymbolizesin‘aRb’isthatRoccursbetweenaandb.(NL98)Atthispointweseemtohaveatrulybizarrehistoricalsequence.WeseemtoﬁndWittgensteinendorsingoneview\n186SENTENCESASMODELSin1913,changinghismindoveritin1915,changingitbackagainintheﬁnalversionofthebook(around1918),onlyforhimtochangehismindyetagain(whilestillmakinguseoftheimageryoftheTractatusitself)intheacademicyear1930–31.ThislookslikealevelofvacillationanduncertaintyoveramajorissuewhichitisveryhardtoattributetoWittgenstein.Infact,thereisnosuchveryseriousanomaly,eveniftheinterpretationofwhatWittgensteinisdoingisnotaltogetherobvious.IwillstartbytryingtogetclearaboutthepositionoftheTractatus,beforegoingbacktoconsiderthestagesintheprocessbywhichWittgensteinreachedthisposition.Itwillturnoutthattheprocessdoesnotinvolveanyverypeculiarvacillation.Tobeginwith,weshouldrecallwhatqualitiesandrela-tionsaretraditionallytakentobe.Theyareentitieswhicharecorrelated(insomeway)withpredicates:one-placepre-dicates,inthecaseofqualities;andmany-placedpredicates,inthecaseofrelations.Inthelightofthat,theﬁrstthingweneedtodoisdistinguishbetweentwoquestions,asemanticquestionandanontologicalone,eveniftheyareboundtoberelated:(SQ)Arethereanypredicatesinelementarysentences?(OQ)Aretheresomequalitiesandrelationsamongthefundamentalobjects?Letusbeginwiththesemanticquestion,(SQ).Inordertoanswerthis,weneedtoknowwhatapredicateis.Inthemostneutralsense,apredicateiswhatisleftofasentencecontainingnamesonceoneormorenameshavebeenremoved.32Clearlytheremustbepredicates,inthisminimalsense,amongelementarysentences,ifelementarysentencesincludenamesatall.Forasentencemustbemorethanjustasinglename,sotheremustbesomethingleftofasentenceonceanamehasbeenremoved.Itisclearfromthisthatanyonewhoraises(SQ)atallmusthavealessminimalsenseof‘predicate’inmind.Wemightcallthisarichsense\nSENTENCESASMODELS187oftheterm‘predicate’,andexplainitasfollows:apredicate(inthisrichsense)isanon-namelikebasiccomponentofsentences,whichyieldsawholesentencewhencombinedappropriatelywithoneormorenames.Thosewhothinkthatthereisafundamentallinguisticcontrastbetweennamesandpredicates(between‘subject’andpredicateinanolderterminology)holdthateventhemostbasicsentencesincludepredicatesinthisrichsense.Wittgensteinclearlydisagrees:4.22Theelementarypropositionconsistsofnames.Itisahangingtogether[‘Zusammenhang’],alinkinginachain[‘Verkettung’],ofnames.Thewholepointof4.22(astext(d)conﬁrms)seemstobetosaythatwedonotneedanythingotherthannamestoglueasentencetogether:thenameshanginoneanotherontheirown.Sotherearenopredicatesinelementarysentences,if‘predicate’isunderstoodintherichsense,asanon-namelikebasicsententialcomponent.Thismightseempuzzling,sinceWittgensteinisclearlyhappytousethefamiliarpredicatelettersofmodernpre-dicatelogic(in3.1432,forexample).Buttheuseofthosefamiliarpredicatelettersrequiresnothingmorethantheminimalsenseof‘predicate’.Wecanspellthepointoutexplicitlyasfollows.Supposethatelementarysentencesarejuststringsofnames,suchasthesethree:(1)abcdef(2)nbcdef(3)mbcden(1)and(2)canbeseentoshareacommonform:theybothrepresentacombinationofanobject(aandn,respectively)withtheobjectsb,c,d,e,andf.Wecanperfectlywellusetheletter‘F’tosymbolizewhattheyshare,andthen,fol-lowingthefamiliarmodernordering,representthatfactbyrewritingthemasfollows:\n188SENTENCESASMODELS(1a)Fa(2a)FnBothsentencescannowbesaidtohavetheform‘Fx’.Again,wecanseethat(1)and(3)shareacommonform:theybothrepresentcombinationsofpairsofobjects(aandf,andmandn,respectively)withthefurtherobjectsb,c,d,ande.Again,wecoulduse‘R’tosymbolizewhattheyshare,andrewrite(1)and(3)asfollows:(1b)aRf(3b)mRnBoth(1)and(3)cannowbeseentohavetheform‘xRy’.In(1a),(2a),(1b),and(3b),theletters‘F’and‘R’donotfunc-tionasnames.Rather,theyarefunctionalexpressionsinaveryparticularsense:theyrepresentwholesentencesasbeingfunctionsofcertainselectednames.Thus‘Fa’repre-sentsthesentence‘abcdef’asafunctionofthename‘a’,and‘aRf’represents‘abcdef’asafunctionofthetwonames‘a’and‘f’.33(Forthisideaofasentencebeingafunctionofoneormorenameswithinit,see3.318and4.24:thisissueisconsideredfurtherinChapter5,section5B,below.)Theuseof‘R’in3.1432isquitecompatiblewiththis:itﬁguresthereasnomorethanawayofsymbolizingacommonalityshar-ablebyothersentences—evenifitisonewhichcould,inprinciple,bespelledoutasconsistingjustofastringofnames.Doesthismeanthatsentencesusingpredicateletterscannotbeelementarysentences?Mustwesaythat‘aRb’,asitoccursin3.1432,forexample,isnotanelementarysen-tence?Thereisaslightlytrickyissuehereabouttherela-tionshipbetweensentencesandnotations.Ifwelookattheway‘F’wasintroducedonthebasisof(1)and(2),and‘R’onthebasisof(1)and(3),wecanseethatthesepredicatelettersarenomorethanconvenientwaysofwritingchunksofsentences—waysdesignedtomakecommonalitiesobvious.Sowemightregard(1a)and(2a)asjustwaysofwriting(1)and(2),and(1b),and(3b)asjustwaysofwriting(1)and\nSENTENCESASMODELS189(3).Since,byhypothesis,(1),(2),and(3)arethemselveselementarysentences,(1a),(2a),(1b),and(3b)wouldallbeelementarysentencestoo,thoughtheyarenotwritteninwaysthatshowallthenamesofwhichtheyarecomposed.Aslongasweareclearaboutwhatwearedoing,thisseemsaper-fectlylegitimatewayofdescribingthem.Soeveniftherearenopredicatesinelementarysentences,intherichsenseof‘predicate’(anon-namelikebasicsen-tentialcomponent),therecanstillbealegitimateuseofthepredicatelettersofstandardpredicatelogic,asfunctionsoftherelevantkindfromnamestosentences.Anditseemsperfectlylegitimatetocountatleastsomesentencesinwhichthefamiliarpredicatelettersareusedaselementarysentences.Nowletusturntotheontologicalquestion(OQ).Justastheanswerto(SQ)dependsonwhatismeantby‘predicate’,sotheanswerto(OQ)dependsonwhat,precisely,ismeantby‘quality’and‘relation’.Itisnaturaltotakequalitiesandrelationstobetheontologicalcorrelatesofpredicates,understanding‘predicate’intherichsense:thatis,wemightdeﬁnequalitiesandrelationsasthecorrelatesofappropriatenon-namelikebasicsententialcomponents.Ifwedeﬁne‘quality’and‘relation’inthisway,andwetakewhatcountsasnon-nameliketobedeterminedbyWittgenstein’scon-ceptionofnames,Wittgenstein’sanswerisunequivocal,sinceheclearlydoesnotacceptthattherearesuchnon-namelikebasicsententialcomponents.Butadifferentconceptionofnameswouldgenerateadif-ferentconceptionofwhatcountsasnon-namelike.AndweneedlooknofurtherthantoFregetoﬁndsuchadifferentconceptionofnames.Fregereservedtheterm‘name’(‘propername’,strictlyspeaking)foroneoftwobasickindsofsub-sententialexpression;aswesawinChapter2,hecontrastednamesinhissensewith‘concept-expressions’orpredicates.Thiscontrastbetweenbasickindsofsub-sententialexpressionisparalleltoacontrastbetweenbasickindsofentity.Fregereservedtheterm‘object’forthereferentsofnames(inhissenseof‘name’),andusedtheterm‘concept’forthereferentsofpredicates.Fregetookobjects(inhissense)\n190SENTENCESASMODELStobe‘saturated’orcomplete,and‘concepts’(inhissense)tobe‘unsaturated’orincomplete.Ifthesetwocontrasts—betweennames(inFrege’ssense)andpredicates,andbetween‘saturated’and‘unsaturated’entities—canbemadegood,wecandeﬁnequalitiesandrelationsintheirterms.Qualitiesandrelationscanstillbedeﬁnedasthereferentsofpredicatesintherichsense:thatis,theywillbethereferentsofnon-namelikebasicexpressions(asbefore),buttheconceptionofwhatcountsasnon-namelikewillbedeterminedbyFrege’sconceptionofnames,ratherthanbyWittgenstein’s.Thatistosay,wecandeﬁnequalitiesandrelationsasunsaturatedentities,inwhateversenseof‘unsaturated’itisthatFregeisconcernedwith.34WhethersomeofWittgenstein’snamesrefertosuch‘unsaturated’entitiesisatleastnotimmediatelyruledoutby4.22(whichisparalleltotheexplicitlyontological2.01and2.03).ThereisnoimmediatereasonwhyaTractariannameshouldnotbenon-namelikeinFrege’sterms.ForitmightbethattheexpressionswhichWittgensteincountsasnamescaninfactbedividedintoexactlytwotypes,andtypesofexactlytherightkinds:thosewhichFregewouldcountasnamelike,andthosewhichFregewouldcountasnon-namelike.AnditmightbethatacorrespondingsimpledistinctioncanbemadeamongtheentitieswhichWittgensteincountsasobjects:somewouldbecountedas‘saturated’byFrege,andsomeas‘unsaturated’.Whatisimmediatelyruledoutby4.22istheideathatallTractariannamesmightbenamelikeinFrege’ssense,andthatalloftheobjectstowhichWittgenstein’snamesrefermightbesaturatedentities.Forthatwouldinvolvemakingthefollowingthreeassumptionssimultaneously:(i)Asentencemightbecomposedjustofnames;(ii)AllnamesarenamelikeintheFregeansense;and(iii)Nosentencecanbecomposedjustofnamelikeexpressions,intheFregeansenseof‘namelike’.Andthesethreeassumptionsquiteobviouslyformaninconsistentset.\nSENTENCESASMODELS191OntheFregeanpicture,thereisasinglecrucialdistinctiontobemadebetweentheentitiescorrelatedwithdifferentcomponentsofthemostbasicsentences;andweonlygetawholesentenceofthemostbasictype,whenwehavesome-thingmadeinanappropriatewayfrombothkindsofcom-ponentexpression.But,althoughFregethoughtthatthemostbasicsentencesareconstructed,ultimately,ofcompo-nentsofjusttwofundamentalkinds,thisisnottheonlywayinwhichwemightthinksentenceswereconstructed.Wemightsupposethattherewasagreatervarietyoffunda-mentalkindsofcomponentofbasicsentencesthanthissimpleFregeanasymmetryallows.Differentkindsoffunda-mentalexpressionmighttakequitedifferentkindsofcomplementstoformwholesentences.ButeventhismorevariegatedconceptionofthecompositionofsentencesiscompatiblewithcountingqualitiesandrelationsamongWittgenstein’sobjects,givenasuitablemodiﬁcationofourconceptionofwhatqualitiesandrelationsare.Forwemightsupposethatamongthelargevarietyofdifferentkindsofobjectwhicharecorrelatedwiththevariousdifferentkindsoffundamentalexpression,therewasaprincipledreasontosingleouttwoinparticular;andbecause(asitmightturnout)thelinguisticexpressionswhichcorrespondtothesetwoparticularkindsofobjectstandincloseproximitytocertaineverydayquality-wordsandrelationalexpressions,wemightlegitimatelycallobjectsofthesetwokindsqualitiesandrelations.Thiswouldmeanbreakingorqualifyingthetra-ditionalconnectionbetweentheconceptsofqualityandrelation,ontheonehand,andtherelativelysimplegram-maticalcategoryofpredicates,ontheother.ButitmightneverthelessprovideanotherwayofallowingqualitiesandrelationstobeincludedamongtheobjectsoftheTractatus.Andthis,too,wouldbeconsistentwith4.22(aswellas2.01and2.03).Weseem,then,tohaveatleasttwowaysinwhichWittgensteincouldholda‘realist’position—thatis,acceptthattheobjectsoftheTractatusincludequalitiesandrela-tions—consistentlywithhisclaimthatthemostbasic\n192SENTENCESASMODELSsentencesarecomposedjustofnames.HecouldadopttheFregeanview,accordingtowhichtheunityofsentencesdependsonasingle,particularkindofasymmetry;orhecouldsupposethatthereisavarietyofdifferentkindsofcomplementarity,whichpermitstheunityofsentencestoberealizedinavarietyofdifferentways,withthenotionsofqualityandrelationdoingnomorethanmarkoutdistinctivecommonalitieswithinthatvariety.35TheTractatusitselfisneutralbetweenthesetwoviews.Perhaps,indeed,itisdeliberatelyneutral:itisquiteplausibletosuggestthatWittgensteintooktheﬁnaldeterminationofthenatureofobjectstobesomethingthatcouldnotbeset-tledapriori—thatis,beforeadetailedanalysisoflanguagehadactuallybeencarriedout.ThisseemstobetheviewofthetextheldbyFrankRamsey(hintedatinRamsey(1923),andarguedforexplicitlyat(1925b:133)).AnditseemstohavebeenendorsedopenlybyWittgensteinhimselfin1929(WVC:42).36Furthermore,itisnotjustthattheTractatus,ingeneral,isneutralonthefundamentalnatureoftheobjectstowhichthenamesinelementarysentencesrefer:thereisnothingin3.1432whichdisruptsthisneutrality.Inparticular,thereisnothingherewhichinvolvesdenyingthattherearequalitiesandrelationsamongtheobjects—providedmerelythatqualitiesandrelationsarenotdeﬁnedasthereferentsofexpressionswhicharenon-namelikeinWittgenstein’sterms.Forallweknow,‘a’or‘b’mayrefertoaqualityorarela-tion;and‘R’itselfmaybeareplacementforacommoncomponentofsentenceswhichincludesnamesforqualitiesandrelations.Bearingallthisinmind,whatstorycanwetellofthehistoryofWittgenstein’sthought?In1913heseemstohavethoughtthatqualitiesandrelationswerenotincludedamongtheobjectsreferredtobynames:instead,qualitiesandrela-tionsseemtobeforms.37(Thisviewwasasigniﬁcantchangeinitself,astext(b)suggests:bymakingqualitiesandrela-tionsthemselves‘copulae’orforms,Wittgensteinaimedtoremovetheneedtoaddanextracopulativecomponentto\nSENTENCESASMODELS193gluethemontoobjects.38)Butby1915,andapparentlythereafter—withnointerruptionintheTractatus,asfarascanbeseenfromthetext—heseemshappytocountqua-litiesandrelationsasobjects.Itlooksasifasigniﬁcantstageinthistransitionismarkedbythefollowingtext(alsofromthe1913NotesonLogic):Buttheformofapropositionsymbolizesinthefollowingway:Letusconsidersymbolsoftheform‘xRy’;tothesecorrespondprimarilypairsofobjects,ofwhichonehasthename‘x’,theotherthename‘y’.Thexsandysstandinvariousrelationstoeachother,amongotherstherelationRholdsbetweensome,butnotbetweenothers.Inowdeterminethesenseof‘xRy’bylayingdown:whenthefactsbehaveinregardto‘xRy’sothatthemeaningof‘x”standsintherelationRtothemeaningof“y’,thenIsaythatthe[thefacts]are‘oflikesense’withtheproposition‘xRy’;otherwise,‘ofoppositesense’;Icorrelatethefactstothesymbol‘xRy’bythusdividingthemintothoseoflikesenseandthoseofoppositesense.Tothiscorrelationcorre-spondsthecorrelationofnameandmeaning.Botharepsychological.ThusIunderstandtheform‘xRy’whenIknowthatitdiscriminatesthebehaviourofxandyaccordingasthesestandintherelationRornot.InthiswayIextractfromallpossiblerelationstherelationR,as,byaname,Iextractitsmeaningfromallpossiblethings.39(NL:104)Twothingsarestrikingaboutthispassage.OneisthatWittgensteindrawsacloseparallelbetweenthedeﬁnitionofthemeaningofnamesandthedeﬁnitionofthemeaningof‘forms’:eachkindofsententialelementismeaningfulinvirtueofanarbitrarypsychologicalcorrelation.Theotheristheideathatatleastsomepartsofsentenceshavetheirmeaningdeﬁnedintermsofacorrelationbetweensentences,ontheonehand,andfactswhicharespeciﬁedasbeing‘oflikesense’and‘ofoppositesense’,ontheother.Letusconsiderthesetwostrikingthingsinturn.EarlierintheNotesonLogic(NL:96;text(b)above)Wittgensteinhadinsistedthattherearetwosortsof‘inde-ﬁnables’:namesandforms.Thisisasinglefundamental\n194SENTENCESASMODELSdistinctionbetweenkindsofbasicexpression,whichisparallelto,evenifnotquitethesameas,Frege’sdistinctionbetweencompleteandincompleteexpressions.40Buttheobservationinthislaterpassage(NL:104)thatthereisafundamentalsimilaritybetweenthetwokindsof‘indeﬁnable’encouragesonetothinkthatthatdistinctionmightnotbeasfunda-mentalasitseemed.Inthatcase,wemightassimilatethesetwokindsof‘indeﬁnable’toasinglecategory,andcallthemalljustnames.AndthatseemstobejustwhatWittgensteindid.ButifthisiswhatWittgensteindid,weshouldbecarefulnottoexaggeratethemagnitudeofthetransitionwhichisinvolvedhere.ItisnotthatWittgensteinmaintainedthesame(basicallyFregean)conceptionofbothnamesandobjectsfromearly1913onwards,withthedifferencebeingthathelatercametothinkthatsomeexpressionswhichhehadearliercountedas‘copulative’were,afterall,namesinthatoriginalsense,andthatsome‘unsaturated’entitieswereincludedamongthe(‘saturated’)objects.Itisratherthathechangedhisconceptionofnamesandobjects:hecametothinkthat,forhispurposesatleast,therewasnotafunda-mentaldifferencebetweenthoseexpressionswhichheori-ginallycountedasnames,andthosewhichheoriginallycountedas‘copulative’.Andhecametothinkthattherewasnotafundamentaldifference,forhispurposesatleast,betweentheentitieswhichheoriginallycountedasobjects,andthosewhichhewaspreviouslyinclinedtodistinguishfromobjects.ItisslightlyexaggeratingthepointtosaythatthechangeinWittgenstein’sviewsisverbalratherthansub-stantial;butatleastthereisnotthekindofsubstantialdiffer-encewhichthereisusuallytakentobebetweentraditional‘realists’and‘nominalists’aboutuniversals.WittgensteinmayhavebeenencouragedtochangehisconceptionofthenatureofnamesandofobjectsbythesubstanceofhisownsuggestedaccountofthemeaningofformsinthelaterpassagefromtheNotesonLogicwhichIhavequoted.Aremarkablefeatureofthisaccountisthatitexplicitlyanddeliberatelyexplainsthemeaningofformsintermsoftheircontributiontowholesentencesofwhichthey\nSENTENCESASMODELS195canbepart.Itwas,ofcourse,animportantpartofFrege’sviewthatthesameholdsforeverykindofsubsententialexpression:indeed,heemphasizedthepointinparticularinconnectionwithsingularterms(whathecalled‘propernames’).IfWittgensteinwasnotparticularlyconcernedwiththepointofFrege’scontrastbetween‘saturated’and‘unsa-turated’entities(whatever,exactly,thatmayhavebeen),wecanimaginehimreﬂectingfurtheronFrege’sContextPrinciple,andcomingupwiththefollowingthought.Theaccountwhichishere(inNL:104)providedofthemeaningjustofformscouldbegeneralizedtoprovideuswiththebasisofanaccountofthemeaningofallfundamentalexpressions—includingthosewhichwerepreviouslycalled‘names’incontrastwiththosecalled‘forms’.Thatis,wecanimagineWittgensteinassimilatingFrege’sContextPrinciplemorethoroughlythanhehadbefore,andtakingallfunda-mentalexpressionstohavetheirmeaninginvirtueofadis-tinctionbetweenthosefactswhichare‘oflikesense’andthosewhichare‘ofoppositesense’.TherearetwofurtherfeaturesoftheaccountofthemeaningofformsintheNotesonLogicwhichareworthnoting.Theﬁrstisitsconceptionoftherelationbetweenthemeaning-determiningsubjectandtheworld.Themeaning-determiningsubjectseemstobeimaginedasseeingtheworld,ontheonehand,therewithallitsfacts,indepen-dentlyoflanguage,whilehavingwholesentences,ontheotherhand,readytocorrelatewiththosefacts.Thisideaofakindoflanguage-independentaccesstothefacts,justassuch,seemstobederivedfromRussell:itdoesnotsurviveintotheTractatus.41Theothernotablefeatureoftheaccountofthemeaningofformsdoessurvive,however.Thisisthatthemeaningevenofpartsofthemostbasicsentencesisexplainedintermsjustofthedifferencetheymaketothetruthorfalsityofwholesentencesinwhichtheymayoccur.Thefacts‘oflikesense’arethosewhichmaketherelevantsentencestrue,andthefacts‘ofoppositesense’arethosewhichmaketherelevantsentencesfalse.Andthisdifferenceissupposedtobeenough\n196SENTENCESASMODELStoestablishcompletelythemeaningoftherelevantexpressions.Thisisthedeepunderlyinglinkbetweentheaccountofele-mentarysentencesasmodels,andtheaccountofcompoundsentencesastruth-functionsofelementarysentences,whichisthetopicofmuchofChapter5.424GTHESOLUTIONOFTHEPROBLEMSINHERITEDFROMFREGEANDRUSSELLTheso-called‘picturetheory’—thetheorythatsentencesaremodels,likethePariscourtroommodelofthetrafﬁcaccident—isdesignedtodealwiththeproblemsinthephilosophyoflanguagewhichfacedFregeandRussell.Wittgensteinclearlyfeltthatitwastheonlypossiblesolutiontothoseproblems:thisconvictionunderlieshisconﬁdencethatthereisnowayofdoingphilosophyatallwithoutbeingunderminedbytheparadoxeswhichfacethepicturetheory.RecallfromthelastchapterthatWittgensteinwasoperatingwiththesetwofundamentalassumptions:(Corr)Languagesdependfortheirmeaningfulnessoncorrelationsbetweencertainlinguisticitems,ontheonehand,andextra-linguisticitems,ontheother.(Obj)Theextra-linguisticitemswithwhichthoselinguisticitemshavetobecorrelatedforlanguagestobemeaningfulareitemsintheworld(objects).Andinthelightofthese,hefacedtwofundamentalproblems:(P1)Whichlinguisticitemsneedtobecorrelatedwiththingsintheworldforlanguagestobemeaningful?(P2)Howistheunityofthesentencetobeexplained?Problem(P1)relatesinparticular(inthecontextofthenewlogicdevelopedbyFregeandRussell)tothreecategoriesoflinguisticexpression:apparentsingularterms,predicates,andwholesentences.Inthecaseofapparentsingularterms,thedifﬁcultyistodealwiththefactthatcertainapparent\nSENTENCESASMODELS197singulartermscanseemtobemeaningful,eventhoughthereisnorealobjectintheworldwithwhichtheyarecorrelated.(ThisispartofwhatIcalledtheproblemofthinnessofmeaninginChapter2,section2C.)Wittgensteinherefol-lowsRussell,inrestrictingtherangeofgenuinesingulartermstothoseforwhichtheproblemcannotarise.Hissin-gularterms—thenameswhicharecombinedinelementarysentences—arecorrelatedwithobjectswhichexistnecessa-rily.Otherapparentsingulartermsarenotreallysingularterms,buttheyaremeaningfulinthesamewayasdeﬁnitedescriptionsare,onRussell’saccountofdeﬁnitedescriptions:sentencescontainingtheminvolveassertionsofexistence,sothesentencesaresimplyfalse,ratherthanmeaningless.Aproblemarisesifpredicatesarecorrelatedwithitemsintheworld.Iftheitemsintheworldhaveadistinctivechar-acter,inorderforthemtobecapableofexplainingthegrammarofthecorrespondingpredicates,thenwefacedifﬁ-cultiesincountingtheseitemsasobjects—thedifﬁcultieswhichfacedFregeovertheconcepthorse.Ontheotherhand,ifwefollowRussellandtreatpredicatesinverymuchthemannerinwhichnameshadbeentreated,wewillbeatalosstoexplainhowpredicatesarecapableofcombiningwithsingulartermstoformwholesentences.Wittgenstein’ssolution,Ithink,istobequiteexplicitinthinkingofthemeaningofallexpressionsasbeingnomorethanthedifferencetheymaketothetruthorfalsityofsentencesinwhichtheyoccur.Asforwholesentencesthemselves,ifwetakethemtobecorrelatedwithobjectsintheworld,weseemtohaveachoicebetweentwooddtheories.OntheonehandisFrege’stheory,whichcorrelatessentenceswithtruth-values—theTrueandtheFalse—andtheseareveryoddentities.OntheotherhandthereisRussell’searlytheorywhichcorrelatedsentenceswithpropositions:thesentence‘OttolinelovesBertie’willbecorrelatedwiththepropositionthatOttolinelovesBertie,forexample.Theproblemthenistoexplainwhatitisforthatpropositiontoexistwhenthesentenceisfalse,sincetheactualexistenceofthepropositionseemstodependonOttoline’sactuallylovingBertie.Onceagain,\n198SENTENCESASMODELSWittgensteinavoidstheseproblemsbydenyingthatsen-tencesarecorrelatedwithanything.Allthatneedstobecommonbetweenasentenceandtherealityitdepictsisaform:thatis,itselementsmustbecapableofthesamerangesofpossiblecombinationasthecorrespondingobjectsare.Thereneedbenofalsefactcorrespondingtoafalsesentence.Somuchforproblem(P1).TheTractatus’ssolutiontoproblem(P2)isdevastatinglysimple.ThedifﬁcultyforbothFregeandRussellwasthattheyhadtoexplainthedistinctiveunityandcompletenessofwholesentencesintermsofsomethingexternaltolanguage.ButWittgensteindoesnot.Thisisbecause,forWittgenstein,sentencesthemselves—likeallpictures—arefacts.Afactisanentityintheworldwhichhasadistinctiveunity:exactlythekindofunitywhichsentencespossess,tobeprecise.ButWittgensteindoesnotneedtoexplaintheunityofsentencesintermsofthesupposedlypriorunityoffacts:instead,sentencesthemselveshavethisunity,becausetheyarethemselvesfacts,injustthesamewayasanyfactintheworldis.Thatmeansthattheunityofsentencesdoesnotneedtobeexplainedbyanythingelse.Noristheunityofasentencesomethingconstructed.ThisiswhereWittgenstein’shard-lineinsistenceontheletteroftheContextPrinciplecomesintoplay.Since,forWittgenstein,wordsstrictlydohavemeaningonlyinthecontextofasentence,itturnsoutthatthoseverywordscannotoccurexceptwithinsentences.Sosentencesarenotconstructedfrompartswhichmightoccurinisolation.Sentencesarecomposedofpartswhicharealwaysalreadypartofthem.Thereisthereforenoneedtounderstandhowthepartsofasentencecanbejoinedtogetherinawaywhichensuresthecompletenessandunityoftheresult:theyonlyoccurwithinanentitywhichalreadyhastherequiredcompletenessandunity.4HTHEMETAPHYSICSOFTHETRACTATUSInChapter1wediscernedthefollowingmajormetaphysicalcommitmentsoftheTractatus:\nSENTENCESASMODELS199(T1)Thebasicorganicunitiesoftheworldarefacts;(T2)Factsaredifferentinkindfromthings(objects);(T3)Factsareeitheratomicfactsorcombinationsofatomicfacts;(T4)Theexistenceofanyatomicfactisindependentoftheexistenceofanyotheratomicfact;(T5)Atomicfactsarecombinationsofobjects;(T6)Whichatomicfactsarepossibleisdeterminedbythenatureofobjects;(T7)Itisessentialtoanobjectthatitcancombinewithotherobjects,inthewaysitcan,toformatomicfacts;(T8)Nothingisessentialtoanobjectbeyondthefactthatitcancombinewithotherobjects,inthewaysitcan,toformatomicfacts;(T9)Objectsexistnecessarily;(T10)Itisnecessarythatjustthoseatomicfactsarepossiblewhichare,infact,possible.Thebulkofthesecommitmentsderivedirectlyfromthetheorythatsentencesaremodels.(T1)isultimatelyacon-sequenceofthesame-formassumption,(SM3).Aswesaw(section4C),thatassumptionleadsWittgensteintoinsistthatnamescannotbecombinedinwayswhicharenotmatchedbythewaysinwhichthecorrespondingobjectscanbecombined:therecanbenoillegitimatecombinationsofwords.Anditseemshardtoinsistthattherecanbenoillegi-timatecombinationsofnameswithoutinsistingthatnamescanonlyoccuratallinlegitimatecombinations—thatistosay,inwholesentences.Butifnamescanonlyoccurinwholesentences,andtherangeofpossiblecombinationofnamesmustbethesameastherangeofpossiblecombinationofobjects(as(SM3)requires),thenobjectscanonlyoccurincombinationwithotherobjectsinwholefacts.Thatmeansthatobjectscannotexistindependentlyofallotherobjects,oroffacts;ifanyentitiesatallcanexistindependentlyofotherentitiesofthesamekind,itisonlyfactswhichcandothat.Soifthereareanybasicorganicunities,inthissense,theymustbefacts.Wethereforegetaconditionalconﬁrmationof(T1):(T1)istrueifthereareanybasicorganicunities.\n200SENTENCESASMODELSThatfacts—or,atleast,atomicfacts—actuallyaresuchbasicorganicunitiesrequiresthemtobeindependentofoneanother.Theclaimthattheyareindependentofoneanotheristiedupwithtwootherbasiccommitmentsofthemeta-physicsoftheTractatus:(T3)and(T4).Thevindicationofthesetwocommitmentsdepends,strictlyspeaking,notsimplyonthetheorythatsentencesaremodels—sincethattheoryappliesdirectlyonlytoelementarysentences—buttotheTractatus’saccountoflogic.Accordingly,thesetwocommitmentswillbeconsideredinthenextchapter.Thatthereissomecontrast,however,betweenatomicfactsandfactsofotherkindsisrequiredbytheideathatnoteverysentenceis‘completelyanalysed’:thatistosay,noteverysentenceofeverydaylanguageconsistswhollyofnamesforobjectswhosepossibilitiesofcombinationarethefundamentalpossibilitiesoftheworld.(T2)and(T5)arereﬂectionsofthefactthatthereisadis-tinctiveissueabouttheunityoftheproposition.ThisissuepresentedFregeandRussellwithoneoftheprincipaldifﬁ-cultieswhichanytheoryoflanguageoftheirworld-orientedkindhadtodealwith:theunityofasentenceisdifferentfromtheunityofanyotherkindofthing,andseemstoneedaspecialkindofexplanation.InthetheoriesoftheearlyRussellandoftheTractatus,theunityofsentencesneedstobeunderstoodintermsoftheunityofaspecialkindofentityintheobjectiveworld—objective‘propositions’inRussell’searlytheory,andfactsinWittgenstein’s.Thepro-blemdisappearsonWittgenstein’saccount,aswehaveseen,intheinsistence(derivingfrom(SM3))thatsentencesthemselvesarefacts.Forallthat,hestillofferssomeaccountofwhatitisforafacttobeuniﬁed.Theunityofafactdoesnotconsist,accordingtoWittgenstein,inthepresenceofaspecialcopulativeelement—akindofpredicativeglue,asitwere—inafactwhichbindstheotherelementstogether.Rathertheunityofthefactsimplyconsistsoftheobjectsappearing,astheyalwaysdo,inthespecialkindofcombinationwithotherobjectswhichfactsare.Thisisthesigniﬁcanceof(T5),whichisthemetaphysicalcounterpartof4.22.\nSENTENCESASMODELS201(T6)followsfromtheTractatus’scommitmentsaboutthenatureofsubstance,combinedwiththethoughtthatthefundamentalpossibilitiesaresimplythepossibilitiesofcom-binationoftheobjectswhichcorrespondtonamesinfullyanalysedsentences.TheTractatus’stheoryofrepresentationrequiresthattheonlypossibilitieswhichcanberepresentedarethepossibilitiesofcombinationoftheobjectivecounter-partstotheelementsofmodels:alternativearrangementisjustthetheory’sconceptionofalternativepossibility.Andthetheoryofsubstanceiswhatgenerates(T7)–(T10).WeconsideredtheargumentfortheconceptionofsubstanceinChapter1.Aswesawthere(section1D),thespeciﬁcassumptionswhichtheargumentneedsarethese:(a)Inthebasiccase,asentenceisacombination(ahanginginoneanother)ofsymbols(names);(b)Inthebasiccase,forasentencetohavesenseisfortwocondi-tionstohold:(i)Itssymbolsarecorrelatedwithobjectsintheworld;(ii)Itispossibleforthesymbolstobecombinedinthewayinwhichtheyareactuallycombinedinthesentence;(c)Itispossiblefortheconstituentsymbolsofasentencetobecombinedinthewaytheyare,andbecorrelatedwiththeobjectswithwhichtheyarecorrelated,ifandonlyifitispossibleforthecorrespondingobjectstobecombinedinthesamewayinreality.Whatwehavehereisjustthebasicconceptionofmodelsappliedtothecaseofsentences.And,infact,aswesawinChapter1,thetextofthatargumentitselfadvertstothetheoryofrepresentation;whatapparentlyrequiresthattherebeobjectswhichsatisfytherequirementsof(T7)–(T10)isthefollowingallegedconsequenceoftherebeingnone:2.0212Itwouldthenbeimpossibletoformapictureoftheworld(trueorfalse).Itseems,then,thatallofthetenbasicmetaphysicalcom-mitmentsoftheTractatus,withtheexceptionof(T1),(T3),\n202SENTENCESASMODELSand(T4),followfromthebook’stheoryofthewayinwhichthemostbasicsentencesrepresenttheworld.Anditwillbeclearinthenextchapterthat(T1),(T3),and(T4)followfromthebook’saccountoflogic.Italsoseemsclearthatthemetaphysicsofthe1sandearly2scanbegroundedinthephilosophyoflanguageofthe3sand4swithoutitselfbeingobviouslyeitherrealistorideal-ist.Infact,thesymmetryofanynotionofsameness,includingtheoneinplayinthesame-formassumption,(SM3),suggeststhattheco-ordinationoflanguageandworldisitselfneutralontheissueofrealism.\n5LOGICANDCOMPOUNDSENTENCES5ATHEPROBLEMSThetheorythatsentencesaremodelsseemstoofferanaccountoflanguagewhichsolvesalargenumberoftheproblemswhichWittgensteininheritedfromFregeandRussell.Italsoseemstovindicateadistinctivemetaphysics,andsotocontributedecisivelytowhathasseemedtobeacentraltaskofphilosophy,throughoutitshistory.Forallthat,thetheoryasitstandsisincomplete,evenasanaccountoflanguage,intwoveryobviousways.Firstofall,thetheorythatsentencesaremodelsseemstoapplysofaronlytobasicnon-compoundsentences.Itseemsnottoapplystraightforwardlytoanycompoundsentences—sentenceswhichhavewholesentencesasparts—ortoanyofthesentencesofoureverydaylanguages,whichWittgensteinseemstoregardasgeneralstatementswhoseinstanceswouldbeelementarysentences.Soitseemsthatthetheorythatsentencesaremodelsappliesstraightforwardly\n204LOGICANDCOMPOUNDSENTENCESonlytosentenceswhichWittgensteinthinksmustbepossible,inprinciple—nottothesentencesweactuallyhave.And,second,noaccounthasyetbeengivenofalargeclassofsubsententialexpressions.Weknowthatsentencesaretakentobefacts,anddescribefacts(correctlyorincorrectly);theyarenotobjectsthemselves,andarenotmeaningfulinvirtueofbeingcorrelatedwithobjects.Weknowthatgenu-inesingularterms—thenamesofwhichelementarysen-tencesareformed—areheldtobemeaningfulinvirtueofbeingcorrelatedwithobjects.Itisplausibletosuggestthatthiscorrelationbetweennamesandobjectsissimplyamatteroftherebeingarulewhichcorrelateswholesentencesinwhichthenamesappearwithcertaintypesoffact.Andthisallowsatleastsomeexpressionswhichwemightpre-viouslyhaveregardedaspredicatestobeclassedasnames.WhatwedonotknowishowWittgensteinthinksthattheso-called‘logicalconstants’shouldbetreated.Wedonotknowhowhethinksthenegationsignismeaningful,orhowtheconnectiveswhichareatthebasisofmodernlogicalsystems—connectiveswhichtranslateordinary-languagetermslike‘if’,‘and’,and‘or’—aresupposedtowork.Andwedonotknowyetwhathisviewisofsignsofgenerality—inparticular,‘all’and‘some’.Sincealmostallsentencesofeverydaylanguagearetobeunderstoodintermsofgen-erality,onWittgenstein’sview,thisisaverysigniﬁcantlacunainthetheorysofar.Furthermore,inadditiontothesetwowaysinwhichtheaccountoflanguageisincomplete,theTractatushasnotyetaddressedanothermajorconcernwhichWittgensteininher-itedfromFregeandRussell,aconcernwhichmightindeedbethoughttounderliehiswholeattitudetophilosophy:toshowhowlogic(andwithitmathematics)wasindependentofeverythingtodowithintuitionoracquaintance,andtherebyrejecttheKantiancommitmenttosyntheticaprioritruths.5BWITTGENSTEIN’S‘FUNDAMENTALTHOUGHT’Thesecondparagraphof4.0312reads:\nLOGICANDCOMPOUNDSENTENCES205Myfundamentalthoughtisthatthe‘logicalconstants’donotrepre-sent.Thatthelogicofthefactscannotberepresented.TheGermanwordtranslatedas‘represent’here(‘vertreten’)isalsostandardlytranslated‘standfor’or‘deputise’.(PearsandMcGuinnesswrite‘Myfundamentalideaisthatthelogicalconstantsarenotrepresentatives’.)Thepointisthatthe‘logicalconstants’donotfunctionasnames,andthereareconsequentlyno‘logicalobjects’whichcorrespondtothem.Wittgensteinputsthepointlikethisalittlelater:5.4Hereitbecomesclearthattherearenosuchthingsas‘logicalobjects’or‘logicalconstants’(inthesenseofFregeandRussell).AswesawinChapter2(section2G),thisissomethingwhichRussellseemstohavevacillatedover,buthisﬁnalviewseemstobepresentedinthisremarkwhichwasquotedthere:Suchwordsasor,not,all,some,plainlyinvolvelogicalnotions;andsincewecanusesuchwordsintelligently,wemustbeacquaintedwiththelogicalobjectsinvolved.(Russell1984:99)AndFregeseemstohaveregardedwordslike‘or’,‘not’,‘all’,and‘some’asnamesoffunctionsofaspecialkind:so,althoughtheydonotstrictlystandforobjects,onFrege’sview,theyareneverthelessexactlywhatWittgensteinthinkstheyarenot—namesorrepresentativesofentitiesintheworld(Frege1893:28).Wittgensteinofferswhatlookslikeadecisiveargumentforhisviewthatthe‘logicalconstants’arenotnamesofconstituentsoffacts:Andiftherewasanobjectcalled‘~’,then‘~~p’wouldhavetosaysomethingotherthan‘p’.Foronepropositionwouldthentreatof~,theotherwouldnot.(5.44)\n206LOGICANDCOMPOUNDSENTENCESThisdisappearanceoftheapparentlogicalconstantsalsooccursif‘~(9x).~fx’saysthesameas‘(x).fx’[‘8x.fx’insomenotations],or‘(9x).fx.x=a’[‘9x(fx&x=a)’insomenotations]thesameas‘fa’(5.441).Thekeyassumptionhereisthat‘p’and‘~~p’saythesamething.Whatisthejustiﬁcationforthat?Wittgensteingivesthisaccountofwhatasentencesays:4.022Apropositionshowsitssense.Apropositionshowshowthingsstand,ifitistrue.Anditsays,thattheysostand.Inthebasiccase,whatasentenceshowsisjustacertainpossiblearrangementoftheobjectswhichitsconstituentnamesreferto.Whatitsaysis,then,justthattheobjectsare,infact,arrangedinthatway.Whatmattershereisthattwosentenceswhichrepresentthesamepossiblearrangementofobjectswillhavethesamesense,andwillthereforesaythesamething.ItisimportanttonoteherethatWittgenstein’snotionofsenseisnotanepistemicnotion,likeFrege’s:itisconcernedjustwithobjectivepossibilities.Wegetfromthisthoughttowhatweneedfortheargu-mentof5.441byrecallingthat,forWittgenstein,allpossi-bilityisultimatelyamatterofthepossiblearrangementsofobjects(seeChapter1,section1D,above).Iftwosentencesaretrueinexactlythesamepossiblesituations,theymustrepresentthesamepossiblearrangementofobjects,andthereforemustsaythesamething.Evidently,‘p’and‘~~p’aretrueinexactlythesamepossiblesituations:consequently,theymustsaythesamething.Oncethisisgranted,thepointhasmuchwiderapplication.Infact,allthedifferentlogicalconnectives(apartfromnegation)whichareinuseinstandardmodernlogiccanbedeﬁnedusinganotherofthem,togetherwithnegation.So‘pq’isequivalent(forexample)to‘~pvq’;‘pvq’isequivalentto‘~(~p&~q)’;and‘p&q’isequivalentto‘~\nLOGICANDCOMPOUNDSENTENCES207(p~q)’.Indeed,HenrySheffer(1913)hadalreadyprovedthatasingleconnectivewasenough.1Thiscaneitherbe‘alternativedenial’,sometimesknownasNAND(‘notbothpandq’),or‘jointdenial’,alsoknownasNOR(‘neitherpnorq’).Itisnowquitecommontoexpresstheﬁrstbymeansof‘|’(‘p|q’)andrefertoitastheShefferStroke,andthelatterby‘#’(‘p#q’)andrefertoitastheShefferDagger(althoughoriginallytheShefferStrokewasusedforjointdenial,asinSheffer’spaperandTractatus5.1311,andthispracticeisstillsometimesfollowed).2IwillfollowthenowcommonpracticeofusingtheShefferDaggerforjointdenial.Wittgenstein’sclaimisthis:ifthelogicalconstantsfunc-tionedlikenames,thentherewouldbeobjectscorrespondingtothem,andthetruthofsentencesinvolvingthoseconstantswoulddependonhowthingswerewiththoseobjects.Thiswouldmeanthattherealitydepictedby‘~~p’wouldhavetobeamatterofthewayinwhichtheobject,~,wasrelatedtotheotherobjectscorrelatedwiththenamesin‘p’.‘p’and‘~~p’wouldthenhavetohaveadifferent‘logicalmultiplicity’(see4.04).Thesameproblemholdsfortheinterdeﬁnabilityoftheotherconnectives.Aformulainvolvingoneconnectivewouldinevitablyhaveadifferentlogicalmultiplicityfromthatofitstranslationintermsofanotherconnective,iftheconnectivesweretreatedasnames.(ThetranslationofnegationintermsofeithertheShefferStroke(alternativedenial)ortheShefferDagger(jointdenial)isparticularlystrikinghere:‘~p’isrenderedas‘p|p’or‘p#p’;whichmakes‘p’equivalentto‘(p|p)|(p|p)’or‘(p#p)#(p#p)’.)Wittgensteinalsooffersanotherargumentfortheclaimthatthefamiliarlogicalconstantsarenotcorrelatedwithanykindof‘logicalobject’:4.0621That,however,thesigns‘p’and‘~p’cansaythesamethingisimportant,foritshowsthatthesign‘~’correspondstonoth-inginreality.Thatnegationoccursinaproposition,isnocharacteristicofitssense(~~p=p).\n208LOGICANDCOMPOUNDSENTENCESThepropositions‘p’and‘~p’haveoppositesenses,buttothemcorrespondsoneandthesamereality.Howisitthat‘p’and‘~p’cansaythesamething?Theclueliesinthephrase‘oppositesenses’,whichisreminiscentoftheaccountoftherelationbetweensentencesandrealitywhichwasoriginallyofferedasanaccountofthemeaningof‘forms’:Buttheformofapropositionsymbolizesinthefollowingway:Letusconsidersymbolsoftheform‘xRy’;tothesecorrespondprimarilypairsofobjects,ofwhichonehasthename‘x’,theotherthename‘y’.Thex’sandy’sstandinvariousrelationstoeachother,amongotherstherelationRholdsbetweensome,butnotbetweenothers.Inowdeterminethesenseof‘xRy’bylayingdown:whenthefactsbehaveinregardto‘xRy’sothatthemeaningof‘x’standsintherelationRtothemeaningof‘y’,thenIsaythatthe[thefacts]are‘oflikesense’withtheproposition‘xRy’;otherwise,‘ofoppositesense’;Icorrelatethefactstothesymbol‘xRy’bythusdividingthemintothoseoflikesenseandthoseofoppositesense.Tothiscorrelationcorrespondsthecorrelationofnameandmeaning.Botharepsycho-logical.ThusIunderstandtheform‘xRy’whenIknowthatitdis-criminatesthebehaviourofxandyaccordingasthesestandintherelationRornot.InthiswayIextractfromallpossiblerelationtherelationR,as,byaname,Iextractitsmeaningfromallpossiblethings.(NL104)3Thecrucialsentencehereisthisone:‘Icorrelatethefactstothesymbol“xRy”bythusdividingthemintothoseoflikesenseandthoseofoppositesense’.Thereisnoindependentnotionofsimilaritybetweenthearrangementofnamesaroundthesymbol‘R’,ontheonehand,andthearrange-mentofobjectsintheworld,ontheother.Thesimilarityofformisconstitutedbydeterminingthatsomearrangementsofobjectscountasbeing‘oflikesense’withsentencesoftheappropriateform.Thismeansthatthosearrangementsofobjectswhichwenowcountasbeing‘ofoppositesense’couldhavebeencountedasbeing‘oflikesense’withsentencesoftheform‘xRy’.\nLOGICANDCOMPOUNDSENTENCES209IsuggestedinChapter4thatthisaccountofthemeaningofso-called‘forms’wasnotabandonedbyWittgensteinintheTractatus,butgeneralizedtoincludeeverykindofexpres-sion—althoughwithoutthecommitmentwhichisfoundinthispassagefromtheNotesonLogictotheideathatonecould,asitwere,haveaccesstotheworldandallitsfactsneat,independentlyofalreadypossessingalanguage.Iftheaccountofthemeaningof‘forms’intheNotesonLogicisnowfunctioning(withoutcommitmenttothepossibilityofneataccesstothefacts)asthegeneralaccountofthemean-ingofexpressionsinelementarysentences—ineffect,astheaccountofthecorrelationofanamewithitsobject—wecanreadilyunderstandhow‘p’and‘~p’cansaythesamething:thebasiccorrelationofsymbolswithrealityalreadypresupposesthepossibilityofaconversecorrelation,withwhatistakentobe‘oflikesense’ononeassignmentcount-ingasbeing‘ofoppositesense’ontheother,andviceversa.What,then,isthefunctionof‘~’onthispicture?Itsfunctionissimplytoswitchthe‘senses’ofasentence:thatis,whatcountsasbeing‘oflikesense’withasentenceisdeter-minedasbeing‘ofoppositesense’withitsnegation,andviceversa.Andessentiallythesameaccountisprovidedofthefamiliar‘logicalconstants’ingeneral.Theotherfamiliarlogicalconstantsdonotmodifythe‘sense’ofjustasinglesentence,ofcourse:whattheydo(toputitcrudely)iscom-bineanumberofsentenceswitheachother.Wittgenstein’sideaisjustthis:thebusinessofthefamiliarlogicalconstantsissimplytodeterminewhichfactscountasbeing‘oflikesense’andwhich‘ofoppositesense’withcompoundsen-tences,giventhatitisﬁxedwhichfactscountasbeing‘oflikesense’andwhich‘ofoppositesense’withthesentenceswhicharetheircomponents.Thenotionsoflikenessandoppositenessof‘sense’areobviouslylinkedwiththenotionsoftruthandfalsity.Thefactswhichare‘oflikesense’withaclassofsentencesarethefactswhichmakethosesentencestrue;andthosewhichare‘ofoppositesense’arethosewhichmakethemfalse.Sincethefamiliarlogicalconstantscanbeexplainedinterms\n210LOGICANDCOMPOUNDSENTENCESofwhattheydeterminetobe‘oflikesense’and‘ofoppositesense’withacompoundsentence,givenwhichfactscountasbeing‘oflikesense’and‘ofoppositesense’withitscompo-nents,itisclearthattheirmeaningcanbecharacterizedintermsoftruth-tablesofakindwhichisnowfamiliar.Wittgensteinissometimescreditedwithinventingthetruth-tableaswenowknowit,althoughthisisalsosome-timesquestioned(Landini2007:118–24).4Howeverthatmaybe,Wittgensteincertainlydoesusetruth-tablesintheTractatus.Usingatruth-table,wecandeﬁnenegation,‘~p’asfollows:ppeTFFTAndwecandeﬁne‘pq’likethis:5pqpqTTTFTTTFFFFTThistruth-tablegivesustheruleforcomputingthetruth-valueofcompoundsentencesoftheform‘pq’,givenjustthetruth-valueofthecomponentsentences.Bythesametoken,itprovidestherulewhichdetermineswhatitisforsuchcompoundsentencestobe‘oflikesense’withthefacts.Ifthetruth-tablegivesusarulewhichexplainsthewayinwhich,asWittgensteinwouldputit,‘pq’‘symbo-lizes’,wecanusethetruth-tabletorevealthatexplicitly,andremovethetemptationtothinkofthesign‘’asaname:\nLOGICANDCOMPOUNDSENTENCES211Ifthesequenceofthetruth-possibilitiesintheschema[thetruth-table]isonceforalldeterminedbyaruleofcombination[thatis,ifwehavesettledtheorderinwhichwewritedowntherowsontheleftofthetruth-table],thenthelastcolumnisbyitselfanexpressionofthetruth-conditions.Ifwewritethiscolumnasarowtheproposi-tionalsignbecomes:…‘(TTFT)(p,q)’.(Thenumberofplacesintheleft-handbracketisdeterminedbythenumberoftermsintheright-handbracket.)(4.442)Thesuggestionisthatwemightsimplyuse‘(TTFT)(p,q)’toexpresswhatwenormallyexpressbymeansof‘pq’.Anyexpressionwhosemeaningcanbedeﬁnedusingatruth-tableiscommonlycalledatruth-function(becauseitsmeaningconsistsinthefactthatitsoutputhascertaintruth-valuesgiventhetruth-valuesoftheinputs).Wittgensteinhimselfpreservesthisuseoftheterm‘truth-function’,eventhough(aswewillseeinamoment)hisviewisthattruth-functionsarenotproperlycalledfunctionsatall.WecanuseWittgenstein’srotated-truth-tablenotation(asin‘(TTFT)(p,q)’)toshowthewayinwhichanytruth-functionalwayofcombiningsentencessymbolizes,nomatterhowmanysen-tencesareinvolved—providedthatwearedealingwithaﬁnitenumberofsentences,expressingaﬁnitenumberofpossibleatomicfacts.Wittgensteinhasalreadygiventheformulawhichdeﬁnesthenumberofrowsweneedinourtruth-tables.Ifwearedealingwithnpossibleatomicfacts,eachofwhichmightormightnotobtainindependentlyofalltheothers,wearedealingwithKnpossibilities,onthecharacterizationofKwhichisprovidedin4.27.6Giventhatntherearejusttwopossibilitiesforeachatomicfact—obtainingornotobtaining—Kwillbeequalto2n.Andnsincethesepossibilitiesofexistenceandnon-existenceofatomicfactsareexpressedinthetruthandfalsityofele-mentarysentences,thesameformulaappliestotherowsweneedinourtruth-tables.Ifwearegivingatruth-tableforatruth-functionalcombinationofnelementarysentences,wewillneedK(i.e.,2n)rowsinourtruth-table.Soifwearen\n212LOGICANDCOMPOUNDSENTENCESdealingwithatruth-functionalcombinationoftwosen-tences,ourtruth-tablewillneedtohave22(=4)rows;ifwithonewhichcombinesthreesentences,wewillneed23(=8)rows;ifwithonewhichcombinesfoursentences,24(=16)rows;andsoon.OncewehaveWittgenstein’saccountofthefamiliarlogi-calconstants,togetherwiththisdeviceforreplacingthefamiliarsymbolsbymeansofarotated-truth-tablecolumn,weshouldhaveremovedanytemptationtothinkofthelogicalconstantsasnameswhicharecorrelatedwithaspecialkindofentityintheworld.Butitisworthtakingalittlecareoverhowtheyshouldbeunderstood.WewillrememberRussellstartingoffwithsimilarintentions:‘Logicalconstants’,whichmightseemtobeentitiesoccurringinlogicalpropositions,arereallyconcernedwithpureform,andarenotactuallyconstituentsofthepropositionsintheverbalexpressionofwhichtheirnamesoccur.(1984:98)Butwesawthathefoundhimselfdriven,byvariousepiste-mologicalconsiderations,toconsiderthese‘pureforms’asobjectsofacquaintance,andhence,ultimately,as‘logicalobjects’(1984:99).Wittgenstein,however,rejectsRussell’sconceptionoflogicalconstantsas‘pureforms’.Theapplicationofalogicalconstanttoasentencehecallsanoperation;andconcerningsuchoperationshesaysthis:5.241Theoperationdoesnotcharacterizeaformbutonlythediffer-encebetweenforms.AndwecanunderstandwhyWittgensteinwassokeentoinsistonthis,ifIamrightinmyinterpretationofhimasgeneralizinghisearlieraccountofthemeaningofforms,sothatitbecomesageneralaccountofthemeaningofexpres-sionsfromwhichelementarysentencesarecomposed.ItisobviouseveninthecharacterizationintheNotesonLogic\nLOGICANDCOMPOUNDSENTENCES213thatthereisatleastaverycloseparallelbetweenthecorrelationssetupbetweennamesandobjects,ontheonehand,andthosebetween‘forms’andthefactswhichcountasbeingoflikeandofoppositesensewiththem,ontheother.Ifwesimplycountedlogicalconstantsas‘forms’wewouldnothavepre-ventedtheirunderstandingbeingamatterofunderstandingacorrelationbetweensentencesandtheworld.Wewouldnothaveremovedthetemptationtothinkthatsomekindofintuitionoracquaintanceisneededtounderstandthem.Wittgenstein’sdescriptionofatruth-functionaloperatorassimplycharacterizinga‘differencebetweenforms’isbothsufﬁcienttoavoidthistemptation,andpreciseinitsdescrip-tionoftheirrole,onWittgenstein’sowntheory.Whatsuchoperatorsdoissimplydeterminelikenessandoppositenessof‘sense’forcompounds,giventhedeterminationoflikenessandoppositenessof‘sense’fortheircomponents.WhatWittgensteinisdoingherebelongswithhisrejectionofthetemptationtoassimilatesentencestonames,whichisoneofthecornerstonesoftheTractatus.Thisleadshimtoadoptanimportantdistinctionofterminology.AlthoughWittgensteincontinuestousethealreadyfamiliarterm‘truth-function’,hisviewisthattruth-functionsshouldnotreallyberegardedasfunctionsatall.Weneedtorecallsomeofthehistoricalbackgroundtounderstandthepointbeingmade.OnFrege’stheory,functionsarethereferentsofcer-tainkindsofexpression:ineffect,theyare‘unsaturated’orincompletereferents—thereferentsof(thingsreferredtoby)expressionswhicharethemselvesvisiblyincomplete.TheytherebycontrastforFregewithobjects,which,onhistheory,are‘saturated’orcomplete.Inthesimplestcase,afunctiontakesoneormoreobjectsasinput(orargument),andyieldsasingleobjectasoutput(orvalue).So‘xisugly’isafunctionforFrege:supplyanobjectforx,andtheresultisanotherobject—eithertheTrueortheFalse,dependingonwhetherxisorisnotugly.Andagain‘~p’(where‘p’isstrictlyavariable)isafunction:supplyanobject—inthiscaseeithertheTrueortheFalse—asthereferentof‘p’,andtheresultis,onceagain,anobject—eithertheFalseortheTrue.\n214LOGICANDCOMPOUNDSENTENCESThewholeofthisapparatusneedstobechanged,onWittgenstein’saccount.Firstofall,wewillnotwanttocountsuchexpressionsas‘xisugly’asreferringtofunctions,becausethepointofthatistomakeacontrastbetweenfunctionsandobjectsamongtheitemscorrelatedwithbasicexpressionsinelementarysentences;andWittgenstein’sviewisthattheitemscorrelatedwithbasicexpressionsinelementarysentencesareallobjects(though,ofcourse,thatmeansthathecannolongerregardallobjectsasunpro-blematically‘saturated’orcomplete).And,second,hewillnotwanttoregardsuchexpressionsas‘~p’asreferringtoanything:thatmisconceivesthewaytheyworkaltogether,onWittgenstein’saccount.SoWittgensteinreservestheword‘function’forsome-thingwhichisnotthereferentofanybasicexpressionofelementarysentences.Thekindoffunctionwhichconcernshimisapropositionalfunctioninthefollowingsense.Insteadofbeingsomethingwhichanexpressionrefersto,itisitselfanexpression—moreparticularly,anexpressionwhichtakesanotherexpressiontoformapropositionorsentence.Forexample,theexpression‘nwasrich’isafunc-tionwhichtakesthename‘Wittgenstein’asinput(orargu-ment)toyieldthesentence‘Wittgensteinwasrich’asoutput(orvalue).Thatistosay,tocallanexpressionafunctionistosaysomethingaboutitsgrammar,notaboutitsreferent.AfunctioninWittgenstein’sterminologyiswhatwenowcallapredicate:somethingwhichtakesoneormorenames(orsingularterms)toformasentence.7Forthispointsee,forexample,thesetworemarks:3.318Iconceivetheproposition—likeFregeandRussell—asafunctionoftheexpressionscontainedinit.TheelementarypropositionIwriteasfunctionofthenames,intheform‘fx’,‘u(x,y)’,etc.(4.24)Anoperation(weoftencallitanoperator),ontheotherhand,isanexpressionwithaquitedifferentgrammar.Atleastfor\nLOGICANDCOMPOUNDSENTENCES215thecasehehasinmindhere(theso-calledtruth-functions),thedifferencecanbecharacterizedverysimply.Whereasafunctiontakesoneormorenamestoformawholesentence,whatanoperationdoesistakeoneormorewholesentencestoformanotherwholesentence.ThusWittgensteinsaysthatwecanpresent‘apropositionastheresultofanopera-tionwhichproducesitfromotherpropositions(thebasesoftheoperation)’(5.21).Andagain:5.23Theoperationisthatwhichmusthappentoapropositioninordertomakeanotheroutofit.Giventhatthedistinctionbetweennamesandsentencesisfun-damentalforWittgenstein,itisnotsurprisingthathesaysthis:Operationandfunctionmustnotbeconfusedwithoneanother.(5.25)AndthenextsentencemarksanimportantrespectinwhichWittgensteinthinksthatoperationsandfunctionsdiffer:5.251Afunctioncannotbeitsownargument,buttheresultofanoperationcanbeitsownbasis.Aswewillsee,thiswillbecrucialforWittgenstein’streatmentofarithmetic.5CTHEN-OPERATORThereisanobviouslacunainWittgenstein’streatmentofthe‘logicalconstants’sofar:whataboutthequantiﬁers—and,indeed,generalityingeneral?Howdothequantiﬁerswork?WehavealreadyseenthatWittgensteintooktheequivalenceof‘~(9x).~fx’and‘(x).fx’(‘8x.fx’insomenotations)toshowthatthesymbolsheredonotfunctionasnames.Buthowcanweunderstandthemascharacterizing‘differencesbetweenforms’?TheansweristhatWittgensteinoffersatruth-functionalaccountevenofthequantiﬁers.\n216LOGICANDCOMPOUNDSENTENCESThetruth-functionaloperatorsofstandardlogicalsystemseithertakejustonesentencetoformasentence(inthecaseofnegation)orjusttwosentencestoformasentence(inthecaseoftheothers).ButWittgenstein’srotated-truth-tablenotationcanbeadaptedtoprovideauniformtreatmentofcombinationsofanynumberofsentences.Wittgenstein’saccountofthequantiﬁers—andhisﬁnalaccountofthewholerangeoflogicalconstants—dependsonanadaptationofthisthought.RecalltheShefferDagger,‘p#q’,whichrepresentsjointdenial(‘neitherpnorq’).Itispossibletodeﬁneallofthestandardtruth-functionsinitsterms.TheShefferDagger,likemoststandardconnectives,takestwosentences(the‘p’andthe‘q’)toformasentence.WittgensteinﬁrstintroducesageneralizedvariantoftheShefferDaggerusinghisrotated-truth-tablenotation:5.5Everytruth-functionisaresultofthesuccessiveapplicationoftheoperation(-----T)(n,.…)toelementarypropositions.Thisoperationdeniesallthepropositionsintheright-handbracketandIcallitthenegationofthesepropositions.Herethenotationintheﬁrstbracket—‘(-----T)’—ismeanttoindicatethattheoperationyieldsthevaluetrueonlyatthelastlineofthetruth-table—thelineatwhichallofthecomponentsentencesaregiventhevaluefalse.(Thereisanintuitiveoddityaboutthisexpression,sinceitisunclearhowitsbeginningistobewritten,untilithasbeendeter-minedhowmanyelementarysentencesweareconsidering.)WittgensteinthentakesthebasicideaofthegeneralizedShefferDaggerandprovidesamoreperspicuousnotationforexpressingit.First(in5.501),heintroducesavariable,‘n’,whichcantakeasvaluesanyofapre-determinedrangeof–sentences.Thenhewritesalineaboveit—‘n’—toindicatethatallofthesentencesinthatpre-determinedrangearetobetreatedtogether.Finally,heintroducesasymbol—‘N(…)’—whichexpressesthejointdenialofanysen-–tencesindicatedwithinthebrackets.Theresultisthat‘N(n)’\nLOGICANDCOMPOUNDSENTENCES217expressesthejointdenialofallofthesentencesintherangeofvaluesforthevariable‘n’:–5.502ThereforeIwriteinsteadof‘(-----T)(n,.…)’,‘N(n)’.–N(n)isthenegationofallthevaluesofthepropositionalvariablen.Wecanobviouslyexpressallofthestandardsententialcon-stantsusingthisoperator,bycarefulpre-determinationoftherangeofsentenceswhichcanbevaluesofthevariable‘n’,andrepeatedapplicationsofthe‘N’-operator.Tomakethisclear,itwillbeconvenienttohaveawayofindicatingtherangeofvaluesof‘n’whichwecankeeptabson.So,forexample,iftherangeof‘n’isrestrictedtojustthesingle–sentence‘p’,wecanreplace‘n’withjust‘p’;ifitisthethree–sentences‘p’,‘q’,and‘r’,wemightreplace‘n’with‘p,q,r’.(ThisisthenotationalruleWittgensteinhimselfprovidesin5.501.)Thus,ifwerestricttherangeof‘n’tothesingle–sentence‘p’,‘N(n)’—‘N(p)’here—isequivalentto‘~p’(5.51).Andwecanexpress‘pq’byseveralapplicationsof‘N’,asfollows.First,werestrict‘n’tothesinglesentence‘p’,andapply‘N’tothat—as‘N(p)’.Thenwelettherangeofthevariablebethetwosentences‘N(p)’and‘q’,andapply‘N’tothose—as‘N(N(p),q)’.Andthenwelettherangeofthevariablebejusttheresultofthat—‘N(N(p),q)’—andapply‘N’tothat.Weendupwithasentence—‘N(N(N(p),q))’—whichmeansnot:neithernot-pnorq,andisequivalentto‘pq’.WittgensteinthenusestheN-operatortoexplainquanti-ﬁcation:5.52Ifthevaluesofnarethetotalvaluesofafunctionfxforallvalues–ofx,thenN(n)=~(9x).fx.Whatisgoingonhere?Intheﬁrstplace,itisimportanttobeclearthatWittgensteinisnothereproposingtodeﬁneuniversalquantiﬁcationsimplyintermsofconjunction—‘(x)fx’asequivalentto‘fa&fb&fc&fd&…’—orexistentialquantiﬁcationsimplyintermsofdisjunction—\n218LOGICANDCOMPOUNDSENTENCES‘(9x)fx’asequivalentto‘favfbvfcvfdv…’.At5.501Wittgensteindistinguishesbetweenthreedifferentwaysofdeterminingtherangeofvaluesofthevariable‘n’:1.Directenumeration.Inthiscasewecanplacesimplyitscon-stituentvaluesinsteadofthevariable.2.Givingafunctionfx,whosevaluesforallvaluesofxarethepro-positionstobedescribed.3.Givingaformallaw,accordingtowhichthosepropositionsareconstructed.Inthiscasethetermsoftheexpressioninbrackets[intheconstruction‘N(…)’]areallthetermsofaformalseries.Thedirect-enumerationmethodistheonewehavealreadyencounteredinexplainingthestandardtruth-functionalconnectivesintermsoftheN-operator:thisiswhatwould,ineffect,beinplayifuniversalquantiﬁcationwerebeingdeﬁnedsimplyintermsofconjunctionandexistentialquantiﬁcationsimplyintermsofdisjunction.Butin5.52Wittgensteinisobviouslyadoptingmethod2—deﬁningtherangeofthevariable‘n’astherangeofvaluesofafunction.Therearetwoobviousproblemswithdeﬁninguniversalquantiﬁcationintermsofconjunctionandexistentialquan-tiﬁcationintermsofdisjunction.Theﬁrstisthatgeneralstatementsareunspeciﬁc:theydonotactuallysaywhichthingshavetherelevantproperty;indeed,theydonotactu-allymentionthosethingsatall.ThisisapointWittgensteinhasalreadymade(3.24),anditconstituteshisargumentfortheclaimthatitmustbepossiblefortheretobesimplesigns,andelementarysentenceswhichconsistsolelyofthem(aswesawinChapter4,section4E).Thesecondproblemisthatifgeneralizationsaredeﬁnedintermsofconjunctionsordisjunctions,itishardtoseehowthegeneralizationscanrangeoveraninﬁnitenumberofobjects:afterall,aconjunctionordisjunctioncanonlybeﬁnitelylong.DoesWittgenstein’saccountavoidtheseproblems?Alittleexplanationisneededbeforethiscanbesettled.FirstweneedtorecallwhatWittgensteinmeansby‘function’,asthe\nLOGICANDCOMPOUNDSENTENCES219termisusedin5.52.Whathehasinmindiswhathesometimescallsa‘propositionalfunction’:thatis,itissomethingwhichyieldsawholesentencewhenaparticularname,orsetofnamesisspeciﬁed.Workingfromtheotherend,itistheresultofreplacingoneormorenamesinasentencewithavariable.Thefunction‘fx’is,then,pre-sumablysomethingwhichyieldsasentencewhenaparti-cularnameisputinplaceofthe‘x’;andtherangeofvalues(outputs)ofthatfunctionisallthesentenceswhichresultfromreplacingthe‘x’withaname.Suppose,then,thattherearejustthreesentenceswhichmightbeconsideredhere:‘fa’,‘fb’,and‘fc’.Thosethreesentencescanbepickedoutasvaluesofthevariable‘n’fortheN-operatoreitherbydirectenumeration,or,simply,asthevaluesofthefunction‘fx’.IntheexplanationofhowtheN-operatorcanbeusedtogivethemeaningof‘pq’,wefounditconvenienttoindicatewhichsentencesweweretakingasvaluesofthevariable‘n’atdifferentpoints,byadoptinganotationalrulewhichallowedustowritesome-–thingotherthan‘n’withinthebracketsin‘N(…)’.Forthecaseof‘pq’,therangeofvaluesofthevariablecouldbeindicatedbysimpleenumeration(method1),soIfollowedWittgenstein’sowndevice(speciﬁedin5.501,undermethod1)ofsimplylistingthesentenceswithinthebrackets.Weneedtoadoptsomeotherdevicewhenthevaluesofthevariable‘n’aredeterminedbyafunction,asinthecaseofWittgenstein’saccountofquantiﬁcation:Wittgensteindoesnothimselfofferanysuggestion.8WecangetwhatwewantbyadaptingWittgenstein’snotationforfunctionsslightly,anduseexpressionsoftheform‘x:ux’accordingtothefollowingrule:(F)Whenusedwithinthebracketsin‘N(…)’,‘x:ux’indicatesthewholerangeofsentenceswhicharevaluesofthefunction‘ux’forallvaluesof‘x’.9Adoptingthisnotationalrule,wecanuse‘x:fx’withinthebracketsof‘N(…)’toindicatethevaluesofthefunction‘fx’.\n220LOGICANDCOMPOUNDSENTENCESSowecanuse‘N(x:fx)’tosaythatallthesentencesoftheform‘fx’—allthesentenceswhichareformedbyreplacingthe‘x’in‘fx’withaparticularname—arefalse.ThisiswhatWittgensteintakestobeequivalentto‘~(9x)fx’in5.52.IfwethenapplytheN-operatortothissentenceinturn,weendupwith‘N(N(x:fx))’,which,accordingtoWittgenstein,willbeequivalentto‘~~(9x)fx’,or‘(9x)fx’.Thisgivesusanaccountofexistentialquantiﬁcation.Wehaveheresomethingwhichis,inasense,equivalenttothedisjunction‘favfbvfc’,intheimaginedsituationwherethereareonlythreesentencesoftherelevantform,althoughitdiffersfromitinnotexplicitlymentioninganyoftheobjectsa,b,orc.Letustrytousethesameproceduretoprovideanaccountofuniversalquantiﬁcation.Again,forsimplicity,supposethatwehavejustthreesentencesoftheform‘fx’:‘fa’,‘fb’,and‘fc’.EachofthesecanbenegatedusingtheN-operator:as‘N(fa)’,‘N(fb)’,and‘N(fc)’.Thesenegationsallhaveacommonform:theyarevaluesofthefunction‘N(fx)’.10Usingourrule(F),wecanusetheexpression‘x:N(fx)’withinthebracketsof‘N(…)’toindicatethewholerangeofvaluesofthefunction‘N(fx)’.Theexpressionweendupwith,‘N(x:N(fx))’,saysthatnoneofthenegations—noneofthevaluesofthefunction‘N(fx)’—istrue.Thatistosaythatallofthenegatedsentences—allofthevaluesofthefunction‘fx’—aretrue.So‘N(x:N(fx))’seemstobeequivalentto‘(x)fx’,andwehaveanaccountofordinaryuniversalquantiﬁcation.Wehavesomethingwhichis,ineffect,equivalenttotheconjunctionofthesentences‘fa’,‘fb’,and‘fc’inthepeculiarcircumstanceswehaveimagined;butitdiffersfromtheconjunctioninexplicitlymentioningnoneoftheobjectsa,b,orc.ThisexplanationhasalreadyshownushowWittgenstein’saccountofquantiﬁcationdiffersfromonewhichdeﬁnesexistentialquantiﬁcationintermsofdisjunction,anduni-versalquantiﬁcationintermsofconjunction,inthatitallowsthatquantiﬁedsentencesdonotinvolveexplicitlymention-inganyoftheobjectsinthedomainofquantiﬁcation.Does\nLOGICANDCOMPOUNDSENTENCES221hismethodallowustoquantifyoverinﬁnitenumbersofobjects—theothercrucialpointofdifferencebetweenquantiﬁcation,asordinarilyunderstood,anddisjunctionandconjunction?Ithinkthistooisrelativelyunproblematic.11Wittgensteinseemsquitehappytosupposethatthereareinﬁnitelymanynamesinalanguage:Whattheaxiomofinfinity[theassumptionthatthereareinfinitelymanyindividualobjects]ismeanttosaywouldbeexpressedinlan-guagebythefactthatthereisaninfinitenumberofnameswithdifferentmeanings.(5.535)Andthiswillmeanthatthereareinﬁnitelymany‘valuesofx’togenerate‘valuesofafunctionfx’.Howcanwesupposethatthereareinﬁnitelymanynamesinalanguage?Itisnaturaltothinkthatthissuppositionamountstonothinggranderthanthesuppositionthatthereisalready,withinthelanguage,amechanismforgeneratinganinﬁnitenumberofnameswithdifferentmeanings.(Standardnumeralsystemsmightbetakentobeexamplesofsuchmechanisms.)ThispointservestolessentheimportanceofanissuewhicharisesinconnectionwithWittgenstein’saccountofquantification:areWittgenstein’squantiﬁersobjectualorsubstitutional?Wecanexplainthedifferenceasfollows.12Supposewestartwithananglicizedquantiﬁer-variablesentence:(B)Forsomex,xisbeautiful.Totreatthisobjectually,weproceedasfollows.Wetakeourselvestohavesomerelativelywell-deﬁneddomainofobjects.Then(B)istrueifthepredicate‘xisbeautiful’istrueofatleastoneobjectinthedomain.Conversely,totreatthissubstitutionally,wesaysimplythat(B)istrueifthereisatleastonetruesubstitution-instanceof‘xisbeautiful’:thatistosay,thatatleastonesentencewhichresultsfromrepla-cingthevariable‘x’in‘xisbeautiful’withanameistrue.\n222LOGICANDCOMPOUNDSENTENCES‘Ganymedeisbeautiful’mightbesuchasubstitution-instance;ifitistrue,then(B)istrue,onthesubstitutionalreading.Thedifferencebetweenthesetworeadingslookslessseverewhenweaskwhatitisforapredicatetobetrueofanobjectinadomain.Theanswerwhichitisnaturaltogive,forthecaseof‘xisbeautiful’isthis:‘xisbeautiful’istrueofanobjectjustincase,ifwetreatthe‘x’in‘xisbeautiful’temporarilyasanameofthatobject,‘xisbeautiful’sounderstoodisatruesentence.13Evenso,thetwointerpretationsofthequantiﬁersdodiffersigniﬁcantly,ifwemakeoneoftwoassumptions.Oneassumptionisthattherearesomeobjectswhichhavenonames:inthatcase,thoseobjectswillbebeyondthereachofsubstitutionalquantiﬁcation.Theotherassumptionisthattherearesomemeaningfulnameswhicharecorrelatedwithnoobjects(wemightthinkthatthisistrueofﬁctionalnames,forexample).Ifwemakethissecondassumption,theremaybesometruesubstitution-instancesofapredicate,evenwhenthepredicateisnottrueofanyobject.ButWittgensteinmakesneitheroftheseassumptions.First,aswehavejustseen,heseemshappy,inprinciple,toaccepttheexistenceofinﬁnitelymanynames,andthisseemstoensurethatitwillbepossibleforanyobjecttohaveaname.14And,second,hedoesnotallownamestobemean-ingfulunlesstheyarecorrelatedwithobjects.Thismeansthatthedifferencebetweenobjectualandsubstitutionalread-ingsisnotverysigniﬁcantforhim.Whichreadingistruertowhathesays?Ithinkitisclearthatthesubstitutionalreadingiscloser.Thekeytermsarethoseof5.52:thetotalvaluesofafunctionfxforallvaluesofx.Aswehaveseen,functionsforWittgensteinareproposi-tionalfunctions:thatis,theyareexpressionsofacertainkind;theyareexpressionswhichtakenamesasargumentstoyieldwholesentencesasvalues.Sowherehewrites‘afunc-tionfx’heshould,strictly,havewritten‘afunction“fx”’.Thevaluesofthiskindoffunctionarewholesentences:these\nLOGICANDCOMPOUNDSENTENCES223arepreciselysentencesascribingthepredicatetosomegivenobject.Asforthephrase‘valuesofx’,somethingsimilarapplies.Heshould,strictly,havewritten‘valuesof“x”’,andthevaluesof‘x’willthenbesubstitution-instancesof‘x’—thatis,nameswhichcouldbeputinplaceofthevariable.Thereisafurtheradvantagetothesubstitutionalinter-pretationofWittgenstein’squantiﬁers.Itremovesthepro-blemofquantiﬁcationintoanon-nameposition.ThisissomethingwhichWittgensteinseemshappytodo;see,forexample,theuseofthisexpressionat5.5261:(9x,u).ux.Ingeneral,one-placepredicates(‘propositionalfunctions’,inWittgenstein’sterminology)intheTractatusshouldnotbeassumedtobenames:rather,theyaresimplythatpartofasentencewhichtakesasinglenametoformasentence(seeChapter4,section4F).Butifaone-placepredicateisnotaname,thentherecannotbeanobjecttowhichitrefers;andthatmeansthatanobjectualreadingofquantiﬁcationintoaone-place-predicateposition—suchquantiﬁcationasweﬁndat5.5261—cannotbelegitimate.LetusreturntoWittgenstein’sgeneralapproachtoquantiﬁcation.Isitacceptable?Evenifquantiﬁcationoverinﬁnitenumbersofthingsisunproblematic,itisarguablethatWittgenstein’saccountfacesadifferentproblem.Wecan,withrelativeease,saythatalanguagecontainsaninﬁ-nitenumberofnameswithdifferentmeanings,providedthatwehave,now,themeanstogeneratethisinﬁnityofnames.Andthismayindeedbepossibleincertaincases.Butitisnotsoobviouslypossibleincertainmoremundanecases.WhenhereturnedtotheTractatus’streatmentofgeneralityinthe1930s,hethoughtithadcertainobviousproblems:Butforcaseslike‘allmendiebeforetheyare200yearsold’myexplanationisnotcorrect.(PG268)\n224LOGICANDCOMPOUNDSENTENCESItisnotquiteclearwhatWittgensteinthinkstheproblemwiththiscaseis,butitisnotimplausibletodescribeitasadifﬁcultywithsimplygeneratingnamesforalltheindivi-dualsinquestion.Inpart,heseemstohavethoughtthattheproblemlaywithdifﬁcultiesindeterminingpreciselywhichindividualsfallundertheheadof‘allmen’.Theconceptman,heseemsnowtothink,isnotjustamethodforcol-lectingtogetheragroupofpreviouslyidentiﬁedindividuals.Itis,rather(heseemstothink),aconceptwhichhasalifeofitsownandmayleadtoindeterminateresultsincertaincases.ThisisaproblemraisedfortheTractatusfromtheperiodwhenWittgenstein’sviewofthingswasundergoingquitearadicaltransformation.ButwemightthinkthattheTractatus’saccountofquantiﬁcationfacedaprobleminthebook’sownterms.IntheTractatus’ssystem,quantiﬁcationoverinﬁnitedomainswouldrequiretheretobeaninﬁnitenumberofsentencesofthesameform(aninﬁnitenumberofsentences—orpossiblesentences—oftheform‘fx’,forexample,forthecaseof‘(9x)fx’,oroftheform‘fxy’forthecaseof‘(9x,y)fxy’).Butforthecasewherethereisaninﬁnitenumberofsentencesofthesameform(andwherethisincludesthefullrangeofformswemightexpectforstandardpredicatelogic),itseemsthatwecannotstrictlydeﬁnetheN-operatorintermsofatruth-table—asequivalentto‘(-----T)(n,.…)’.ForifithadbeenpossiblestrictlytodeﬁnetheN-operatorintermsofatruth-table,forthecasewhereaninﬁnitenumberofsentences(includingthoseinvolvingmany-placedpredicates)arejointlynegated,therewouldhavebeenamechanicaldecision-procedurefordeterminingwhichsentencesformedbymeansoftheN-operatoraretautologies(truewhateverthetruth-valuesofthesentencestowhichtheoperatorisapplied).Butthereisawell-knownformalresult,accordingtowhichtherecanbenosuchdecision-procedure.15ItseemstofollowthattheN-operatorcanonlybestrictlydeﬁnedintermsofatruth-tableifitisapplicableonlytoﬁnitedomains.ItseemsclearthatWittgensteinhadhopes(toputitnomorestrongly)ofamechanicaldecisionprocedureofthe\nLOGICANDCOMPOUNDSENTENCES225kindwhichhasturnedouttobeunavailableforlogicalsys-temsinvolvingquantiﬁcationoverinﬁnitedomains:16thisissomethingtowhichwewillreturninsection5Ebelow.Butifweleavethosehopestooneside,doesitmattertoWittgensteinwhethertheN-operatorisstrictlydeﬁnableintermsofatruth-table—asequivalentto‘(-----T)(n,.…)’?Itisnotclearthatitdoes.Forhislargerphilosophicalpur-poses,allthatmattersisthateverypossiblesentenceisexpressibleasbeingtheresultofsuccessiveapplicationsoftheN-operatortoelementarysentences—orcollectionsofelementarysentences.Andthetruthofthatisquiteindepen-dentofhowwehappentocometounderstandtheN-operator.Itisimportanttobeclearaboutthispoint,ifwearetoavoidmisunderstandingthecentralphilosophicalpurposeoftheN-operator.RecallthattheN-operatorwasoriginallyintroducedwiththesewords:–5.502ThereforeIwriteinsteadof‘(-----T)(n,.…)’,‘N(n)’.–N(n)isthenegationofallthevaluesofthepropositionalvariablen.Thesecondlineheremakesexplicituseoftheconceptsbothofnegationandofgenerality(‘all’).SoiftheN-operatoristobeintelligibleindependentlyofthoseconcepts,itmustbebymeansoftherotated-truth-tableformulation‘(-----T)(n,.…)’.Butthatexpressionitselfwasintroducedearlierwiththesewords:5.5Everytruth-functionisaresultofthesuccessiveapplicationoftheoperation(-----T)(n,.…)toelementarypropositions.Thisoperationdeniesallthepropositionsintheright-handbracketandIcallitthenegationofthesepropositions.Andheretherotated-truth-tableformulationisitselfexplainedintermsoftheconceptsofnegationandgeneral-ity.FromthisitseemsclearthattheN-operatorcannotbedesignedtoprovideagraspoftruth-functionsandgeneralitywhichiswhollyindependentoftruth-functionsandgen-erality.Itisnotsupposedtoprovideanepistemicfoundation\n226LOGICANDCOMPOUNDSENTENCESeitheroflogicoroftheconstructionofsentences.Rather,thepointistoshowthatalltheapparentlydifferentwaysofconstructingsentences,andalltheapparentlydifferentwaysofrepresentinglogicalrelations,havesomethingincommon.Whattheyallhaveincommonisrepresentedinthefact(asWittgensteintakesittobe)thateverysentencecanbeexpressedasaresultofsuccessiveapplicationsofasingleoperationtoelementarysentences.Thisisenoughtoshowthatthereisageneralformofsentences—and,further,whatthatgeneralformis.ForthispurposeitsimplydoesnotmatterwhethertheN-operatorisintelligibleindependentlyoftheconceptsofnegationandgenerality.5DLOGICANDTHEGENERALFORMOFTHESENTENCEWittgensteinintroducestheN-operatorinordertosecurethefollowingtwoclaims:–––6Thegeneralformoftruth-functionis:[p,n,N(n)].Thisisthegeneralformofproposition.Heexplainsthishimselfinthefollowingremark:6.001Thissaysnothingelsethanthateverypropositionistheresult–ofsuccessiveapplicationsoftheoperationN(n)toelementarypropositions.Thesquare-bracketnotationemployedintheﬁrstlineof6isanadapationofthenotationwhichisexplainedin5.2522,whereitisusedtodescribe,ingeneral,thetermofaseries:5.2522Thegeneraltermoftheformalseriesa,O’a,O’O’a…Iwritethus:‘[a,x,O’x]’.Thisexpressioninbracketsisavariable.Thefirsttermoftheexpressionisthebeginningoftheformalseries,thesecondtheformofanarbitrarytermxoftheseries,andthethirdtheformofthattermoftheserieswhichimmediatelyfollowsx.\nLOGICANDCOMPOUNDSENTENCES227Atermofaseriesissimplyanitemintheseries:sotheﬁrstfourtermsoftheseries2,4,6,8…are2,4,6and8.5.2522presentsawayofcharacterizinganyterminaformalserieswhichistheresultofapplyinganoperationO,beginningfromacertainstartingpoint(theﬁrstterm).Theseriesischaracterizedasbeginningfromthatﬁrstterm,andeachlatertermissimplytheresultofapplyingtheoperationOtothepreviousterm.Unfortunately,theuseofthisnotationinsection6isnotimmediatelyobvious.Thevariable‘p’rangesoverelemen-tarysentences—thesentenceswhichconsistwhollyofnamesinrelationtoeachother.Butthisvariablehasalineoverit,andithasnotbeenmadeclearhowthisistobeunderstoodinconnectionwiththesquare-bracketnota-tion.Followingthepracticeof5.501,thevariablewithalineoveritshouldstandforallthevaluesofthevariable—inthiscase,alltheelementarysentences.Thenaturalwayofreading6isthenthattheﬁrsttermoftheseriesinquestionisthetotalityofelementarysentences.Thesuggestion,then,seemstobethateverypossiblesentencewillﬁguresome-whereinasingleseriesofsentencesformedbysuccessiveapplicationsoftheN-operatortothetotalityofelementarysentences.Itisveryquicklyobviousthatthiswillnotwork.17AsingleapplicationoftheN-operatortothetotalityofele-mentarysentencesyieldsasentencewhichsaysthatnoneoftheelementarysentencesistrue.IfyouapplytheN-opera-tortothat,yougetasentencewhichsaysthatatleastoneoftheelementarysentencesistrue.IfyouapplytheN-opera-tortothat,youget,onceagain,asentencewhichsaysthatnoneoftheelementarysentencesistrue—andsoon.Bythismeansyoucanonlysayoneoftwothings:eitherthatnoneoftheelementarysentencesistrue,orthatatleastoneofthemis.Thisisinadequateintwoveryobviousrespects.First,itleavesoutalargenumberoftruth-possibilities.Andsecond,itleavesouttheelementarysentencesthemselves—atleast,ifthereismorethanoneelementarysentence:forifthereismorethanoneelementarysentence,nosingle\n228LOGICANDCOMPOUNDSENTENCESelementarysentenceistheresultofanynumberofapplicationsoftheN-operatortothetotalityofelementarysentences.Infact,ifwereadthesquare-bracketformulationin6inthisway,itsaysmuchmorethan6.001.Forthesquare-bracketformulation6seemsonthisreadingtosaythateverypos-siblesentenceappearssomewhereinasingleseriesofsuc-cessiveapplicationsoftheN-operator,withtheﬁrsttermbeingthetotalityofelementarysentences.But6.001ismoremodestintworespects:ﬁrst,itdoesnotsaythateverypos-siblesentenceappearssomewhereinasingleseriesofsuc-cessiveapplicationsoftheN-operator;andsecond,itdoesnotsaythattheﬁrstterminanyseriesofapplicationsoftheN-operatoristhetotalityofelementarysentences.And,infact,bothofthesepointsofextramodestyarepointsinfavourof6.001,sinceeachofthesedemandingconditionsisfailedbysomepossiblesentences.18Thisleavesuswithaminorinterpretativequandary:dowetakeWittgensteintobesayingwhatisstrictlymeantbythenaturalinterpretationofthesquare-bracketnotationof6,onitsmostnaturalreading,sothat6.001expresseshispointrathercarelessly—ordowetake6.001toexpresswhathereallywantstosay,withthesquare-bracketnotationof6beinganineptorlazywayofformulatingit?Mypreferenceisforthelatter:Itaketheintroductionofthelineoverthevariablein6tobealazywayofindicatingarangeofseriesofapplicationsoftheN-operator,beginningwithanynumberofelementarysentencesastheﬁrstterm.SupposewehaveawayofdescribingaterminanyoneofanumberofseriesofsuccessiveapplicationsoftheN-operator,beginningwithanynumberofelementarysen-tences.Whyshouldthisbethe‘generalformoftruth-func-tion’,asWittgensteinclaimsintheﬁrstsentencesof6?Notethattheterm‘function’hastworelateduses.Ontheonehand,itmaybeusedtodescribesomethingwhichtakesacertaininput(oneormore‘arguments’)toyieldacertainoutput(a‘value’).Inthissenseof‘function’,thefamiliarlogicalconstantsofsentencelogic—‘~’,‘’,‘&’,and‘v’—orsuchthingsastheShefferStrokeorDagger,orWittgenstein’s\nLOGICANDCOMPOUNDSENTENCES229own‘N(n)’aretruth-functions(operations,oroperatorsinthekindofuseWittgensteinreallyprefers).Andontheotherhand,itmaybeusedtodescribethevalueofafunc-tion(intheﬁrstsense)foragivenargument(orarguments):suchavalueofafunction(intheﬁrstsense)maybedescri-bedasafunction(inthissecondsense)ofagivenargument.Itisthissecondsensewhichisinplayin6:heisusingthetermheretodescribetheresultofapplyingtruth-operatorstoothersentences:so‘~p’isa‘truth-function’of‘p’,and‘pq’isa‘truth-function’of‘p’and‘q’.(SeeRussell1922:13.)Theﬁrstsentenceof6—understoodintheway6.001suggests—thereforemakesarelativelymodestclaim:theclaimisjustthatevery‘truth-function’ofsentences(inthissense)canbeexpressedastheresultofsuccessiveapplicationsoftheN-operatortoelementarysentences.AndthisclaimamountstolittlemorethantheclaimthattheN-operator—liketheShefferStrokeandtheShefferDagger—canbeusedasthesingleprimitivelogicalconstant.Thereallysigniﬁcantclaim,however,isthesecondsen-tenceof6,withitsparaphrasein6.001.Wecan,infact,separatetwodistinctclaimsthatWittgensteiniscommittedto:(F1)Allsentencesshareacommonform;(F2)ThecommonformsharedbyallsentencesconsistsinthefactthateachoneistheresultofsuccessiveapplicationsoftheN-operatortoelementarysentences.Iwillreturnto(F2)insection5Fbelow.Thesigniﬁcanceof(F1)liesinthefactthatitmarksapointofdistinctionbetweensentencesandothertypesofexpression.Wittgensteindoesnotthinkthatthereisacommonformsharedbyallnames,forexample;northatthereisacommonformsharedbyallpredicates.Oneclearreasonforthinkingthatpredicates,inparticular,donotallhavethesameformisthatotherwiseweareliabletobestuckwithaversionofRussell’sparadox.RecallthatRussell’sparadoxaroseinconnectionwithFrege’sattempttogroundarithmeticinclasses:inthisform,theproblemiswiththeideaofaclassbeing(ornotbeing)a\n230LOGICANDCOMPOUNDSENTENCESmemberofitself.(Thisissuewasconsideredbrieﬂyinsec-tion2HofChapter2,above.)Analogousparadoxesariseifweallowpropertiestobe(ornotbe)possessedbythem-selves,orpredicatestobetrue(orfalse)ofthemselves.Russell’ssolutionwastoestablishahierarchyofpredicates(andcorrelativelyofclasses),andrulethatpredicatescouldonlymeaningfullybeappliedtoobjectsatlowerlevelsinthehierarchy.Wittgensteinhimselfdealswiththeproblemin3.333;hereistheparagraphwhichiscrucialforourpresentpurposes:If,forexample,wesupposethatthefunctionF(fx)couldbeitsownargument,thentherewouldbeaproposition‘F(F(fx))’,andinthistheouterfunctionFandtheinnerfunctionFmusthavedifferentmean-ings;fortheinnerhastheformu(fx),theoutertheformw(u(fx)).Commontobothfunctionsisonlytheletter‘F’,whichbyitselfsig-nifiesnothing.TheprecisebackgroundtothisremarkistheruleintroducedbyWhiteheadandRusselltopreventtheformulationofRussell’sparadox.Hereitis,intheforminwhichtheystateit:[T]hefunctionstowhichagivenobjectacanbeanargumentareincapableofbeingargumentstoeachother,and…theyhavenotermincommonwiththefunctionstowhichtheycanbearguments.(WhiteheadandRussell1927:48)Herewehavearulewhichaimstoavoidtheparadoxbyrestrictingtheuseofpredicates;anditrestrictstheuseofpredicatesbyrestrictingtherangeofobjectstowhichtheycanapply.In3.333Wittgensteinformulatesarulewhichisdesignedtohavethesameeffect—restrictingtheuseofpredicatesinordertoavoidRussell’sparadox—butwithoutanymentionoftherangeofobjectstowhichtheyapply.(WewillreturntoWittgenstein’sreasonforthatvariationinsection5Ebelow.)Instead,theruleisstatedjustintermsoftheformofpredicates—thatis,intermsoftheirpossiblecombinations,theirsyntax.\nLOGICANDCOMPOUNDSENTENCES231Whatwehavein3.333isaninsistence,ineffect,thatnotallpredicatescanhavethesameform.Thatistosay,therearesomepositionsinsentencesinwhichsomebutnotallpredicatescanbeplaced.WhatWittgensteinsaysaboutpre-dicates(‘functions’)hereisthecrucialpointofdifferencebetweenpredicates(functions)andoperations,aswesawearlier:5.251Afunctioncannotbeitsownargument,buttheresultofanoperationcanbeitsownbasis.Thepointof3.333ispartofWittgenstein’sinsistencethatwholesentencesarealtogetherdifferentinkindfromtheircomponents.Thisdifferenceallowsittobepossiblefortheretobeageneralformofsentences,somethingwhichallwholesen-tencescanbecommon.Ifawholesentencecanbeplacedinacertainpositionwithinasentence,thenanyothersentencecanbeplacedinthesameposition.Everysentencehasthesamepossibilitiesofcombinationwithothersentencesaseveryother.Whatthisrulesout,inparticular,isahierarchyoflevelsofsentencesinwhichsentencesfromonelevelarepreventedfrombeingcombinedwithsentencesatanother.19Whydoeshethinkthis?Hehasaquitegeneralreason:Thatthereisageneralformisprovedbythefactthattherecannotbeapropositionwhoseformcouldnothavebeenforeseen(i.e.constructed).(4.5)ThisremarkinturnisderivedfromthefollowingclaimfoundintheNotebooks:Thusitmustbepossibletoerectthegeneralformofproposition,becausethepossibleformsofpropositionmustbeapriori.Becausethepossibleformsofpropositionareapriori,thegeneralformofpropositionexists.(NB:89)\n232LOGICANDCOMPOUNDSENTENCESThisfundamentalargumentfortheconstructabilityofanypossibleformisnotentirelyclear,butaplausiblereconstructionseesitasinvolvingthefollowingassumptions:(CF1)Ifaformofsentenceispossible,itisnecessarilypossible;(CF2)Ifaformofsentenceisnecessarilypossible,itisapriorithatitispossible;(CF3)Ifitisapriorithataformofsentenceispossible,thatformofsentencemustbeconstructibleapriori.Theseassumptionsarenatural,thoughnotcompulsory.(CF1)involvesanendorsementofsomethinglikethemodalprinciple(S5),whichwesawatworkin(andindeedjustiﬁedby)thesubstanceargumentof2.021–2.023(seeChapter1,section1D,above).(CF2)involvesapremisewhichwasalmostuniversallyacceptedatthetimethatWittgensteinwrote—thatwhatisnecessarymustbeapriori:thispre-misewascentraltoKant’sconceptionoftheaprioricityofphilosophy,andwasnotgenerallychallengeduntilKripke’spioneeringworkinthe1970s;20wealsosawthiskindofassumptionatworkinthesubstanceargumentof2.0211–2.0212(seeChapter1,section1D,above).And(CF3)involvesaverynaturalmodelofaprioriknowledge:thatwhatisaprioriknowableisopentoacertainsortofdemonstra-tiveprooforderivation.ThisisthekindofassumptionwhichwasputinquestionindifferentwaysbytheworkofGödel,Church,andTuringinthe1930s,butthereissomereasontothinkthatWittgensteinwasnotawareofitsdoubtfulstatus(aswewillsee,insection5E,below)(CF1)–(CF3)seemtorequirethatanypossibleformofsentencemustberepresentableasbeingtheresultofapplyingtosomethingwhichisantecedentlygivenanoperationwhichwecansupposetobeantecedentlygivenalso.Anditlooksasiftheaccountpresentedin6.001meetsthatcondition.Wittgensteinthereclaimsthateverypossi-blesentenceistheresultofsuccessiveapplicationsoftheN-operatortoelementarysentences.Thisseemsclosetowhat(CF1)–(CF3)require—butonlyifthereissomesense\nLOGICANDCOMPOUNDSENTENCES233inwhichtheN-operator,ortruth-functionalityingeneral,isgiventousthemomentwehaveanysentences.Andthatinturnisplausible.RecallagainWittgenstein’searlyaccountofthedeterminationofthemeaningofwhathethencalled‘forms’:Inowdeterminethesenseof‘xRy’bylayingdown:whenthefactsbehaveinregardto‘xRy’sothatthemeaningof‘x’standsintherelationRtothemeaningof‘y’,thenIsaythatthe[thefacts]are‘oflikesense’withtheproposition‘xRy’;otherwise,‘ofoppositesense’;Icorrelatethefactstothesymbol‘xRy’bythusdividingthemintothoseoflikesenseandthoseofoppositesense.(NL:104)AndwemightalsonotethefollowingpassagefromtheNotesDictatedtoG.E.Moore:‘[T]rue’and‘false’arenotaccidentalpropertiesofaproposition,suchthat,whenithasmeaning,wecansayitisalsotrueorfalse:onthecontrary,tohavemeaningmeanstobetrueorfalse:thebeingtrueorfalseactuallyconstitutestherelationofthepropositiontoreality,whichwemeanbysayingthatithasmeaning(Sinn[sense]).(NM:113)Wittgenstein’searlydeﬁnitionofsamenessofformbetweensentenceandtheworld,inthecaseofelementarysentences,intermsofthecontrastbetweenfacts‘oflikesense’andfacts‘ofoppositesense’,alreadyprovidesthematerialsfortruth-functionaltransformation,andhencefortheideaofatruth-functionaloperator.Intheseterms,negation(totakejustthesimplestexample)canbesaidjusttotransformfacts‘oflikesense’intofacts‘ofoppositesense’,andviceversa.Infact,onceweunderstandWittgenstein’searlyaccountofthemeaningof‘forms’asbeinggeneralizedtoallbasicexpres-sions(theviewwhichIarguedforinChapter4,section4G),itseemsclearthat,whateverkindofbasicexpressionweareconcernedwith,wecouldhavebegunwiththeopposite\n234LOGICANDCOMPOUNDSENTENCESunderstandingofwhatcountsas‘oflikesense’and‘ofoppositesense’totheoneweactuallyuse.Thesepointsaremadeinitially(intheNotesonLogic)intermswhich,iftakenliterally,supposethatthesense-deter-miningsubjectcouldhaveaccesstotheworldandallitsfactsquiteindependentlyofanylanguage.WittgensteinnolongerseemstoacceptthatwayofthinkingbythetimeoftheTractatus,butthisdoesnotstopthegeneralmoralbeingapplicabletothetheoryoftheTractatus.Itremainsthecasethatthereisasenseinwhichtheideaofatruth-functionisembeddedintheverydeﬁnitionofsamenessofform,betweenlanguageandtheworld,forelementarysentences.AndthisgivesadeeprationaleforthefollowingclaimwhichWittgensteinmakes:Foralllogicaloperationsarealreadycontainedintheelementaryproposition.(5.47)Givensome(lessmetaphysicallycontentious)versionoftheNotesonLogicdeﬁnitionofsamenessofformforelemen-tarysentences,andtheideathateverysentenceisa‘truth-function’(inWittgenstein’ssense)ofelementarysentences,weseemtohaveallthatisrequiredbyassumptions(CF1)–(CF3).Moreover,wealsoseethatWittgensteinhasgivenusanaccountoftheformofsentencesinthedeepestsenseinhisclaimthateverysentence’sbeingtheresultofsuccessiveapplicationsoftheN-operatorconstitutesthegeneralformofthesentence.ThereisariskofunderstandingWittgenstein’saccountoflanguage,andwithitoftheformofsentences,asfallingintotwocompletelyunconnectedparts:onewhichisappropriatetotheconceptionofelementarysentencesasmodels,theotherwhichconcernstheconstructionofothersentencesoutofelementarysentences.21Fortheaccountofelementarysentencesasmodels,thecrucialnotionofsententialformseemstobeconcernedwiththewaysinwhichnamescanbearrangedtoformasentence—or,equivalently,thewaysinwhichobjectscanbearrangedtoformanatomicfact.Bycontrast,thenotionofsentential\nLOGICANDCOMPOUNDSENTENCES235formwhichseemstoberelevanttotheaccountoflogicseemstobeconcernedwiththewaysinwhichwholesentencescancombinewitheachother.Butoncewerealizethatthenotionofthewaysinwhichnamesarearrangedtoformelementarysentencesisitselftobeunderstoodintermsofadivisionwhichiseffectivelyadivisionbetweentruthandfalsity,thenwecanseethat,atafundamentallevel,therearenotreallytwonotionsofsententialforminplayafterall.Samenessofformbetweensentenceandworldisalways—whetherwearedealingwithelementaryornon-elementarysentences—amatterofwhichsentencescountasbeing‘oflikesense’,andwhich‘ofoppositesense’,withthefacts.Ofcourse,ifallsentencesmusthavethesamebasicform,wedo,indeed,enduprejectingahierarchyofsentences.Andwehavereasontoinsistthattheverysametruth-functions—indeed,thesingleN-operator—canbeappliedtoallsentences.AsWittgensteinsays:Iflogichasprimitiveideasthesemustbeindependentofoneanother.Ifaprimitiveideaisintroduceditmustbeintroducedinallcontextsinwhichitoccursatall.Onecannotthereforeintroduceitforonecontextandthenagainforanother.Forexample,ifdenialisintroduced,wemustunderstanditinpropositionsoftheform‘~p’,justasinpropositionslike‘~(pvq)’,‘(9x).~fx’andothers.Wemaynotfirstintroduceitforoneclassofcasesandthenforanother,foritwouldthenremaindoubtfulwhetheritsmeaninginthetwocaseswasthesame,andtherewouldbenoreasontousethesamewayofsymbolizinginthetwocases.22(5.451)Finally,6.001allowsustodoalittleaccounting.OneofthemetaphysicalcommitmentsoftheTractatuswhichweiden-tiﬁedinChapter1wasthis:(T3)Factsareeitheratomicfactsorcombinationsofatomicfacts.Thisisanimmediateconsequenceof6.001:indeed,6.001evenspeciﬁesthekindofcombinationwhichisinvolved—itmustbetruth-functionalcombination.\n236LOGICANDCOMPOUNDSENTENCES5ELOGICANDTAUTOLOGYWittgenstein’scentralconcerninhistreatmentoflogiccanbesummarizedinhiscommitmenttothethesiswecon-sideredinChapter2,thethesisoftheworld-independenceoflogic:(WIL)Logicdoesnotdependonanythinginparticularbeingthecase.HerejectsaltogethertheKantianthoughtthatnecessarytruthsaresyntheticaprioritruths,knowledgeofwhichrequiressomekindofintuitionof,oracquaintancewithreality.Wittgenstein’scommitmentto(WIL),andhisrejectionofKantianismaboutnecessarytruthsisexpressedinthefollowingtwoclaims:6.1ThepropositionsoflogicaretautologiesThereisonlylogicalnecessity.(6.37)TheimportanceoftheclaimthatthepropositionsoflogicaretautologiesliesinWittgenstein’stheoryoftautology,whichislaidoutinsections4.46–4.4661.Atautologyisaproposi-tionwhichis‘trueforalltruth-possibilitiesoftheelemen-tarypropositions’(4.46:Wittgensteinhimselfmayinfactbethesourceofthisuseoftheterm‘tautology’23).Forthecaseofsentenceswhosetruth-possibilitiescanactuallybeenum-erated,atautologyisasentencewhichhasa‘T’ateverylineofitstruth-table,andistruenomatterwhat.Atthetime,thisaccountofthepropositionsoflogic(whatwemightcalllogicaltruths)asbeingtautologiesseemstohavebeenhailedasasuccinctandverynecessarydeﬁnition:itmakespossiblethedemarcationoflogicfromallotherspheres—somethingwhichpreviousaccountshadnotachieved.24Forourlarger,philosophical,purposes,itissigniﬁcantinotherwaystoo.\nLOGICANDCOMPOUNDSENTENCES237AccordingtoWittgenstein,atautologysaysnothing.Ithasnotruth-conditions,becauseitisunconditionallytrue(4.461).Thesameholds,fortheoppositereason,ofcontra-dictions.Contradictions(whichare,presumably,theonlyimpossibilities,accordingtotheviewof6.37)arefalsenomatterwhat;theysaynothing,andhavenotruth-conditionsbecausetheyaretrueonnocondition.Tautologiesandcon-tradictionsaretherefore‘withoutsense’(‘sinnlos’;4.461).Theyarenotpictures,becausetheydepictnoparticularstatesofaffairs:tautologiesarecompatiblewitheverything,contradictionswithnothing(4.462).Importantly,however,thisdoesnotmeanthattautologiesandcontradictionsarenonsense(4.4611).25Wittgensteinclaimsthattheyarenotjustnonsensebecausetheyare‘partofthesymbolism’.Thisisareasonableclaim:ifallsentencesaretheresultofsuccessiveapplicationsoftheN-operatortoelementarysentences,theexistenceoftautologiesandcontradictionsisforeseeablefromthestart.Tautologiesandcontradictionsarethelimitcasesoftruth-functionsuponelementarysentences.Moreover,accordingtoWittgenstein,althoughtheydonotsayanything,thatdoesnotmeanthattheydonothing:6.12Thefactthatthepropositionsoflogicaretautologiesshowstheformal—logical—propertiesoflanguage,oftheworld.Thatitsconstituentpartsconnectedtogetherinthiswaygiveatautologycharacterizesthelogicofitsconstituentparts.Inorderthatpropositionsconnectedtogetherinadefinitewaymaygiveatautologytheymusthavedefinitepropertiesofastructure.Thattheygiveatautologywhensoconnectedshowsthereforethattheypossessthesepropertiesofastructure.Wehavehereanotheruseofthecrucial,butawkward,con-ceptofshowing.Wecameacrossthisconceptearlier,inWittgenstein’saccountoftherelationbetweenapictureanditsownpictorialform:2.172Thepicture,however,cannotrepresentitsformofrepresentation;itshowsitforth.\n238LOGICANDCOMPOUNDSENTENCESTheuseoftheconceptofshowinginrelationtotautologiesmayberelatedtothis,butitseemsdifferent,atﬁrstblush.Afterall,picturesormodelsshowtheirownform;andso,therefore,dosentenceswhichsucceedinsayingsomething—sentenceswhicharenottrueorfalsenomatterwhat.Anditisnotthetautologiesthemselveswhichshowanything:itis,rather,theirbeingtautologieswhichshowssomething;thoughwhatisshownbytautologies’beingtautologiesseemsverysimilarwhatisshownbyanylogicalpictureormodel—thatistosay,thelogicalformoftheworld.Thedifferencelies,perhaps,intheabstractnessofwhatisshownbythetautologousnessofatautology.Whereasasentencewhichsayssomething(asentencewhichisapictureormodel)showsthepossibilitiesofarrangementofitscon-stituentobjects,thetautologousnessofatautologyshowsjustthegeneralpossibilitiesoftruthandfalsehood,nomatterwhatobjectsareinvolved.Onemightthinkthatwehavehereadoctrinewhichis,afterall,notallthatdissimilarfromtheKantianconceptionofthesyntheticapriori:itseemsthattautologiessucceedinshowingsomethingabouttheworld(its‘formal—logical—properties’).ButWittgensteinwantstoinsistthathisviewisquitedifferent.Thedifferenceemergesinthefollowingcrucialclaim:Itisthecharacteristicmarkoflogicalpropositionsthatonecanper-ceiveinthesymbolalonethattheyaretrue;andthisfactcontainsinitselfthewholephilosophyoflogic.(6.113)Thepointisthatthetautologousnessofatautologyisevident(insomesenseofevident)fromthesymbolalone:itisafact(asitwere)thatconcernsnothingbutthepossi-bilitiesofcombinationofthesymbolsfromwhichthetautologyisconstructed.Wedonotneedtolookattheworldinordertodiscoverthatatautologyisatautology:nointuitionoracquaintanceofanobjectiveworldisinvolvedhereatall.\nLOGICANDCOMPOUNDSENTENCES239This,inturn,leadstoacertainconceptionofadequatesym-bolismwhichrunsthroughWittgenstein’sapproachtologicalnecessity:ifanotationisadequateitought,insomesense,torevealinitselfthelogicalrelationsamongsymbols;thereshouldbenoneedtoconsideranythingtodowiththeworldatall.ThisliesbehindWittgenstein’streatmentofRussell’sownresponsetotheparadoxhefoundinFrege’sattempttoconstructarithmeticfromsettheory.Wittgensteinﬁrstinsists:3.33Inlogicalsyntaxthemeaningofasign[i.e.,theobjectreferredtobyasign]oughtnevertoplayarole;itmustadmitofbeingestablishedwithoutmentionbeingtherebymadeofthemeaningofasign;itoughttopresupposeonlythedescriptionoftheexpressions.Andthenhedrawsthefollowingmoral:3.331Fromthisobservationwegetafurtherview—intoRussell’sTheoryofTypes.Russell’serrorisshownbythefactthatindrawinguphissymbolicruleshehastospeakaboutthethingshissignsmean.Wittgensteinmay,infact,bebeingunfairhere:Russellmaynot,strictly,havehadtospeakaboutthethingshissignsmean.26Thefactis,however,thathedidproceedinthatway,andthat,Wittgensteinthinks,showsanimportanterror.Logicalpossibilitiesandnecessitiesmustdependonnothingmorethanthesymbolsthemselves—nothingmore,thatis,thanthesignstogetherwiththerulesoftheircombination,whichrulesinturnneedmakenoreferencetotheworld.AndWittgenstein’sso-called‘picturetheory’ofmeaning—thetheorythatsentencesaremodelsofreality—provides,toputitnomorestrongly,furthersupportforthispoint.For,accordingtothattheory,thepossibilitiesofcombinationofsymbolsarestrictlyparalleltothepossibilitiesofcombinationofobjects,andhencemustbe,inasense,recognizablewithoutourinspectingthewaysinwhichobjectscanbecombined:becausethepossibilitiesof\n240LOGICANDCOMPOUNDSENTENCEScombinationofsymbolsarethesameasthepossibilitiesofcombinationofobjects,thereisnoneedtolookattheworldtoseewhichcombinationsarepossible.Thisseverelysymbol-directedapproachtologicalnecessityisalsobroughtinbyWittgensteintoexplainwhatmightotherwiseseemtoposeaproblemforhim:thenotionofidentity.Theproblemisthatthenotionofidentityseems,onthefaceofit,tofurnishlogicaltruthsofitsown.Thefollowing,forexample,isabasiclogicaltruthinstandardpredicatelogicwithidentity:(x)(x=x).Indeed,thatthisisalogicaltruthwasessentialtoFrege’sclass-theoreticconstructionofarithmetic,aswesawinChapter2(section2H).ButWittgensteinclaimsthatalllogicaltruthsaretautologies,intheprecisesenseofbeingtrueforalltruth-possibilitiesofelementarysentences.And‘(x)(x=x)’cannotmeetthatcondition.ItcouldonlyevenbetheresultofsuccessiveapplicationsoftheN-operatortoele-mentarysentences,ifsentencesoftheform‘a=a’werethemselveselementarysentences.Butif‘a=a’isanele-mentarysentence,itmustbecontingentandaposteriori,whereasitisobviouslybothaprioriandnecessary(ifitisgrantedthat‘a’isthenameofasimpleobject).Thispointismadein5.434:Andweseethatapparentpropositionslike:‘a=a’,‘a=b.b=c.a=c’,‘(x).x=x’,‘(9x).x=a’,etc.cannotbewritteninacorrectlogicalnotationatall.AndWittgensteinsupportsthiswayofputtingthepoint(whichdependsonhisownaccountofthegeneralformofthesentence)withthefollowingpieceofintuitivereasoning:5.5303Roughlyspeaking:tosayoftwothingsthattheyareidenticalisnonsense,andtosayofonethingthatitisidenticalwithitselfistosaynothing.\nLOGICANDCOMPOUNDSENTENCES241Wegetahintofexactlyhowlittlecanbesaidbysayingthatonethingisidenticalwithitself,onWittgenstein’sview,ifweimagineﬁttingthatclaimintothebasicaccountofthenatureoffactswhichbelongswithWittgenstein’sconceptionofsentencesasmodels:thebasicfactsconsistofseveralobjectsinrelationtoeachother;anidentityclaimwouldseemtoinvolvejustoneobject,allonitsown.Wittgensteinisalsodismissiveofattemptstodeﬁneasubstantiverelationofidentity,suchasRussell’s,accordingtowhichaisidenticalwithbifandonlyifaandbshareallthesameproperties:275.5302Russell’sdefinitionof‘=’won’tdo;becauseaccordingtoitonecannotsaythattwoobjectshavealltheirpropertiesincommon.(Evenifthispropositionisnevertrue,itisnever-thelesssignificant.)Theverynotionofidentitynowseemstobeunderthreat,andthisisveryseriousfortheapproachtomathematicsfoundinFregeandRussell.AswesawinChapter2(section2H),thecoreoftheirapproachrequiresthatthenotionofequinumerousness—ofhavingthesamenumberas—canbedeﬁnedwithoutuseofthenotionofnumber,simplyusingquantiﬁcationandidentity.Ifthenotionofidentityisabandoned,thisapproachisindangerofcollapsing.Wittgenstein’ssolutionistoinsistthatnoadequatelogicalnotationwouldincludetheidentitysign,andtoclaimthatthesignbecomesunnecessaryifwetakepropercareovertheuseofnames:5.53IdentityoftheobjectIexpressbyidentityofthesignandnotbymeansofasignofidentity.Differenceoftheobjectsbydifferenceofthesigns.Wittgensteinoffersnoformalproofthatthisprocedurewouldworkforeverythingthattheidentitysignmightbecalledontodo,buthedoesoffervariousproposalsforreformulatinglogicalclaimsmadebymeansoftheidentity\n242LOGICANDCOMPOUNDSENTENCESsignsintermsofanotationwhichsimplydistinguishesbetweennamesandvariableswhenandonlywhenthereisadifferenceofobject(see5.531–5.321).28AccordingtoWittgenstein,theonlylegitimateuseofthesignofidentityisatameta-level,preciselytotalkaboutthemeaningofsigns,andnottoassertanythingsubstantiveabouttheworld.Thushesays:4.241IfIusetwosignswithoneandthesamemeaning,Iexpressthisbyputtingbetweenthemthesign‘=’.‘a=b’meansthen,thatthesign‘a’isreplaceablebythesign‘b’.(IfIintroducebyanequationanewsign‘b’,bydeterminingthatitshallreplaceapreviouslyknownsign‘a’,Iwritetheequation—definition—(likeRussell)intheform‘a=bDef.’.Adefinitionisasymbolicrule.)4.242Expressionsoftheform‘a=b’arethereforeonlyexpedientsinpresentation:Theyassertnothingaboutthemeaningofthesigns‘a’and‘b’.ThisaccountoftheidentitysignisinstarkcontrasttothatofFrege,whohadoriginallyadoptedsomethinglikeWittgenstein’sviewhimselfinhisearlyBegriffsschrift,29butrejecteditin‘OnSenseandReference’.Thegroundsforthisrejectionwerethatthemetalinguisticaccount—theviewadoptedbyWittgensteinintheTractatus—madeidentitystatementsingeneral(andmathematicalequationsinparticular)intorelativelytriviallinguistictruths,whereasreallytheywerecapableofexpressingsubstantialknowledge.30ThisdifferencerevealsacrucialfeatureofWittgenstein’sphi-losophyofmathematics,towhichheremainedtruethroughouthiscareer.ThecoreofWittgenstein’soverallapproachtomathematicsintheTractatusisrevealedbythesetworemarks:6.2Mathematicsisalogicalmethod.Thepropositionsofmathematicsareequations,andthereforepseudo-propositions.\nLOGICANDCOMPOUNDSENTENCES243Theﬁrstsentenceherealliesmathematicaltruthswithlogi-caltruths:theparallels,aswellasthedifferences,arelaidoutinthesetwosections:6.22Thelogicoftheworldwhichthepropositionsoflogicshowintautologies,mathematicsshowsinequations.6.23Iftwoexpressionsareconnectedbythesignofequality,thismeansthattheycanbesubstitutedforoneanother.Butwhetherthisisthecasemustshowitselfinthetwoexpressionsthemselves.Itcharacterizesthelogicalformoftwoexpressions,thattheycanbesubstitutedforoneanother.Wittgensteinclaimsherethatwhatareordinarilythoughtofasidentitystatementssimplyassert—orseemtoassert(wewillreturntothatinamoment)—thattwoexpressionscanbesubstitutedforoneanother.Fortwoexpressionstobecapableofbeingsubstitutedforoneanotheritisatleastrequiredthattheybecapableofcombiningwithotherexpressionsinthesameways.Asweknowfromtheﬁrstintroductionofthetheoryofsentencesasmodels,logicalformisamatterjustofpossibilitiesofcombination.Tosaythattwoexpressionshavethesamelogicalformisjusttosaythattheycanbecombinedinthesamewayswithotherexpressions.Sofortwoexpressionstobecapableofbeingsubstitutedforoneanotheritisatleastrequiredthattheyhavethesamelogicalform.Butgenerallymoreisrequiredthanthat.Wittgensteinholdsthattwoobjectscouldhavethesamelogicalform(2.0233).Thismeansthattheirnameswillbecapableofcombiningwithotherexpressionsinexactlythesameways:thatis,theirnameswillhavethesamelogicalform.Butitdoesnotfollowfromthisthattheirnamescanbesubstitutedforoneanother,orthatthesentenceformedbyputting‘thesignofequality’(theidentitysign)betweenthetwonameswouldbecorrect.Forbyhypothesisthetwonamesrefertodifferentthings.ThissuggeststhatWittgenstein’sclaimin6.23cannotbeasgeneralasitseemstobe:itcannotapplytoeverythingwhichlookslikeastatementofidentity.Inthecontext,itis\n244LOGICANDCOMPOUNDSENTENCESnaturaltotakehisclaimtobeintendedtoapplyjusttomathematicalequations.Hispointwillbethatinanadequatenotationformathematicstheexpressionsthemselveswillshowthattheyareintersubstitutable.Anadequatenotationwillshowthattheyhavethesameform;andinthemathematicalcase,thatisenough—noindependentcheckontheworldisneeded.HeexplicitlycontrastshisviewherewiththatofFrege:6.232Fregesaysthattheseexpressionshavethesamemeaning[reference]butdifferentsenses.Butwhatisessentialaboutequationisthatitisnotnecessaryinordertoshowthatbothexpressions,whichareconnectedbythesignofequality,havethesamemeaning:forthiscanbeperceivedfromthetwoexpressionsthemselves.Really,however,WittgensteinandFregearetalkingpasteachotherhere.Fregeintroducedhisnotionof‘sense’toexplainhowanequationcouldbetrue,andyetitbepossiblenottorealisethatitistrue.Wittgensteinisconcernedtoexplainhowitispossible—inmathematics,atleast—torealisethatanequationistruewithoutindependentlylook-ingattheworld.Wittgenstein’sanswertohisproblemisthatequationsareclaims(asitwere)ofintersubstitutability,intersubstitutabilityissamenessofform,andsamenessofformcanalwaysberevealedinanadequatenotation.AsforFrege’sproblem,Wittgensteinshouldprobablyhavedis-misseditasanissueforpsychology,ratherthanphilosophy.Unfortunately,heseemstosuggestthatitcannotreallyarise(atleastinmathematics):6.2322Theidentityofthemeaningoftwoexpressionscannotbeasserted.Forinordertobeabletoassertanythingabouttheirmeaning,Imustknowtheirmeaning,andifIknowtheirmeaning,Iknowwhethertheymeanthesameorsomethingdifferent.ItisdifﬁculttogivethisaninterpretationwhichgivesWittgensteinanycredit.Thesecondsentencelooksasifitisputtingforwardanargumentwhichisobviouslyunsound:it\nLOGICANDCOMPOUNDSENTENCES245isobviouslynottrue,ingeneral,thatIcanonlyknowaandbifIknowwhetherornotaisthesamethingasb—otherwiseitwouldbeimpossiblesuddenlytorecognizesomeone,ortofailtorecognizesomeoneoneknows.ItisjustbecausethisisobviouslynottruethatFregeintroducedhisnotionof‘sense’.Itmaybe,however,thatWittgensteinisnotputtingfor-wardpreciselythisunsoundargument.Herearetwoalter-nativepossibilities.First,Wittgensteinmaybeclaimingthatinthespecialcaseofnamesofsimpleobjects—thefundamentalexistentsontheTractatus’stheory—itisnotpossibletoknowthemeaningoftwosuchnameswithoutknowingwhethertheyhavethesamemeaning.SomethinglikethismightplausiblybecountedastrueaccordingtoRussell’slogicalatomism—thesystemwhichRussellintroducedundertheinﬂuenceofearlydraftsofthematerialwhichlaterbecametheTractatus.31ThefundamentalobjectsofRussell’slogicalatomismareconstituentsof‘immediate’experience,andarethingsaboutwhoseexistenceonecouldnotpossiblybemistaken.Itisplausibletosupposethatifonecouldnotpossiblybemistakenabouttheexistenceofsomething,onecouldalsonotpossiblymistakethatthingforsomethingelse.ButRussell’sfundamentalobjectslookill-suitedtoplaytheroleoftheobjectsoftheTractatus.Evenwhilepursuinghismathematicalconcerns,RussellwasallalongconcernedtoproduceatheoryoflanguagewhichcouldaddresstheveryproblemswhichFrege’snotionof‘sense’wasintro-ducedtosolve(seeRussell(1905)),butwithoutappealingtothenotionof‘sense’atall.WittgensteinseemsnottohavebeenespeciallyconcernedwithFrege’sproblems;andhisfundamentalobjectsaredesignedtobethenodesofmodalityratherthantoaccountforanythingepistemic—itisthepossibilitiesofcombinationofWittgenstein’sfundamentalobjectswhicharethefundamentalpossibilitiesintheworld.Alternatively,Wittgensteinmaysimplybeoverstatingtheperspicuousnessinanidealnotationofthesubstitutivityoftwoexpressions.Hisgeneralphilosophicalview(including,inparticular,thewayherejectsKant’sideaofsynthetica\n246LOGICANDCOMPOUNDSENTENCESprioritruths)requireshimtoinsistthatthebasisofthepossibilityofcombinationofsymbols,andhencethebasisoftheintersubstitutabilityofexpressionsinthemathematicalcase,mustlieinthesymbolsthemselvesandnotintheworld.Buthehasatendency(aswewillseeinamoment)tooverstatethis:hehasatendencytoslidefromthinkingthatiflogicalformliesinthesymbolsthemselvesitmustbeveryeasilyvisibleinthosesymbols.Wittgensteinclaimsin6.2thatthepropositionsofmathe-maticsare‘pseudo-propositions’.Whatdoesthismean?Theanswerisnotentirelyclear:itlooksasifWittgensteiniscommittedtoarangeofslightlydifferentreadingsoftheclaim.First,ofcourse,heseemstothinkthatmathematicalequationshavethesamestatusastautologies:theyshowthelogicoftheworld.Wesawearlierthatinthecaseoftautol-ogiesthispropertyisboundupwiththemfailingtosayanything:tautologiesarereallyonlyalimitingcaseofsen-tences,sincetheyaretruesimplybecauseofthesymbolism,andarenotinanysensemodelsofreality.SoitmaybethatWittgensteinwantstoclaimthatmathematicalequationssaynothinginjustthesamesenseastautologiessaynothing.Butequationsareoddinanotherwaytoo:theidentitysignattheircoreis,accordingtoWittgenstein,onlyan‘expedientofpresentation’.32Thisisboundupwithaviewofthesig-niﬁcanceofmathematicswhichWittgensteinheldforthewholeofhiscareer.IntheTractatusitisexpressedlikethis:6.211Inlifeitisneveramathematicalpropositionwhichweneed,butweusemathematicalpropositionsonlytoinferfromproposi-tionswhichdonotbelongtomathematicstootherswhichequallydonotbelongtomathematics.(Inphilosophythequestion‘Whydowereallyusethatproposi-tion?’constantlyleadstovaluableresults.)ThewholeapproachofWittgenstein’slaterphilosophyisverylargelypreﬁguredintheparenthesishere.Andtheﬁrstsentenceanticipatesaviewwhichisalsoclearlyenunciatedlater:\nLOGICANDCOMPOUNDSENTENCES247Iwanttosay:itisessentialtomathematicsthatitssignsarealsoemployedinmufti.Itistheuseoutsidemathematics,andsothemeaningofthesigns,thatmakesthesign-gameintomathematics.(RFM:V.2)Theideaseemstobethatthesentenceswhicharenotmere‘pseudo-propositions’aresentenceswhichgiveusthemeasurementofathing’sactualsizeorspeedormass(orwhatever),andmathematicalequationsenableustoproducetransformationsofsuchgenuinelymodellingsentencestoproducegenuineclaimsabouttheactualsize,speed,mass,orwhateverofotherthings(orthesamethingatothertimes).Thepointseemstobethatthereisnomathematicalrealm,justamathematicalwayofhandlingtherealworld—thepossibilityofwhichmustbeafundamentalfeatureoftheworlditself.Itseems,then,thatmathematicalequationsarecountedas‘pseudo-propositions’atleastinpartbecausetheyarenotdescriptionsofamathematicalrealm.Ofcourse,tomakethisclaimgood,Wittgensteinneedstoshowthatarithmetic,inparticular,isnottobeconstruedasbeingconcernedwitharealmofspecialobjects,thenumbers.Andthatmeansthatheneedstoshowhowtheaxiomsofarithmetic(theso-calledPeanoAxioms)—orsomethingwithequivalentpower—canbederivedwithoutappealingtothekindofconstructionwhichFregeandRussellbothused,whichinvolvedtreatingnumbersasclasses,andclassesasobjectsofaspecial‘logical’kind.IntheTractatusWittgensteindoesindeedofferasketchofawayofdoingjustthat.Thisisnottheplacetoconsiderthisinanydetail,33butitisworthpausingbrieﬂytoconsiderWittgenstein’sviewthatnumbersarenotobjects,but‘exponentsofoperations’.Theclaimthat‘anumberisanexponentofanoperation’ismadeat6.021,andisacommentontheprevioussection,6.02,inwhichnumbersaredeﬁnedpreciselyintheseterms(theGreekletter‘X’isasymbolforanoperation).Butwhatdoestheclaimmean?First,whatdoeshemeanby‘operation’here?Whenweﬁrstencounteredtheterm,in\n248LOGICANDCOMPOUNDSENTENCESsection5Babove,itseemedtobeintelligiblechieﬂybymeansofacontrastwiththeterm‘function’.Forthatpoint,itseemedcrucialthatfunctionsareexpressionswhichtakenamestoformsentences,whereasoperationstakewholesentencestoformsentences.TheonlyexamplewehavebeenofferedofanoperationistheN-operator,andthisdoesindeedﬁtthisdescription.Somepeoplehaveaccordinglysupposedthattheoperationwhichisinplayin6.02and6.021isnothingotherthantheN-operator,butthisispro-blematic.Ifweallowthatinﬁnitelymanysentencesmaybeincludedintherangeofthevariable‘n’intheconstruction–‘N(n)’—whichwewillhavetodoifwearetoallowtheretobeinﬁnitelymanythings—thentheN-operatordoesnotgenerateaconsecutiveseries,andsocannotbeusedtogen-erate(acounterpartof)theseriesofnaturalnumbers.34Ontheotherhand,itseemsthatwemustcontinuetoinsistthatoperationstakewholesentencestoformsentences,ifwearenottolosethegroundforthecrucialcontrastbetweenfunctionsandoperations:5.251Afunctioncannotbeitsownargument,buttheresultofanoperationcanbeitsownbasis.Iftheoperation(oroperations)Wittgensteinhasinmindin6.021does(ordo)nottakewholesentencestoformsen-tences,itseemsthattherecanbelittlemoretothedistinc-tionbetweenoperationsandfunctionsthanisofferedby5.251itself:anoperationwillsimplybeanexpressionwhichcanbeappliedtoitsownresults.35Itseemstomenaturaltosupposethatanoperation,hereaselsewhere,issomethingwhichtakeswholesentencestoformsentences,butthatwhatwewanthereissomeoperationotherthantheN-operator.WhatWittgensteinprincipallywantsfor6.02and6.021isanoperationwhichgeneratesaconsecutiveseries.Suchaserieswillbeginfromacertainprimitivebase,somethingwhichisnotitselftheresultofanypreviousapplicationoftheoperation(whichwecansymbolizeitbymeansoftheletter‘X’).Letthisthingbex.\nLOGICANDCOMPOUNDSENTENCES249ThensincexisnottheresultofanypreviousapplicationoftheoperationX,wecancountitastheresultofapplyingtheoperationXnotimestox.Wemightthenwritethatasfollows:(1)X0x.Herethenumeral‘0’iswrittenasexpressingthe‘power’oftheoperationX,toindicatethenumberoftimestheopera-tionhasbeenappliedtox.36SupposenowthatweapplytheoperationXtox(i.e.,toX0x).Wemightwritetheresultlikethis:(2)X’X0xWecanindicatethatwearehereapplyingitonemoretimethan0timesbyadding‘+1’toourexpressionofthe‘power’oftheoperation,andsoexpress(2)likethis:(2p)X0+1xIftheoperationXisappliedtwicetox(i.e.,toX0x),thenaturalwayofwritingtheresultisthis:(3)X’X’X0x.Butifweadd‘+1’totheexpressionofthe‘power’in(2p)wecanrewrite(3)likethis:(3p)X0+1+1x.Ingeneral,wecancharacterizetheuseof‘+1’toindicatethattheoperationXhasbeenappliedonemoretime,bymeansofthefollowingdeﬁnition:X’Xvx=Xv+1xdfOfcourse,thiswillleaveuswithacumbersomeexpressioniftheoperationisappliedmanytimes.Whatweneedisan\n250LOGICANDCOMPOUNDSENTENCESarrayofsimplersymbolswhichcanbewritteninplaceoftheincreasinglylargeexpressionsoftheform‘0+1+1+1…’inordertoexpress‘powers’oftheoperation.ThenaturalchoiceisthefamiliarrangeofArabicdecimalnumerals.Whatwehave,then,isanoperationwhichcanbeappliedtoitsownresultsanindeﬁnitenumberoftimes,andamethodofabbreviatingtheexpressionofsuchrepeatedapplications.ThisiswhatWittgensteinpresentsin6.02.Heusestheidentitysignthereintheonlywayhethinksislegitimate:astheexpressionofadeﬁnition—thatis,asawayofintroducinganotationalabbreviation.Themethodofabbreviationheusesinvolvestreatingnumeralsasexpres-sing‘powers’oftheoperation:thatis,asindicatingthenumberoftimestheoperationhasbeenapplied,beginningfromaprimitivebasewhichisnotitselftheresultofanapplicationoftheoperation.These‘powers’oftheoperationarewhatWittgenstein(intranslation)calls‘exponents’oftheoperation.Andthatiswhathehasinmindwhenhemakeshiskeyclaim:6.021Anumberistheexponentofanoperation.Clearly,thepointofthisistodenythatnumbersareobjects,buthowhasthatresultbeenachieved?Frege’sclaimthatnumbersareobjectsdependedontwothings:ﬁrsttheclaimthatthebasicgrammarofnumberwords(numerals)isthatofsingularterms(thereferentsofwhichareobjects);andsecond,theidentiﬁcationofaseriesofobjectstobethenumbers—theclassesheusedinhisconstruction.Itakeitthatthepointof6.02istoshowthatnumeralsdonotreallyhavethegrammarofsingularterms.Theonlygenuinesin-gulartermsintheTractatusarethenamesfortheobjectswhichconstitutetheformoftheworld.Anyotherexpres-sionwhichhasthesuperﬁcialgrammarofanamemustreallybesomethingwhichcanberegardedasbeing,ineffect,introducedbydeﬁnition,asanabbreviationforsomemorecomplexexpression.In6.02theArabicnumeralsother\nLOGICANDCOMPOUNDSENTENCES251than‘0’and‘1’areintroducedasdeﬁnitionalabbreviationsoftermsoftheseries‘0+1+1+1+1…’.Andthisseriesitselfisnothingmorethanawayofwritingtherepeatedapplicationofanoperation,beginningfromabasewhichisnotitselftheresultofapplyingtheoperation.Sohehopestohaveshownthatthereisnoreasonatalltotakenumeralsasnames.37ToseeexactlywhatWittgensteinisdoinghere,weneedtorecallFrege’smethodofestablishingtheclaimthatnumbersareobjects.WhatFregedoesisestablishthefollowingequivalence:(E)ThenumberofclassC1=thenumberofclassC2ifandonlyifclassC1isequinumerouswithclassC2.Sincethisallowsustousesubstantivalexpressionslike‘thenumberofclassC1’,itseemstoensurethatthosesub-stantivalexpressionsaremeaningful.Butthesesubstantivalexpressionshavethesurfacegrammarofsingularterms.OnFrege’stheory,meaningfulexpressionswhichhavethegrammarofsingulartermsrefertoobjects.SoFregecon-cludesthatnumbersareobjects.WhatWittgensteinclearlyrejectsistheassumptionthatthesurfacegrammarofanexpressionrevealsitsrealgrammar.HecreditsRussellwiththerealizationthatthisassumptioncanberejected:Russell’smeritistohaveshownthattheapparentlogicalformofthepropositionneednotbeitsrealform.(4.0031)SinceWittgensteinthinksthattheonlyexpressionswhichreallyfunctionassingularterms—byhavingmeaninginvirtueofbeingcorrelatedwithobjects—arethesimplenamesofwhichelementarysentencesarecomposed,heholdsthattherealfunctionofotherexpressionsistobeunderstoodonlybyrecognizinghowsentencesinvolvingthemaretobeanalysedintoelementarysentences(andcompoundsofelementarysentences).\n252LOGICANDCOMPOUNDSENTENCESWittgensteinthereforetakeshimselftohavedoneallthatheneedstodo,byshowinghowthenumeralscanbeintro-ducedasawayofabbreviatinganindexingoftherepetitionofanoperation.You(orFrege)mightbetemptedtosaytohim:‘Yes,Iseehowthenumeralsareused,butwhatofthethingsthenumeralsreferto—whatarethenumbers?’Tothishewouldhavetorespond,inthemannerofhislaterphilosophy:‘Nosuchthingswereinquestionhere,onlyhowthenumeralsareused’.38SomuchforabriefaccountofWittgenstein’sclaimthatnumbersarenotobjects,but‘exponentsofoperations’.Nowletusreturntohismorecentralcontentionsonthenatureoflogicandmathematics.ThecoreofWittgenstein’sphiloso-phyoflogicandnecessityistheanti-Kantianviewthatlogicaltruth,mathematicaltruth,andnecessarytruthingeneralneedsnoinsightorintuitionoftherealworldtobediscovered:rather,oneneedonlylookatthesymbols,andanadequatesymbolismshouldshowtheformofthesym-bols,whichiswheremodalityingeneralresides.ButitseemstomethatWittgensteinclearlythoughtthatiftheformofthesymbolscouldbeshowninanadequatenota-tion,itcould,insomerelativelystraightforwardway,beseeninthatnotation.Therearehintsofthisviewinseveralplaces,buthecommitshimselfmostexplicitlytoitinthefollowingremark:6.122Whenceitfollowsthatwecangetonwithoutlogicalpropositions,forwecanrecognizeinanadequatenotationtheformalpropertiesofthepropositionsbymereinspection.ThislooksasifitcommitsWittgensteintotheviewthateverylogicaltruthisdecidable—thatistosay,canbederivedbyamechanicalprocedureoralgorithminaﬁnitetime.Thisclaimistrueifitisrestrictedtosimplesentencelogic(propositionalcalculus),39butisfalseofstandardpredicatelogicifitincludesmany-placedpredicates,anddomainsofquantiﬁcationareallowedtobeinﬁnite(anditisfalseofmathematics,ifthatisclaimedtobepartoflogictoo).40Onecan\nLOGICANDCOMPOUNDSENTENCES253understandhowsomeoneconcernedtorejecttheKantiancommitmenttosyntheticaprioritruths,inthewayinwhichWittgensteinwas,mightﬁndtheclaimof6.122extremelynatural:butitgoeswellbeyondwhathewasentitledto.ItisnotclearhowimportantthisistotheTractatus.Someareinclinedtothinkof6.122aslittlemorethanaslip.Itissometimesevenclaimedthatthenotionofshowing—whichmightseemtobethecounterpartofrecognition‘bymereinspection’—isnotreallyanepistemicnotionatall.41Othersgototheoppositeextreme,andclaimthatinsistingonthedecidabilityofallnecessarytruthsisthepointofWittgenstein’swholetreatmentoflogicandnecessity.42Myownviewisthatthetruthisbetweenthetwo.ItseemstomethatwhatreallymatteredtoWittgensteinwassimplythatlogicandmathematicsdonotfurnishuswithsub-stantialtruthsabouttheworld,andarenot,therefore,knowableonlybysomekindofacquaintancewithorintui-tionoftheworld:hewasprincipallyconcernedtorejecttheKantianideaofsyntheticaprioritruths.Butitalsoseemstomethathewasledbythisconvictiontoexpectallnecessarytruthstobedecidable:thisexpectationwasmorethanhehadanyrightto,butIthinkitwasnotallthatunreasonableintherelativeinnocenceoftheera.43IfWittgensteinrejectsKant’saccountofnecessarytruths—mathematicaltruths,inparticular—wemightthinkthathecanhavenoanswertooneofthequestionswhicharenaturallyseenastemptingustowardsaKantianview.Thequestionis:howisitthatlogic,mathematics,andtherest,applytotherealworld?ButinfactWittgenstein’spicturetheoryoflanguagegiveshimareadyanswertothisques-tion,withoutweakeninghisoppositiontoKant.Accordingtothepicturetheory—theviewthat,inthebasiccaseatleast,sentencesaremodelsofreality—sentencescanonlyrepresentrealityatallinvirtueofhavingthesameformasreality:thatis,ifthepossibilitiesofcombinationofthecomponentsofthesentences(atleast,whenthosesentenceshavebeenreformulatedinaperspicuousnotation)arethesameasthepossibilitiesofcombinationofthecorrespondingobjectsin\n254LOGICANDCOMPOUNDSENTENCESreality.Ifthisisright,therecanbenopossibilityoflogicormathematicsfailingtoapplytotherealworld:logicandmathematicssimplyshowtheformwhichiscommontobothlanguageandtheworld.Butitisstillthecasethatweneverneedtolookattheworld,independentlyofthesym-bolism,toseewhatthepossibilitiesofcombinationare.Thefactthattheformoflanguageisthesameastheformoftheworldguaranteesthatlookingatlanguageisalwaysenough.5FEXTENSIONALITYWittgensteinclaimsthat‘everypropositionistheresultof–successiveapplicationsoftheoperationN(n)toelementarypropositions’(6.001).SincetheN-operatoristruth-func-tional,whatthismeansisthateverycombinationofele-mentarysentencesistruth-functional;whichistosaythatnothingbutthetruthorfalsityofasentencecanmakeadifferencetothetruthorfalsityofsentencesinwhichitﬁguresasacomponent.Thisisacommitmenttothetruth-functionalityofalllanguage,orextensionality.And,ofcourse,itwasalreadyannouncedinthisearlierremarkinthetext:5.Propositionsaretruth-functionsofelementarypropositions.(Anelementarypropositionisatruth-functionofitself.)Thereareanumberofapparentcounter-examplestothisclaim,themostfamousofwhichareusesofsentenceswithin‘that’-clausesusedtosaywhatsomeonethinksorfeels.Theseapparentcounter-exampleswerewellenoughknownbythetimeWittgensteinwrote:Fregeusedthenotionofsensetodealwiththeminhis(1892a),andRussellhopedtousehistheoryofdescriptionstodealwiththem,withoutappealingtothenotionofsense(Russell1905).Wittgensteinshowsthathewasawareoftheproblem:5.541Atfirstsightitappearsasiftherewerealsoadifferentwayinwhichonepropositioncouldoccurinanother.\nLOGICANDCOMPOUNDSENTENCES255Especiallyincertainpropositionalformsofpsychology,like‘Athinks,thatpisthecase’,or‘Athinksp’,etc.HereitappearssuperficiallyasifthepropositionpstoodtotheobjectAinakindofrelation.(Andinmodernepistemology(Russell,Moore,etc.)thosepropo-sitionshavebeenconceivedinthisway.)(TheparenthesishereisareferencetotheviewsofRussell(1903)andMoore(1899):seeChapter2,above.)Theproblem,putbrieﬂy,isthis.Iftheoccurrenceofsen-tencesinthe‘that’-clausesofthesepsychologicalcontextsweretruth-functional,anumberofsubstitutionswouldbepermissiblewhichinfactwereject.Supposethatwebeginwithasentencelikethis:(a)CarolbelievesthatEverestisthehighestmountainintheworld.Infact,itistruethatEverestisthehighestmountainintheworld,sothesentencewithinthe‘that’-clausehere—‘Everestisthehighestmountainintheworld’—istrue.SinceEverestisChomolungma,itcouldmakenodifferencetothetruthofwhatiscontainedinthe‘that’-clauseifweswappedthename‘Chomolungma’forthename‘Everest’—iftheoccurrenceofthesentenceinthe‘that’-clauseweretruth-functional.Ifwedidthat,wewouldgetthis:(b)CarolbelievesthatChomolungmaisthehighestmountainintheworld.ButeventhoughEverestisChomolungma,Carolmaynotknowthat.Ifshedoesnotknowit,then,weusuallythink,(b)willbefalse,eventhough(a)istrue.Thisseemstoshowthatitisnotjustthetruthorfalsityofthesentenceinthe‘that’-clausewhichmakesadifferencetothetruthorfalsityofthewholesentence.Infact,thesituationisevenworse.ItistruethatEverestisthehighestmountainintheworld.Itisalsotruethattheareaofacircleispr2.Ifthetruthorfalsityofthesentenceinthe‘that’-clausewereallthat\n256LOGICANDCOMPOUNDSENTENCESmatters,thetruthof(a)shouldensurethatthisistrueaswell:(c)Carolbelievesthattheareaofacircleispr2.ButifCarolknowsnogeometry,(c)willbefalse,eventhough(a)istrue.Whatthisshowsisthatiftruthorfalsityisallthatmattersinthe‘that’-clausesofreportsofwhatpeoplethinkandfeel,anyonewhobelievesonetruthwilltherebybecountedasbelievingalltruths,andanyonewhobelievesonefalsehoodwilltherebybecountedasbelievingallfalsehoods.Itseemsclear,onthefaceofit,thatthesepsychologicalcontextsarenon-truth-functional,andthatWittgensteinisthereforewrongaboutthegeneralformofsentences.ButWittgensteindoesoffersomeresponse:5.542Butitisclearthat‘Abelievesthatp’,‘Athinksp’,‘Asaysp’areoftheform‘“p”saysp’:andherewehavenoco-ordinationofafactandanobject,butaco-ordinationoffactsbymeansofaco-ordinationoftheirobjects.Fromwhichheconcludes:5.5421Thisshowsthatthereisnosuchthingasthesoul—thesubject,etc.—asconceivedincontemporarysuperficialpsychology.Acompositesoulwouldnotbeasoulanylonger.Unfortunately,thisresponseishardtomakesenseof.WhatWittgensteinseemstobesayingisthatthesepsychologicalstatementscannotreallybemadetruebyanobject(aperson,asoul)beingrelatedtoanotherthing,asentenceoraproposition,inacertainway.Rather,whatisgoingonisthatacertainfact—apictureormodel—representsthatsomethingisthecase.Theideaseemstobethatitisnottheperson,thesoul,orwhatever,thatisrelatedtoacertainpossiblesituation;rather,itissomethinginthemindoftheperson—somementalpicture—whichrepresents.Herewe\nLOGICANDCOMPOUNDSENTENCES257havearejectionofthetraditionalconceptionoftheperson,orthemind,whichisratherreminiscentofHume;44andthiswillhavesomesigniﬁcanceforthediscussionofsolipsism,whichwewillconsiderinthenextchapter.Butthedifﬁcultyistoseehowthisisasolutiontotheprobleminhand.Theoriginalproblemwastheapparentappearanceofsentencesinnon-truth-functionalcombina-tions:the‘p’positioninsentencesoftheform‘Abelievesthatp’seemstobenon-truth-functional.Butthesecond‘p’positioninsentencesoftheform‘“p”saysthatp’isequallynon-truth-functional,andforexactlythesamereason:ifitweretruth-functional,thenif‘p’saidsomethingtrue,itwouldsayalltruths,andifitsaidsomethingfalse,itwouldsayallfalsehoods.AlthoughIthinkthatthereisaproblemherewhichWittgensteincannotreallysolve,wewillmissthewayWittgensteinapproachedtheissueifwetreatitintheseterms.Ihavesupposedthattheproblemsarisewithsen-tenceswhosecanonicalmodeofexpressionincludesa‘that’-clause:‘abelievesthatp’,forexample,or‘“p”saysthatp’.Wittgenstein’sﬁrstmentionoftheissuedoesuseafor-mulationofthiskind,buthequicklyreplacesitwithanother,whichthenremainshisstandardformofexpres-sion:‘Athinksp’,‘Asaysp’,‘“p”saysp’.Andintheseexpressions‘p’seemstoﬁgureasaname—ofafact,orofaRussellian‘proposition’(theobjectivecorrelateofawholesentence).ThistreatmentofthesecontextsisexactlywhatRussell’sﬁrsttheorysuggests(seeChapter2,section2D,above).Wittgenstein’sresponsenowmakessense.Russell’soriginalaccountmakesthesecontextsexpressarelationbetweenanobjectnamedbytheﬁrstname(thisobjectisaperson,asubject,athinker)andadifferentkindofobjectnamedbythesecondname(whichisafact,oraRussellianproposition).Wittgensteinobjectsthatwedonotreallyhavearelationbetweenaperson-typeobjectandafact-typeobject:whatwehaveiswhatwemightﬁrstdescribeasarelationbetweentwofact-typeobjects—asentenceandwhatitdepicts.Butthisﬁrstdescriptionis,ofcourse,wrong,\n258LOGICANDCOMPOUNDSENTENCESaccordingtotheTractatus’sgeneraltheoryoflanguage:theseexpressionsarenotnames,andwedonothaveobjectshereatall;sotherecanbenoquestionofarelation,literallyspeaking,betweenthem.Theonlyrealrelationsinvolvedherearerelationsbetweentheelementsofsentences,ontheonehand,andtheobjectswhichconstitutethefacts,ontheother.Sotheproblemissupposedsimplytodisappear.Unfortunately,asRamseypointedoutinhisoriginalreviewoftheTractatus,thiswillnotwork:‘thesenseisnotcompletelydeterminedbytheobjectswhichoccurinit;noristhepropositionalsigncompletelyconstitutedbythenameswhichoccurinit’(Ramsey1923:471).And,ofcourse,thepointisWittgenstein’sown:WhenwesayAjudgesthatetc.,thenwehavetomentionawholepropositionwhichAjudges.Itwillnotdoeithertomentiononlyitsconstituents,oritsconstituentsandform,butnotintheproperorder.Thisshowsthatapropositionitselfmustoccurinthestate-mentthatitisjudged.(NL:94)ThethoughtevenliesbehindtheverynextremarkoftheTractatusitself,inwhichheobjectstoRussell’s‘multiple-relation’theoryofjudgement:5.5422Thecorrectexplanationoftheformoftheproposition‘Ajudgesp’mustshowthatitisimpossibletojudgeanonsense.(Russell’stheorydoesnotsatisfythiscondition.)45TheconsequenceisthatWittgenstein’streatmentofsen-tencesoftheform‘abelievesthatp’,oreven‘“p”saysthatp’canonlyreallybeacceptedifwesupposethatsuchexpressionsarereallyjustmalformed,andarenotreallymeaningfulatall.Andthatreallyisnotcredible.Weareboundtoﬁndithardtobelieveatheorywhichnotonlysaysthatthereisnosoul(becausethereisnosinglesubjectwhichhasabelief),butalsodeniesthatwecaneversaywhatsomeonesaysorthinks.Suchscepticismevenseemsatodds\nLOGICANDCOMPOUNDSENTENCES259with5.5422itself,whereWittgensteinseemstoholdouthopeofapositiveandsubstantialsolutiontotheproblemofanalysingthesesentences.ItistemptingtothinkthatpartoftheproblemisthatWittgensteinwasjustdazzledbythepowerofmodernlogic,thelogicinventedbyFregeandRussell,andasaresultsimplydidnotconsiderthepossibilitythattheremightbeconstructionswhichitcouldnotaccommodate.Here,afterall,wasasystemwhichcouldexpressavastlygreaterrangeofargumentsthanAristotle’slogicevercould.Moreover,itseemedtoofferexplanationsofwhythevalidargumentsarevalid,and(inthecaseofsentencelogic,atleast)toprovideasimpleprocedurefortestingforvalidity.Inthelightofthisextraordinaryincreaseinwhatcouldbedonewithlogic,itwouldperhapsbenaturaltothinkthatmodernlogicactuallyrevealedthelogicoftheworld:thatitwasnotjustonesystemforformalizingarguments,butshowedtheproperformofallpossiblevalidargument.Consequently,wecanunderstandhowitmightbenaturaltothinkthatwhatcouldnotbedealtwithbythatlogiccouldnotreallymakesense.46ButIthinkWittgenstein’scommitmenttoextensionality—theinsistencethatsentencescanonlybeconstructedtruth-functionally—runsmuchdeeperthanthat.Infact,itseemscompletelyintegraltohiswholesystem.Wecanseeitevenintheearlyaccountofthemeaningof‘forms’intheNotesonLogic(NL:104),whichwehavealreadylookedat(seeChapter4,section4F;andagaininsections5Band5Dofthischapter).Theideaisthatwhatneedstobedeterminedisjustwhichfactsare‘oflikesense’andwhich‘ofoppositesense’witharangeofsentences,whichiswhatsettleswhichsentencesaretocountastrueandwhichfalse.IarguedinChapter4thatintheTracatusthisaccountisextendedtoapplytoallelementsofelementarysentences.Theresultisthatthereseemstobenomoretothemeaningofthepartsevenofelementarysentencesthantheircontributiontothedeter-minationofthetruth-valueofthesentencesofwhichtheyarepart.Andthisalreadymeansthatwhatultimatelymattersaboutwholesentencesisjustwhethertheyaretrueorfalse.\n260LOGICANDCOMPOUNDSENTENCESWittgenstein’sextensionalismalsomanifestsitselfinthefollowingbasiccommitmentofthemetaphysicsoftheTractatus,oneofthetwowhichhavenotyetbeenexplainedasbeingaconsequenceoftheTractatus’stheoryoflanguage:(T4)Theexistenceofanyatomicfactisindependentoftheexistenceofanyotheratomicfact.Ifthelogicoftheworldisextensional,andeverysentenceistheresultofsuccessiveapplicationsoftruth-functionstoelementarysentences,itfollowsthatelementarysentencesmustbelogicallyindependentofeachother.Forsupposethatsomeelementarysentencesarenotlogicallyindepen-dentofallotherelementarysentences.ThiswouldmeanthattherearewhatinChapter1(section1E)Icalleddependencefacts—factsofthefollowingform(where‘p’and‘q’mightbereplacedbyelementarysentences):(D)Itsbeingthecasethatpdependsonitsbeingthecasethatq.AswasnotedinChapter1,therecanonlybeapointinsinglingoutanynotionofdependencebetweenfacts,iftherelevantdependencerelationsholdbetweensomefactsandnotbetweenothers.Butthatmeansthattwofactsbeingfactsisnotenoughtodeterminewhetherthereisadependencerelationbetweenthem.Andthatmeansthatthecorrespondingsentencescanbothbetruewithoutitsbeingdeterminedwhetherthereisadependencerelationbetweenthem.Andthatmeansthatthetruthofstatementsofsuchdependencecannotjustdependonthetruth-valueofthesentencesofwhichtheyarecomposed.Thatistosay,(D)itselfcannotbetruth-functional,ifdependenceistomeananything.SinceWittgensteininsiststhatsentencescanonlyoccurtruth-functionallyinothersentences,(D)cannotbealegitimateformofsentence,where‘p’and‘q’arereplacedbyelementarysentences.Sonoelementarysentencecandependonanyother.Ifelementarysentencesarelogicallyindependentofeachother,thentheirontologicalcounterparts,theatomicfacts,\nLOGICANDCOMPOUNDSENTENCES261aremutuallyindependentexistences.Thisimmediatelygivesus(T4).Anditleadstotheﬁnalunexplainedmetaphysicalcommitmentaswell.Giventhatnamesareonlymeaningfulwhenlinkedtogetherwithothernamesinasentence(sothatobjects,thecounterpartsofnames,cannotexistexceptincombinationwithotherobjects),(T4)meansthatthisclaimisalsotrue:(T1)Thebasicorganicunitiesoftheworldarefacts.Itisonlythecounterpartstoelementarysentenceswhichareindependentofoneanother.ThewholemetaphysicsoftheTractatusisﬁnallyseenasnomorethanwhatisrequiredbythework’sphilosophyoflanguageandphilo-sophyoflogic.ThisshowshowcloselyextensionalityisboundinwiththemetaphysicsoftheTractatus.Itwasalsoattheheartofthework’seventualunravelling.Itfollowsfromthethesisofthelogicalindependenceofelementarysentencesthatneitherofthefollowingtwosentencescanplausiblyberegardedaselementary,whateverthename‘a’istakentoreferto:(1)aisredallover;(2)bisblueallover.For(1)and(2)seemclearlytocontradicteachother.Butalthoughthatmeansthattheycannotbecountedaselemen-tarysentences,itisunclearwhatanalysisofthemcouldbeprovidedwhichavoidsthesameproblemrecurringatanotherpoint.Wittgensteinfacesaseriouschallengetoexplainthelogicalrelationsbetween‘red’and‘blue’.IntheTractatusitselfheseemssimplytohaveassumedthattheproblemissoluble:6.3751Fortwocolours,e.g.tobeatoneplaceinthevisualfield,isimpossible,logicallyimpossible,foritisexcludedbythelogicalstructureofcolour.\n262LOGICANDCOMPOUNDSENTENCESLetusconsiderhowthiscontradictionpresentsitselfinphysics.Somewhatasfollows:Thataparticlecannotatthesametimehavetwovelocities,i.e.thatatthesametimeitcannotbeintwoplaces,i.e.thatparticlesindifferentplacesatthesametimecannotbeidentical.(Itisclearthatthelogicalproduct[conjunction]oftwoelementarypropositionscanneitherbeatautologynoracontradiction.Theassertionthatapointinthevisualfieldhastwodifferentcoloursatthesametime,isacontradiction.)Butthislookslikemerebluster:afterall,howisitexplainedthatitislogicallyimpossibleforparticlesindifferentplacesatthesametimetobeidentical?47Wittgensteincamelatertorejecttheviewhehereespouses;andthatrejectionwasthebeginningoftheeventualabandonmentofthewholesystemoftheTractatus.48\n6SOLIPSISM,IDEALISM,ANDREALISM6ATHEDRAMATICCLAIMWesawinthelastsectionofthepreviouschapterthatWittgensteindismissedtheideaofasubjectorself,asthatisconceivedofin‘contemporarysuperﬁcialpsychology’(5.5421).Thatsuggeststhattheremightbeasubjectorselfofanaltogetherdifferentkind,whichplaysaratherdifferentroleinphilosophy.And,inasense,thatseemstobejustwhatWittgensteinthinks,thougheventosaythatistocourtcontroversy.Theproblemiscrystallizedinthisremark:Infactwhatsolipsismmeans,isquitecorrect,onlyitcannotbesaid,butitshowsitself.(5.62)Solipsism,traditionallyunderstood,istheviewthatonlytheself(‘solusipse’)exists:nothingbuttheselfisreal.Itisnotclear,however,thatthisisquiteWittgenstein’sview,orthat\n264SOLIPSISM,IDEALISM,ANDREALISMheisconcernedwithit—toputthepointnolessambigu-ously—forpreciselythetraditionalreasons.Wittgensteinhereseemstobemakingthreedistinctclaims:(i)‘Whatsolipsismmeansisquitecorrect’;(ii)‘Whatsolipsismmeans’cannotbesaid;(iii)‘Whatsolipsismmeans’‘showsitself’.Tobeginwith,atleast,Iwilltaketheseclaimsasliterallyaspossible.ThequestionwillthenbetounderstandwhyWittgensteinmakesthem.Thiswillshowwhatkindof‘solipsism’hehasinmind,andwillalsorevealsomethingofthecharacteroftheTractatusasawhole.Wittgenstein’sdiscussionintheTractatusoftheviewhecalls‘solipsism’isverybrief,butmightbeclaimedtobethecentrepieceofthewholework.1InthesingledramaticremarkIhavejustquotedwemightseemtohavethefulﬁl-mentoftheaimofthebookasthatisstatedinthePreface:[Thebook’s]wholemeaningcanbesummedupsomewhatasfollows:Whatcanbesaidatallcanbesaidclearly;andwhereofonecannotspeakthereofonemustbesilent.(TLP,p.27)IhavesuggestedthatthebookcanbeseentobeareactionagainstKant’sapproachtometaphysics—inparticular,againsttheviewthatphilosophicaltruthsaresyntheticaprioritruths.Itistemptingtoseethedramaticclaimof5.62asamovingonfromKant’swholephilosophy.6BTHEBACKGROUNDFirst,though,itwillbeusefultogetsomepurchaseforourselves—independentlyofthetext—onthekindsofissuewhichmightbeinvolvedhere.Solipsismisaformofidealism.Idealismismostsimplyseenasadenialofrealism,andrealism,aswehavealreadyseen,isnaturallyformulatedinsomesuchtermsasthese:\nSOLIPSISM,IDEALISM,ANDREALISM265(R)Thenatureoftheworldasitisinitselfisaltogetherindependentofanythingtodowithanythoughtorrepresentationofit.(R)isconcernedwiththenatureoftheworldasawhole;itisthereforeanexpressionofwhatmightbetermeda‘global’realism.Buttheremightbemorelocalissues:whethertoholdthatthenatureofsomeparticularkindofobject,orsomeparticularkindoffact,wasaltogetherindependentofthoughtorrepresentation.Anypositionwhichhesitatestoendorse(R),orthecorre-spondingclaimaboutsomeparticularkindofobjectorfact,maybetermedanti-realist.Someonewhopositivelydenies(R),holdingthatthereissomedependenceoftheworld—ortherelevantkindofobjectorfact—uponthoughtorrepresentationcanbecountedanidealist.Itisworthnotingthatthereissomethingstipulativeaboutmyuseoftheterms‘idealism’and‘realism’here.FortheissueswhichmattertotheTractatus,thecentralconcerniswhetherthingsareorarenotindependentofthoughtandrepre-sentation.Buttheterms‘idealism’and‘realism’haveotherusestoo.Kant,forexample,seemssometimestouse‘ideal-ism’tomeanscepticism(inthe‘RefutationofIdealism’,inKant(1787)).And‘realism’issometimesusedtodescribeananti-scepticalposition,eventoday:thus‘naïverealism’,inthephilosophyofperception,istheviewthatweperceivethingsastheyareindependentlyofus.Therearetwoformsofidealismwhichbulkparticularlylargeintheliterature.TheﬁrstisthekindofidealismadvocatedbyBerkeley(1734).Hisidealismconcernswhatisperceivable,andhisclaimisthatwhatisperceivablecannotexistwithoutactuallybeingperceived.Thisissometimesknownasempiricalrealism(Williams1981).ThereisadifferentkindofidealismwhichisassociatedwithKantandthetraditionwhichfollowedhim(including,intheirdifferentways,HegelandSchopenhauer).Kantheldthat,althoughperceivablethingsdonotdependfortheirexistenceonactuallybeingperceived,theirnature—or,atleast,suchoftheirnatureaswecanhaveknowledgeof—is\n266SOLIPSISM,IDEALISM,ANDREALISMdeterminedbythenatureofthecognitivefacultiesofthosewhocanhaveexperienceofthem.Herewehaveadifferentsortofidealism:adependenceofthenatureofwhatweperceiveonsomethingtodowiththoughtorrepresentation.Thismightbetermeda‘transcendental’idealism,tomakethecontrastwiththeempiricalidealismadvocatedbyBerkeley(thusWilliams(1981)).Butitwouldbeconfusingtousetheterm‘transcendentalidealism’inthatway,sincethetermisalreadythenameofthewholeofKant’sview,ratherthanjustthisidealistportionofit.Kant’sidealism(inthesenseofarejectionof(R))concernsjustwhatisperceivable—or,tobemoreprecise,justthatwhichwecanunderstandofwhatisperceivable.Butinadditiontothis,Kantassumesthatthereisawayinwhichthingsareinthemselves.(Thereisaninterpretativecon-troversyoverwhetherwhatwearedealingwithherearethesamethings—theperceivablethings—astheyareinthemselves,orwhethertherearespecialthings—thingsinthemselves—whichsomehowliebehindtheperceivablethings.Thisisthedisagreementbetweenone-worldandtwo-worldinterpretationsofKant,adisagreementwhichweneednotconsiderfurtherhere.2)AccordingtoKant,wecannotknowhowthingsareinthemselves.Thewaythingsareinthemselvesiswhollyindependentofanythingtodowiththoughtorrepresentation.SoKantisﬁrmlyrealist,inthesenseof(R),aboutthingsastheyareinthemselves.And‘transcendentalidealism’isthenameofthistotalKantianposition:idealism(inthesenseofarejectionof(R))aboutthingsastheycanbeperceivedbyus,andrealism(inthesenseof(R))aboutthingsastheyareinthemselves.Idealismhas,historically,beenaresponsetoscepticism.Someargumentmaymakeitseemthatwecannothaveknowledgeoftheworldasitisinitself,ifitsnatureistoostrictlyindependentofthoughtandrepresentation;soinordertoavoidtheconclusionthatwecannothaveknowledgeoftheworld,itissuggestedthattheworldisnotsostrictlyindependentofthoughtandrepresentation.Andthechar-acteroftheidealismisthendeterminedbythecharacterof\nSOLIPSISM,IDEALISM,ANDREALISM267thescepticism.Berkeleywasconcernedtoavoidempiricalscepticism,theclaimthatwecannothaveknowledgeoftheempiricalfacts,thefactswhichwemightthinkareavailableinperception.Kantwasconcernedtoavoidscepticismaboutwhatisessentialtotheperceivableworld,aboutitsnecessaryfeatures:accordingly,hesupposedthattheessentialfeaturesweareinterestedinwereinsomewaydeterminedbysomethingtodowiththoughtorrepresentation.WhatkindofidealismisthesolipsismwhichWittgensteinisconcernedwithintheTractatus?Wecannoteasilydecidethisbyaskingwhatkindofscepticismhemightberespondingto,sinceitisnotobvious,inadvanceofcon-sideringhisviewsonsolipsism,thathehasanygreatinterestinscepticismintheTractatus;indeed,itisnaturaltothinkthatheseemsonlyslightlyconcernedwithepistemicissuesingeneralatthispointinhiscareer.IfwethinkhismainconcernhereistorespondtotheviewsofRussell,thenwewillthinkthatthesolipsismoftheTractatusissomethingmorelikeBerkeley’sempiricalidealism.ForRussellwasconcernedwithscepticism,injustthekindofwayinwhichtheBritishempiricistsoftheclassicalperiod,includingBerkeley,were.3Thisledhimtobasehismetaphysicalsystemon‘sense-data’,objectsofimmediateexperienceaboutwhoseexistencewecannotbemistaken.ThisseemstometobequiteunlikeWittgenstein’sgeneralconcernsintheTractatus.4AswesawinChapter1,thefundamentalobjectsoftheTractatusarenotthosewhoseexistencecannotbedoubted,butthosewhoseexistenceisnecessary.Hisconcernisnotwithwhatpresentsitselftousasactuallyexisting;butwiththeformoftheworld—whatiscommontoeverypossibleworld.Thegeneralorientationofhisinterest—towardswhatispossibleandwhatisnecessary,ratherthantowardswhatisactuallyexperienced—suggeststhatitwillbeaKantian,ratherthanasimplyBerkeleyanidealismwhichconcernshim.AndtherearestrongtracesintheremarksonsolipsismintheTractatusoftheinﬂuenceofSchopenhauer,5andSchopenhauerwasevidentlyworkingwithintheKantiantradition.\n268SOLIPSISM,IDEALISM,ANDREALISMMoreover,itisaKantianquestionwhichliesattheheartofhisphilosophicalconcernsingeneral.Thus,intheNotebookshewrites:ThegreatproblemroundwhicheverythingthatIwriteturnsis:Isthereanorderoftheworldapriori,andifsowhatdoesitconsistin?(NB:53)ThisisthequestionwhichKantansweredintheafﬁrmative,andwastherebyledtoinsistthattherearesyntheticaprioritruths.Thereisadirectconnectionbetweenthisissue(inthisformulation)andthediscussionofsolipsismintheTractatus.5.634endswiththesewords:Thereisnoorderofthingsapriori.6Itisnatural,therefore,totakethesolipsismoftheTractatustobeaformofidealismwhichaddressesKant’sconcerns.7ThereisalsoasimilaritywithKantinthefollowingrespect.Kantwasconcernedwiththelimitsofwhatcanbeknown:forhim,knowledgeislimitedbywhatisrequiredtomakesenseofwhatcanbeexperienced.Accordingtohim,wecanhavenoknowledgeofthewaythingsareinthemselves;thewaythingsareinthemselvesliesbeyondthelimitsofourknowledge.Theaimofhistheorywastore-establishmetaphysicsasarigorousscientiﬁcdisciplinewithinthelimitsofwhatisrelevanttopossibleexperience,andtoexposeasunconstrained(indeed,paradoxical)anyattempttodometaphysicsbeyondthoselimits.Wittgenstein,ofcourse,wasconcernedwiththelimitsofthought(oritsexpression):Thebookwill,therefore,drawalimittothinking,orrather—nottothinking,buttotheexpressionofthoughts;for,inordertodrawalimittothinkingweshouldhavetobeabletothinkbothsidesofthislimit(weshouldthereforehavetobeabletothinkwhatcannotbethought).(TLP,p.27)\nSOLIPSISM,IDEALISM,ANDREALISM269And,aswewillseeinthenextchapter,Wittgensteinalsousestheselimitstoruleoutmetaphysics(thoughheismoreradicalthanKant,preciselyinnotacceptingthepossibilityofsyntheticaprioritruths,thecategorywhichmakesroominKant’stheoryforthepossibilityofascientiﬁcmetaphysics).Furthermore,Kant’stheorywassubjecttocriticism,fromveryearlyon,ongroundswhichlookrathersimilartothosewhichWittgensteinappealstointhatremarkinthePrefaceoftheTractatuswhichIhavejustquoted.Kantcanonlymakehisdistinctionbetweenthingsastheyappeartous(whichcanbeknown)andthingsastheyareinthemselves(whichcannot)ifhecanatleasttalkandthinkaboutthingsastheyareinthemselves.Hethereforeneedsittobepossi-bletotalkorthinkaboutsomething(orawayinwhichsomethingis)whichwecanhavenoknowledgeof.Butitisnotobviousthatthisisreallyintelligible:itisnaturaltothinkthatwecanonlyreferto,orthinkabout,whatwehavesomeknowledgeof.Ifthatisright,eventostateKant’stheoryrequiresustohavesomeknowledgeofwhat(accordingtohim)cannotbeknown,whichisproblematicinjustthewaythinkingwhatcannotbethoughtis.WecanusethisKantianbackgroundtosketch,inarathersimple-mindedway,somepossibleformsofrealismandidealism,inordertogetabettersenseofthekindofviewWittgensteinmightbeadopting.(Thereasonforcallingthissketch‘simple-minded’willappearshortly.)WecanalsousethegeneralapproachtothoughtwhichtheTractatuspre-sentstosetuptheissuesinawaythathasastraightforwardintuitiveresonance.AccordingtoWittgenstein,tothinkistoformapictureormodelofreality(2.1,3,3.001):thinkingisrepresenting.Intuitively,representationscanbeindifferentmedia:painting,music,writing,andsoon.Nowwemightthinkthatdifferentmediaaredifferentlygoodforrepre-sentingdifferentkindsofthing.Painting,wemightthink,isparticularlygoodforrepresentingcolourandshape,butratherpoorforrepresentingsounds;conversely,music,wemightthink,isgoodforrepresentingcertainkindsofemotionalsigniﬁcance,andcertainkindsofmovement,but\n270SOLIPSISM,IDEALISM,ANDREALISMratherpoorforrepresenting,say,colours.Ifwethinkinthisway,itisnaturaltowonderwhethertherearesomethingswhichsimplycannotberepresentedincertainmedia—whetheramediummighthave,asitwere,arepresentationalblind-spot.8Nowifwecanraisethisquestionaboutrepresentationalmediaingeneral,itseemsnaturaltothinkwecanraiseitaboutlanguagetoo.Consider,then,thisquestion:(Q)Mightlanguagehaverepresentationalblind-spots?Onthefaceofit,thisquestionmighthaveeitheranafﬁr-mativeoranegativeanswer.Supposeweanswer‘Yes’.WeseemnowtohaveapositionwhichistherepresentationalanalogueofKant’s;anditfacesasimilarquestion.Isitevenpossibletostate,inlanguage,thatlanguagehasrepresenta-tionalblind-spots?Weseemtobeabletodistinguishbetweentwopossiblepositions:(A1)Languagemighthaverepresentationalblind-spots,andthatpossibilityisstatable;(A2)Languagemighthaverepresentationalblind-spots,butthatpossibilityisnotstatable.(A2)isobviouslyaparadoxicalposition;wewillreturntothatissueshortly.Inthemeantime,letusconsidertheotherapparentlypossibleanswerto(Q):no,languagecouldnothaverepresentationalblind-spots.Nowthisanswercouldbegivenforoneoftworeasons.Wemightthinkthat,infact,therearenosubstantialconstraintsonrepresentation:anythingatallisinprinciplerepresentableinanymedium,simplybecausetherearenogeneralrequire-mentsabouthowrepresentationsmuststandtowardswhattheyrepresent.Ifweadoptthisresponse,wedonotsuppose,forexample,thattheremustbeanysimilarityinformbetweenproductsofamediumandwhatcanberepre-sentedinthatmedium.Wemightformulatethisresponseasfollows:\nSOLIPSISM,IDEALISM,ANDREALISM271(A3)Languagecouldnothaverepresentationalblind-spots,becausethereisnoconstraintatallonwhatcanberepresentedinanygivenmedium.Thispositionwillholdthatitispossible,inprinciple,torepre-sentsoundsinpainting,forexample,andcoloursinmusic.(A3)cannotbethepositionoftheTractatus,becausetheTractatusseemstoinsistpreciselyonastrongconstraintonrepresentation—therequirementthatamodelmusthavethesameformastherealityitdepicts.Sowearelikelytobemoreparticularlyinterestedintheotherwayofanswering‘No’to(Q).Thisholdsthattherecannotberepresentationalblind-spotsinlanguage,eventhoughtherearesigniﬁcantconstraintsonwhatcanberepresentedinanymedium.Whatthisrequiresisthat,althoughtherearestrictcon-straintsonwhatisstatable,thereisnothingwhichispossi-blewhichisnotstatable.Thequestionthenariseswhythisshouldbeso.Thereseemtobethreepositionswhichcouldbeadopted,whichwemightformulatelikethis:(A4)Languagecouldnothaverepresentationalblind-spots,becauselanguagesimplyadoptstheformofreality;(A5)Languagecouldnothaverepresentationalblind-spots,becauserealityisdeterminedbywhatlanguagecandepict;(A6)Languagecouldnothaverepresentationalblind-spots,becausewhatlimitslanguagealsolimitsreality.Puttingitcrudely,(A4)isarealistposition—itportraysrealityasbeingindependentoflanguage,andlanguageasbeingshapedtoﬁtreality.(A5)isakindofidealistposition—itportraysrealityasbeingconstrainedbythelimitsoflanguage;realitydoesnothavetherobustindependencefromthoughtandrepresentationwhichourformulation(R),forexample,requires.And(A6)isneutralwithrespecttothequestionofrealismandidealism.Butitisimportanttonotethat(A4)isnottheonlyrealistpositionamongtheanswersto(Q).(A1)and(A2)bothlooklikerealistviews(evenif(A2)isaparadoxicalformofrealism),and(A3)iscertainly\n272SOLIPSISM,IDEALISM,ANDREALISMcompatiblewithrealism.(A4)issimplytheonlyunambigu-ouslyrealistpositionamongthosewhichthinkthattheanswerto(Q)is‘No’,whileinsistingthattherearesigniﬁcantconstraintsonwhatcanberepresentedinanymedium.Somuchforthesimple-mindedsketchofthealternativeswhichseemtobeopentous.Wecannowstartputtingthissimple-mindednessinquestionbyconsideringthewaysinwhichvariouspositionsheremaybethoughttorunintoproblemsofparadox.Ihavealreadynotedthat(A2)ispara-doxical:itcannotbecoherentlystated.Forallthat,wemightthinkthatitwastrue:afterall,weseemtobejustapplyingtolanguagethethoughtswhichseemedsointuitiveinthecaseofpaintingandmusic,andthenﬁndingthatbecauseoftheaccidentofthemediumweareworkingin—philosophyisalwayslinguistic—theverytruthwearetryingtofocusonturnsouttolieinoneofthecrucialblind-spots.(A2)invitesustoentertaintheideathattheremightbeunstatable,inexpressible,ineffabletruths.Butparadoxthreatensmoreofourrangeofapparentlypossiblepositions,ifwestartbuildinginmoreassumptions.Supposeweacceptanassumptionwhichwemighttrytoputlikethis:(SC)Itisonlypossibletostatethatpifitiscontingentwhetherp.ThislooksatleastveryclosetooneoftheassumptionswhichWittgensteinneedsforhisclaimthatnopicturecandepictitsownform(2.172–2.174);anditisaclosecousintothePrincipleofBipolaritywhichisoftenattributedtoWittgenstein(seeChapter3,section3D,above).9Anditseemstobestatedexplicitlyin5.634:Everythingwecandescribeatallcouldalsobeotherwise.Suppose,then,thatweaccept(SC).Andsupposethatwealsoacceptthefollowingfamiliarmodalprinciple:(S5)Ifitispossiblethatp,itisnecessarythatitispossiblethatp.\nSOLIPSISM,IDEALISM,ANDREALISM273Aswehaveseen,therearestrongreasonsforthinkingthatWittgensteiniscommittedto(S5)(seeChapter1,section1D).(SC)and(S5)makeaparadoxicalpair.Bothare(attemp-ted)statementsaboutwhatispossible;(SC)requiresthatforthemtobestatementsatall,whatispossiblemustbeonlycontingentlypossible;but(S5)saysthatwhatispossibleisnotcontingentlypossible.Andtheparadoxofthispairofassumptionsalsoinfectsalltheapparentlyintelligibleanswersto(Q),since(Q)itself,andalltheseanswerstoit,areconcernedwithwhatispossible.WecanconstructsimilarproblemsifwegobacktowhatseemtobeevenmorebasicassumptionsinWittgenstein’stheory.Supposeweacceptthefollowingassumption:(SP)Itispossibletostatethatponlyifitispossiblethatp.Thisistheconverseofwhathastobeheldbyallthewaysofanswering‘No’to(Q),whichisthis:(PS)Itispossiblethatponlyifitispossibletostatethatp.ThecoreassumptionofidentityofformwhichliesattheheartofthepicturetheoryensuresthatWittgensteinholdsboth(SP)and(PS).Nowsupposeweacceptthisfurtherassumption:(SPN)Itispossibletostatethatponlyifitispossibletostatethatnot-p.(SPN)and(SP)togetherimply(SC),whichwehavealreadyseenisnaturallyattributedtoWittgenstein.Wittgensteinisalsocommittedtothisfurtherassumption:(SPP)Itispossibletostatethatitispossiblethatponlyifitispos-sibletostatethatp.10(SP),(SPN),and(SPP)togethermakeeverynegativeanswerto(Q)declareitselftobeunstatable.Thisisbecauseevery\n274SOLIPSISM,IDEALISM,ANDREALISMnegativeanswerto(Q)saysthatsomethingisnotpossible,and(SP),(SPN),and(SPP)togetherimplythatwhatisactuallyimpossiblecannotbesaidtobeimpossible.Foronecanonlystatethatitisimpossiblethatpifonecanstatethatispos-siblethatp(by(SPN)andtheeliminationofdoublenega-tion).Andonecanonlystatethatitispossiblethatpifonecanstatethatp(by(SPP)).Nowsupposethattherelevant‘p’isimpossible,aswewilltakeittobeifwegiveanegativeanswerto(Q).Thatmeansthatwecannotstatethatp,fortherelevant‘p’(by(SP)).Sowecannotstatethatitisimpossiblethatp.Furthermore,someonewhoacceptsanegativeanswerto(Q)willbedrivenbythisreasoningtocount(A1)and(A2)unstatabletoo.Forifwecannotstatethatitisimpossiblethatp,wecannotstatethatitispossiblethatpeither(by(SPN)).And(A1)and(A2)dopreciselysay(orattempttosay)thatsomethingispossible.Itfollowsfromthisthat(A2)isparadoxicalonanyaccount,andwewillthinkthatallanswersto(Q)areparadoxicalifwethinkthattherightanswer(asitwere)is‘No’,whilealsoholdingsomeassumptionswhichseemtobecentraltothepicturetheoryoftheTractatus.Moreover,itseemsthattheTractatusitselfhastogivetheanswer‘No’to(Q):itcannotaccommodatetheideaoflanguagehavingablind-spot,becausethetheoryholdspreciselythattheformoflanguageisthesameastheformoftheworld.SoitseemsthattheTractatushastoholdthateverypossibleanswerto(Q)isparadoxical.ThisexposestheprecariousnessofevensettingouttopresentasketchoftheapparentlypossibleoptionswhichsomeoneaddressingtheKantianpositionmightseemtoface.WhatIhavewrittencanonlybeacoherentpresentationofarangeofpossiblepositionsifatleastsomeofthecentralassumptionsoftheTractatusarefalse.Myowninclinationistoaccept(A1)or(A3),andtodenytheassimilationofthepossibleandthestatablewhichisatthecoreofthepicturetheory,butneitheroftheseoptionsiseasytodefend.Inthecaseof(A1),weneedtomakeitconvincingthatwecanstatethatthereisablind-spotwithoutitsbeingpossible,in\nSOLIPSISM,IDEALISM,ANDREALISM275principle,toprovideanexample,andactuallystateablind-spot.Andthisiscertainlydifﬁcultonthequantiﬁer-variableapproachtoquantiﬁcation.11Onthisapproach,tostatethatthereissomethingofacertainkindistosaythatthereisanxsuchthatxisamemberofthatkind.Andthe‘x’hereseemstohavetobeeithersomethingwhichcouldbereplacedbyanameoftherelevantthing,orsomethingwhichitselfcouldacttemporarilyasanameofthething.Soonthequantiﬁer-variableapproachtoquantiﬁcation,onecannotsaythatthereissomethingofacertainkind,withoutitsbeingpossible,inprinciple,tomentionathingofthatkind.Adopting(A3),ontheotherhand,seemsnobetterthanheroic:itseemstorequireustodenytheobviousfactofthelimitsofrepresentation.IwillproceedinwhatfollowsasifthecrucialassumptionsoftheTractatusarewrong,andsomecoherentresponseto(Q)canbeformulated.ThiswillpermitustokeepinplaythefullrangeofanswerswhichIhavesketchedout.Someonewhowantstomaintain(asitwere)therelevantassumptionsoftheTractatuswillhavetotakewhatfollowstopresentmerelytheappearanceofacoherentaccount—somethingwhoseapparentcoherencecanbereliedontem-porarilyuntilonegetsintoapositiontoabandonthewholeapproachwithsomeconviction.6C‘WHATSOLIPSISMMEANSISQUITECORRECT’Wearetryingtomakesenseofthispivotalremark:Infactwhatsolipsismmeans,isquitecorrect,onlyitcannotbesaid,butitshowsitself.(5.62)Thisremarkappearsinmatterwhichispresentedasbeingcommentaryonanapparentlymorecentralclaim:5.6Thelimitsofmylanguagemeanthelimitsofmyworld.\n276SOLIPSISM,IDEALISM,ANDREALISMWhatarewetomakeofthat?Tobeginwith,weneedsomeclariﬁcation.Thewordtranslated‘mean’in5.6—‘bedeuten’—isawordstandardlyandproperlytranslatedeitheras‘mean’oras‘referto’.12ButweshouldnotimaginethatWittgensteinisheresug-gestingthatthereisatechnicalsemanticrelationbetweenthe‘limits’ofmylanguageandthe‘limits’ofmyworld,arelationwhichisparalleltothatwhichholdsbetweensomeelementsofmylanguage(thenames)andsomeelementsoftheworld(objects).Wemightheretranslateit‘represent’,‘indicate’—oreven,perhaps,‘determine’.Whatiscurious(butperhapsnotimportant)isthatWittgensteinherewritesanythingotherthan‘are’:afterall,thecentralclaimofthepicturetheoryisthat,intherelevantsenseof‘limit’,thelimitsoftheworldandthelimitsoflanguagearethesame.Thelimitsoftheworldarejustthelimitsofwhatispossible:theyare,intheend,thelimitsonpossiblecombinationsofobjects.AndtheselimitsaretakenbyWittgensteintobethesameasthelimitsofpossiblecombinationsofsymbols.What,though,isthepointof5.6?Morespeciﬁcally,whydoesWittgensteinemphasizethephrase‘thelimitsofmylanguage’?Presumablynottostressthe‘my’—thatIamsomehowinvolvedinthelimitsoftheworld—since‘my’appearsunstressedinthephrase‘thelimitsofmyworld’.Thecentralpointofthisemphasismustbetohighlightthatitislanguagewhichindicates,represents—oreven,per-haps,determines—thelimitsoftheworld.Thisis,ofcourse,areﬂectionoftheisomorphismwhichliesattheheartofthepicturetheory.Anditsoccurrenceatthebegin-ningoftheaccountofsolipsismshowsthatwearecom-mittedtooneofthewaysofanswering‘No’toquestion(Q)—thatis,to(A4),(A5),or(A6).5.61reiteratesthispoint,andthendrawsaconclusionfromit:13Logicfillstheworld:thelimitsoftheworldarealsoitslimits.Wecannotthereforesayinlogic:Thisandthisthereisintheworld,thatthereisnot.\nSOLIPSISM,IDEALISM,ANDREALISM277Forthatwouldapparentlypresupposethatweexcludecertainpossi-bilities,andthiscannotbethecasesinceotherwiselogicmustgetoutsidethelimitsoftheworld:thatis,ifitcouldconsidertheselimitsfromtheothersidealso.Thislooksasifitcontainstheassertionbothofanegativeanswerto(Q),andoftheclaimthatsuchananswerisunsayable,forreasonsthatmightwellbecapturedintermsof(SC),or(SPN)and(SPP).Buttheemphasisonlanguagein5.6and5.61doesnotgetustoanythingwhichisdistinctivelysolipsistic:5.6uses,butdoesnotstress,the‘my’;and5.61movesoutfrom‘myworld’to‘theworld.Togetanythingwhichlookslikeagenuinesolipsism,weneedtoﬁndanidentiﬁcationoftheworldwithmyworld.Andtheargumentforthatisfoundintheﬁnalparagraphof5.62:Thattheworldismyworld,showsitselfinthefactthatthelimitsofthelanguage(the[only]languagewhichIunderstand)meanthelimitsofmyworld.Butwhatmighttheargumentbe?IhaveherecorrectedtheOgdentranslationofthisparagraphtomakeitreadasitseemsclearthatWittgensteinwantedittoread(Lewy1967:419).14Oncethetranslationiscorrect,itisnotatallclearwhatargumentWittgensteinmighthaveinmindhere.Iwillconsidertwoalternativesuggestionsinthenexttwosections.6D‘THEWORLDISMYWORLD’—AKANTIANAPPROACHHowcouldthethoughtthat‘thelimitsof…the[only]languagewhichIunderstandmeanthelimitsoftheworld’giveussomereasonforthinkingthat‘theworldismyworld’?OnesuggestionisthatwecangetsomepurchaseontheargumentbydrawingaparallelwithafamousthoughtofKant’s.15InoneofthemostdifﬁcultpassagesoftheTranscendentalDeductionoftheCategories,Kantinsists:\n278SOLIPSISM,IDEALISM,ANDREALISMTheIthinkmustbeabletoaccompanyallmyrepresentations;forotherwise…[they]wouldeitherbeimpossibleorelseatleastwouldbenothingtome.16Ifwecangetabitoflogicaldistancebetweenarepresenta-tion’snotbeing‘nothingtome’andthe‘Ithink’accom-panyingit,wecanusethisasthebasisofanargumentfortheclaimthattheworldis‘myworld’inthesensethatitisaworldforme.Moreover,ifwereallycanusethisKantianthought,wemighthopetobeabletounderstandwhytheargumentisintheﬁrstperson:Kant’s‘Ithink’isessentiallytheproductof‘pureapperception’—i.e.,non-empiricalself-consciousness;itissupposedtoexploitanasymmetrybetweentheﬁrstandtheotherpersons.(Veryroughly,thethoughtisthatwhenIsay‘Ithinksummeriscoming’—asdistinctfromwhenIsay‘Shethinkssummeriscoming’—Idonotdoitasaresultofobservingmybehaviourandjud-gingwhatitshowsaboutmystateofmind.)ItisnoteasytoformulateanargumentinthespiritofthispassageofKantwhichmightbethoughttobeanimatingWittgenstein’stext;Iwillofferawaywhichperhapsgetsclosetotheidea.Consider,ﬁrst,anyfact,arbitrarilychosen.GivenWittgenstein’sinsistencethattheformoflanguageisthesameastheformoftheworld,therecannotbeafactwhichisinprincipleinexpressible.Letusthenacceptthatourarbitrarilychosenfactcanbeexpressed,andcallitthefactthatp.Ofcourse,theproperwaytoexpressafactisinasentence,suchasthis:(F)Itisthecasethatp.ThecoreofabroadlyKantianargumentcannowbeformulatedlikethis:(K1)Itcanbeseenthat(F)makessense;(K2)Ifitcanbeseenthat(F)makessense,thereissomeone(me)forwhomitmakessense;so(K3)Thereissomeone(me)forwhom(F)makessense.\nSOLIPSISM,IDEALISM,ANDREALISM279Giventhatthefactexpressedin(F)wasarbitrarilychosen—anyfactintheworldcouldhavedone—andtheformula-tionusedisitselfschematic(itusesthevariable‘p’,ratherthananyparticularsentence),itseemsthat,ifthisargumentworksatall,itshowsthatanythingatallthatmightbesaidorthoughtabouttheworldrequirestheexistence,insomesense,ofasubject,‘me’.Whatisdifﬁculthereisexplainingwhyweshouldaccept(K2),andwhyitisappropriatetoput‘me’inparenthesisinsteps(K2)and(K3).(F)isasentence(ortheinscriptionofasentence).So‘makessense’intheargumentsimplymeans‘hassense’—thatistosay,ismeaningfulinthewaysentencesare.Thecrucialthingtoaskiswhatkindofclaimisbeingmadein(K1).Inparticular,howcanitbeseenthat(F)makessense?ItisatthispointthatthisbroadlyKantianargumentappealstotheideathatthelanguagewearedealingwithis‘the[only]languagewhichIunderstand’.Thatenablesustocontrastthepresentcasewiththatofthefollowingsentence:(L)Itcanbeseenthat‘suntlacrimaererumetmentemmortaliatangunt’makessense.Thetruthassertedin(L)canonlybeafﬁrmedauthoritativelybysomeonewhounderstandsLatinaswellasEnglish;therestofussimplyhavetotakeitontrust,ortakeitstruthtobethebestexplanationofthesympatheticsighingofLatinscholarswhentheyreadit.Butinthecaseof(F)Wittgensteincouldnothavebeenthinkingofsuch‘takingontrust’,orofthiskindofempiricalhypothesis,sincewearesupposedtobeconsidering‘the[only]languagewhichIunderstand’(5.62).So(F)(instantiated)mustbeasentenceinalanguagewhich‘I’understand,andinthatcase(K1)assertsadifferentkindoftruthfromthatwhichmostofuswillhearassertedin(L).Itwillbeatruthaboutthespecialwayof‘seeing’thatsomethinghassense,inwhicheachofusisableto‘see’thatasentenceinourownlanguagemakessense.Thisisnotnaturallydescribedasareportofobserva-tion:wedonotnoticethatasentenceinourownlanguage\n280SOLIPSISM,IDEALISM,ANDREALISMmakessense;norisitthebestexplanationofanyobservablebehaviour.Rather,wemakesenseofit.Thisenablesustoﬁxwhothe‘I’is—toﬁx,thatis,whoitiswhoseworldis‘myworld’.The‘I’willbeeachreaderofthesentencewhichisgivenastheinstanceof(F)—ineachofwhoselanguagesthesentence,itispresumed,iswritten.Andeachreaderisproperlyan‘I’here,becauseeachreaderreadsthesentenceasbeinginalanguagewhichis‘myown’.Eachreader’sreadingthesentenceasbeinginalanguagewhichis‘myown’isjusteachreadermakingsenseofthesentence—ratherthanmerelyobservingthatthesentenceobeyscertainrules,ortakingitontrustthatthesentence(inaforeignlanguage)makessense,orofferingthesenseofthesentenceasanexplanationofcertainbehaviouralphenomena.Ifweunderstandtheargumentofthelastparagraphof5.62inthisway,wecanseehowitmightexploittheﬁrstperson,inparticular:wecanunderstandwhyWittgensteinuses‘my’here.Andtheargumentisobviouslyvalid,pro-videdwerestricttheinterpretationof‘canbeseen’uni-formlyacrossallthesteps.Butistheargumentsound?Arethepremisesalltrue?(K1)willbetrue,foreachinstanceof(F)whichiswritteninalanguagewhichweunderstand.And‘itcanbeseen’canthenbegivenaveryparticularinter-pretation—aninterpretationwhichrulesoutknowledgebyobservationortestimony.Is(K2)true,onthatinterpretationof‘itcanbeseen’?Certainly,forasentenceactuallytobeseentomakesense,onthisinterpretation,theremustbesomeone—‘I’,infact—tomakesenseofit.Butcouldasentencenothavesenseunseen—coulditnothavesensewithoutanyonehavingmadesenseofit?Itisnotclearthatthenotionofmakingsenseofasentencewillbridgethisgaponitsown.Thatisbecauseitisnotclearthatmakingsenseofasentenceisthesameasmakingthesentencehavesense.Buttheissuedoesnotseemveryserious,sinceitisextre-melynaturaltothinkthatnosentencecouldhavesensewithoutsomeone(‘I’)givingitsense(or,atanyrate,givingsensetoitsconstituentsastheyoccurinothersentences,soastoensurethateverysentenceinwhichtheyoccurhassense).\nSOLIPSISM,IDEALISM,ANDREALISM281How,though,doesallofthisrelatetotheworld?Howdoesthisshowtheworldtobemyworld—ratherthanjust‘the[only]languagewhichIunderstand’tobemylanguage?Thelinkcanbemadebymeansofthisthought:(WL)Whatisdescribedbysentenceswhichcanbeseen(byme)tomakesenseisnothinglessthantheworld(nothinglessthanrealfacts);ThisisthethoughtwhichWittgensteinlaterexpressedinthefollowingway:Whenwesay,andmean,thatsuch-and-suchisthecase,we—andourmeaning—donotstopanywhereshortofthefact;butwemean:this—is—so.(PI:I,§95)IntheTractatusitself,itisexpressedlikethis:2.1511Thusthepictureislinkedwithreality;itreachesuptoit.Anditistemptingtothinkthat(WL),sounderstood,isthekeypointof5.6.Theideaof(WL)isjustthis:inmakingsenseofasentence—inthatsentence’sstrikingmeasmakingsenseinthewaythatonlyasentenceinone’sownlanguagecanstrikeoneasmakingsense—Iamconsideringnothinglessthanagenuinelypossibleconﬁgurationoftherealworld.Eventomakesenseofasentencerequirestheretobearealworldwhichisaworldforme—whichis‘myworld’inthatsense.Isitanargumentlikethiswhichliesbehindthelastparagraphof5.62?Itishardtomakeaconvincingcasefortheclaim.Thisargumentshowsnomorethanthattheworldisaworldforme.Itismyworldinthatsense—butnotinthesensethatitisexclusivetome.Nordoesthisargumenthaveanyobvioustendencytoshowthattheworldinsomesensedependsonme,whichiswhatanyformofsolipsismwouldrequire.Forallthat,itdoesprovidesomegroundfortheintroductionoftheﬁrstperson.\n282SOLIPSISM,IDEALISM,ANDREALISMItmightbethoughtthatthemissingidealismissuppliedbyaprinciplewhichcouldbeconfusedwith(WL),althoughitisinfactquitedistinctfromit.Thisotherprinciplecanbeformulatedasfollows:(LW)Thereisnomoretotheworld(therearenomorerealfacts)thanwhatisdescribedbysentenceswhichcanbeseen(byme)tomakesense.(LW)mightbethoughttofollowfromthethoughtthattheformoflanguage(even:theonlylanguagewhichIunderstand)isthesameastheformoftheworld.Theoverallreasoningmightthenbethoughttoworklikethis.(WL)showsthatwhatmylanguagedescribesisnothinglessthantherealworld;andthethesisthattheformoflanguageisthesameastheformoftheworldisthenbroughtintoshow,bymeansof(LW),thattherealworldwhichmylanguagedescribesdependsonmylanguage—andhencecountsasmyworldinastrongersensethanmerelybeingaworldforme.(LW)doesindeedfollowfromthethesisthattheformoflanguageisthesameastheformoftheworld.Butitisnotinitselfanidealistprinciple,andcannotbeusedtoshowthattherealworldismyworldintherequisiteidealistsense.Recallthatweraisedthisquestioninsection6B:(Q)Mightlanguagehaverepresentationalblind-spots?(LW)isconsistentwithallofthefollowingwaysofansweringthatquestion:(A4)Languagecouldnothaverepresentationalblind-spots,becauselanguagesimplyadoptstheformofreality;(A5)Languagecouldnothaverepresentationalblind-spots,becauserealityisdeterminedbywhatlanguagecandepict;(A6)Languagecouldnothaverepresentationalblind-spots,becausewhatlimitslanguagealsolimitsreality.And,ofthese,only(A5)isidealist.\nSOLIPSISM,IDEALISM,ANDREALISM283Wemight,however,thinkthatmaterialsforanotherargument,againbroadlyKantianinspirit,canbefoundelsewhereinWittgenstein’searlywritings.Ihaveseveraltimesdrawnattentiontothisstrikingaccountofthemeaningof‘forms’:Inowdeterminethesenseof‘xRy’bylayingdown:whenthefactsbehaveinregardto‘xRy’sothatthemeaningof‘x’standsintherelationRtothemeaningof‘y’,thenIsaythatthe[thefacts]are‘oflikesense’withtheproposition‘xRy’;otherwise,‘ofoppositesense’;Icorrelatethefactstothesymbol‘xRy’bythusdividingthemintothoseoflikesenseandthoseofoppositesense.(NL:104)IarguedinChapter4(section4F)thatweshouldunderstandWittgensteinasgeneralizingthisaccounttomakeitapplytoalltheelementsofelementarysentences.InotedtherethatbythetimeoftheTractatusWittgensteinseemstohaveabandonedtheassumption,whichisimplicitinthispassageintheNotesonLogic,thatthemeaning-determiningsubjecthasakindofaccesstothefacts,preciselyassuch,indepen-dentofanylanguage.ButIthinkthekeypointaboutthispassageforourpresentconcernscanbemaintainedwithoutthatassumption.ThecrucialthingaboutWittgenstein’sclaimforourpresentpurposesistheemphasison‘by’:theassumptionseemstobethatthereis(orneedbe)noante-cedentsimilarityamongthefactswhichare‘oflikesense’—or,again,amongthefactswhichare‘ofoppositesense’.Whatseemstobehappeninghereisthatthereisanarbi-trarydeterminationofwhichfactscountasmakingarangeofsentencestrueandwhichcountasmakingitfalse.Thisseemstomakethesimilaritiesinthethingswhicharecor-relatedwiththesamesymboldependentonanarbitrarydecision.Anditthendoesnotseemtoomuchtoassumethatsomesuchprocessmightbeinvolvedindeterminingwhatcountsasathingatall.Thatistosay,thispassagemightbereadasencouragingustothinkoftheformoftheworld—theveryidentiﬁcationofitsconstituentobjectsandtheir\n284SOLIPSISM,IDEALISM,ANDREALISMmodesofpossiblecombination—asnothingmorethanaprojectionofthegrammaroflanguage.17ThisviewisrecognizablyKantian:wehavethestructureoflanguageprojectedontotheworldasitisinitself,tocreateaworldwecandescribe.Thisworldwhichwecandescribeisaworldoflanguage,andclearlydependsuponatleastthepossibilityofdescribingitinlanguage.Andweimmediatelyfacetheproblemofblindspotsthatwecon-sideredinsection6B,inarecognizablyKantianform.Thisneo-Kantiantheorycannotevenallowitselftobeformulated,becauseitcannotallowthatanyworldotherthantheworldoflanguagecanbedescribed,andsoitcannotallowtheworldoflanguagetobecontrastedwiththeworldasitisinitself,inthewaythatitmustbeiftheneo-Kantiantheoryisitselftobestated.IfthisistheviewwhichWittgensteinhasinmindwhenhetalksof‘solipsism’,nowonderthathesaysthatitcannotbesaid.ThisinterpretationreallydoesseemtocapturesomethinginWittgenstein’sthought.AndnotethatitiscompatiblewithalltheapparentlyrealistthingswhichWittgensteinsaysabouttheultimateconstitutionoftheworld,thenatureofobjects,andsoforth.IhavebeentakingcaretoshowtheformalcompatibilityofthemetaphysicsoftheTractatuswithbothrealismandidealismastheissuehasarisen(forexample:inChapter1,section1F;Chapter2,section2F;Chapter4,section4B).Herewecanbrieﬂyrepresentthemetaphysicsasaformofidealism.Iftheworldwhichwetalkaboutisindeedaworldoflanguage,aworldwhoseveryexistencedependsonitsbeingprojectedasacounterparttothegrammaroflanguage,thenwecandescribeinoutlinethewholemetaphysicalpictureoftheTractatusasfollows.Thegrammaroflanguagerequirestheworldtobeprojectedasaworldwhosebasicorganicunitiesarefacts—butfactswhicharecontingent,whiletheirdependentconstituents,theobjects,existnecessarilyandsupplythecommonformofeverythingthatcanbeimagined.Wittgensteindoesseemtobedrawntosomesuchneo-Kantianpictureasthis,evenifheisthenimmediatelyforced\nSOLIPSISM,IDEALISM,ANDREALISM285toerasethecontrastwiththeworldasitisinitselfinwhosetermsalonethepicturemakessense.Andthispicturedoesseemtomakesenseofsomefeaturesoftheargumentofthelastparagraphof5.62.Weget,forexample,somepointinusingtheﬁrstpersontomakethepoint,andanexplanationofwhyWittgensteinmighthaveexpressedtheargumentbyappealtosomesuchexpressionas‘the[only]languagewhichIunderstand’.Forsupposesomeoneweretoobjectasfollows.Thisisallverywell;itallowsthattheworldwhichIcanspeakaboutistheworldofmylanguage,butthisisnotenoughtoshowthattheworldistheworldofmylanguage.Fortherecouldbelanguagesspokenbyotherpeople,whichIdonot—indeed,couldnot—understand.Eachsuchlanguagewillhaveitsownworld,andeachoftheseworldswillhaveasmuchclaimtobetheworldasminedoes.TheconceptionimaginedbythisobjectionisalreadyruledoutbyWittgenstein’sview.FortoacknowledgethattherewereotherlanguageswhichIcouldnotunderstandwouldbetoacknowledgethattheremightbewaysinwhichthingscouldbearrangedwhicharedifferentfromthewaysinwhichIcanmakesenseofthembeingarranged:thatistosay,itsupposesthatIcanintelligiblymakesenseofpossi-bilitieswhichIcannotmakesenseof.Andthisseemsalreadytohavebeenruledoutbythesame-formassumptionwhichliesattheheartoftheTractatus’sconceptionoflanguage.Itisnotinsigniﬁcantthatthispointisbroughtoutexplicitlyinthestretchoftextwhichleadsuptothefamousclaimof5.62.18Forallthat,thisinterpretationdoesnotseemtocaptureeverythingthatisgoingoninthepuzzlinglyellipticalargu-mentof5.62.Foronething,althoughitmakesitveryclearwhythis‘solipsism’cannotbesaid—ofcourse,asbecameclearinsection6Babove,thatconclusionisseriouslyover-determinedbythecentralassumptionsoftheTractatus—itdoesnotmakemuchsenseofthefurtherclaimWittgensteinmakeshere:thatwhatsolipsismmeans‘showsitself’.Indeed,\n286SOLIPSISM,IDEALISM,ANDREALISMfarfromsolipsismsimply‘showingitself’intheworld,theworldisapparentlyquiteneutralontheissue.Sofar,atleast,thisneo-Kantianviewlookslikeanantecedentpre-judicewhichhassimplyshapedanapproachtothesubject,buthasnoobviousjustiﬁcation.Theotherthingwhichthisneo-Kantianapproachlacksisanythingwhichrequiresaspecialappealtotheﬁrstpersonsingular,toan‘I’,consideredpreciselyassuch.Whatseemstobeneededisaprojectionoflinguisticstructureontotheworld,andnodoubtthatrequiressomekindofactofwill.Whatisnotclear,however,iswhythewillneedstobemine.Wemightofferanalternative,communitarian,versionofexactlythesamegeneralneo-Kantianism.19Onthisalternativeaccount,theworldoflanguageisdependentonlanguage,butforeachofusitisfoundwithlanguage.Foreachofus,learningalanguageisamatterofinculcationintoaculture—onemightcallthisaBildung—asaresultofwhichtheworldoflanguageisthereforus.20Butforeachofusthisworldoflanguageisalreadythere,justaslanguageitselfisalreadythere.Theworldisnotmyworld:itdoesnotdependonme.Rather,itdependsuponlanguageitself,andontherebeingsomecommunitywhichhasusedthatlan-guagetoformaworldwhichcanbespokenabout.Attheverymost,itisourworld.Andthesetwopoints—abouttheabsenceofanyexplana-tionofthethoughtthatwhatsolipsismmeans‘showsitself’,andabouttheargumentnotjustifyinganydependenceonasingularsubject—canbeputtogether:itissimplynotthecasethatthereisanysenseinwhichtheworldwhichIspeakaboutpresentsitselfasbeingdeterminedbyme.Ouractualexperienceofspeakingalanguageisalwaysanexperienceofworkingwithaframeworkwhichhasbeengiventous:thewordsIusepreciselydonotstrikemeasmine—theyarewordsofEnglish(inmycase)—andIamconsciousalwaysthatitisnotuptometodeterminehowtheywillapplytotheworld.Onlysomeonealreadyinthegripofaradicallyindividualistpictureofourrelationtotheworldcouldthinkthateachofusdeterminesherownlanguage.\nSOLIPSISM,IDEALISM,ANDREALISM287Finally,thisKantianinterpretation,resonantwithinWittgenstein’sthoughtthoughitis,doesnotreallymakesenseofWittgenstein’suseofthephrase‘the[only]languagewhichIunderstand’.WhatthisinterpretationneedsisthethoughtthattherearenolanguageswhichIcannotunderstand.ButwhatWittgensteinoffersushereisthedifferentthought,thatthereisonlyonelanguagewhichIcanunderstand.6E‘THEWORLDISMYWORLD’—ACARTESIANARGUMENTIfwearetomakesenseofthethoughtthatwhatsolipsismmeans‘showsitself’,giveaproperroletotheﬁrstpersonsingular,andoffersomereasontoinsistthatthereisonlyonelanguagewhichIcanunderstand,Ithinkweneedtolookelsewhere.IthinkweneedtoappealtoconsiderationswhichhaveoftenseemedtohavenoplaceintheTractatus,butwhichhavealwayslainbehindtraditionaldiscussionsofsolipsism.21Asawayofgettingstartedonthis,considerthiswayofstatingthesame-formassumptionwhichliesattheheartoftheTractatus:(SF)Whatcanbedescribedin(my)languageisthesameaswhatcanbethecaseintheworld.(SF),likemostofthetheoryoftheTractatus,isitselfneutralbetweenrealismandidealism.Soletusask:whatdistin-guishesbetweenrealistandidealistreadingsof(SF)?Veryroughly,wegetarealistversionifwebegin,asitwere,withtheworld,andask‘Howcan(my)languagedescribethat?’Ifweworkinthatdirectionandoffer(SF)asananswertothisquestion,weseemcommittedtosomeformofrealism.Alternatively,wemaybegin(asitwere)withmylanguage,andask‘Howcanwhatmylanguagedescribesbetheworld?’Ifwethentake(SF)toanswerthatquestion,weseemtobeledintoaformofidealism.SinceWittgensteinsaysthat‘whatsolipsismmeansisquitecorrect’,itseemsthathemust,insomesense,be‘beginning’with(my)language.\n288SOLIPSISM,IDEALISM,ANDREALISMWell,whatmightthis‘beginning’be,andhowmightWittgensteinjustify‘beginning’with(my)language?Thestrikingthingabouttheﬁrstpersonisthatitisepis-temicallydistinctive:‘Iamthinking’hasadifferentepis-temicstatusfromthatof‘Sheisthinking’,‘Youarethinking’,oreven‘Thereisthinkinggoingon.’Ifwearereallytogiveaseriousroletotheﬁrstpersoninthisargu-ment,itishardtothinkofanyothersuggestionthanthis:the‘beginning’inquestionisanepistemicbeginning,andWittgenstein,despitethegeneralappearanceandtenoroftheTractatus,ismotivatedbyaconcerntoavoidscepticism—thatis,epistemologicalscepticism.Ihave,infact,alreadyappealedtoepistemicconsiderationsinreconstructinganargumentfortheconclusionthattheworldis‘my’worldinthesensethatitisaworldforme:acrucialpointtherewasthatthereisaspecialepistemicrelationshipwhichIhavetomyownlanguage.Inthecaseofmyownlanguage,Idonotﬁndoutthatasentenceismeaningfulbycheckingthatitﬁtssomespeciﬁcation,orbysupposingthatitsbeingmeaningfulisthebestexplanationofcertainphenomena.Inthecaseofasentenceinmyownlanguage,ﬁndingoutthatitismean-ingfulisespeciallyimmediate:Iﬁndoutthatitishassensebymakingsenseofit.Thisimmediacygivesmyaccesstomyownlanguageaspecialauthority;correlatively,myownlanguageispresenttomeinaspecialway.ThatspecialauthorityischaracterizedinaparticularwayintraditionalCartesianism,intermsofwhatcannotbedoubted.IfwefollowtheleadoftheKantianapproachconsideredinthelastsection,theclaimwouldbe:Icannotdoubtthemeaningfulnessofmyownlanguage.Howplausibleisthisclaim?ItmightseemthatIcoulddoubtthemeaningfulnessofmyownlanguage:mylanguagemightseemtometobemerenoise.ButwhenIthinkIcandoubtthemeaningfulnessofmyownlanguage,Iseemtoneedtobeable,somewhere,towonderaboutwhetherthatlanguageismeaningful.Ineedsomehowtobeabletocontemplate,orimaginethepossibilityof,thelanguage’snotbeingmeaningful.\nSOLIPSISM,IDEALISM,ANDREALISM289Ofcourse,accordingtoWittgenstein,suchcontemplationorimaginingmustinvolvetheconstructioninmymindofmodelsorpictures,whicharethemselveslikesentencesatleastinthisrespect:whateverotherformtheymayhave,theyalsohavelogicalform,theformofsentences(seeTLP:3).Soitseemsthatmyapparentabilitytodoubtthemean-ingfulnessofmyownlanguagerestsonmynotquestioningthemeaningfulnessofthepicturesormodelsIconstructinordertoframesuchdoubts.ButatthispointtheinsistencethatthereisonlyonelanguagewhichIunderstand(‘the[only]languagewhichIunderstand’)takesonanewsig-niﬁcance.IfallofthepicturesormodelsIconstructinmymindreallybelongtojustonelanguage,thereisindeedsomething—theonlylanguagewhichIunderstand—whosemeaningfulnessIcannotconceivablyquestion.Hereissomethingwhichhasaveryspecialepistemicstatus.Sofarthediscussionhasbeenintermsofthemean-ingfulnessofmyownlanguage.ThisisbecausewehavebeenfollowingthetermsoftheKantianapproachconsideredinthelastsection,anditwasimportanttothatapproachthattheargumentshouldestablish,atleast,thattherealworldisaworldforme.Inorderfortherealworldtobeaworldforme,weseemtoneedthethought,notmerelythatthesyntaxofmylanguagebeinorder,butthatitssymbolsactuallyrelatetotheworld.Butifitistrue,asitseemstobe,thatintheTractatusWittgensteinisreallyconcernedwiththefundamentalnatureofreality,ratherthanwhatisinfactthecase—withwhatispossible,ratherthanwhatisactual—thenitisnotfullmeaningfulnesswhichisimportant.Forthisconcern,whatreallymattersisjustthesyntaxofmyownlanguage.IfWittgensteinisconcernedwiththeformoftheworld,ratherthanthefacts,whatwewanttohaveaspecialepistemicstatusisjustmylanguage’sbeingsyntac-ticallyinorder.Thekeythingwhichitneedstobeimpos-sibleformetoquestioniswhetherthecombinatorialpossibilitieswhichmyownlanguageappearstosanctionaregenuinecombinatorialpossibilities.Anditseemsnohardertosupposethatsyntacticalwell-formednesshasthisstatus,\n290SOLIPSISM,IDEALISM,ANDREALISMthanitistosupposethatmeaningfulnessdoes:itisnotbyanykindofobservation,orasapartofanyexplanationofbehaviour,thatIdeterminethatasentenceinmyownlan-guageiswellformed.ItisplausibletoclaimthatIcannotdoubtthatthesymbolsofmyownlanguage—includingeveryrepresentationIcanconstructinmymind—areindeedsymbolsratherthandeadsigns,meremarksandsounds.22Suppose,then,thatepistemicsecurityissomethingwhichWittgensteinvalues—eventhough,asIhavealreadyacknowledged,epistemicsecuritydoesnotgenerallyseemtobeoneofhisprincipalconcernsintheTractatus.Suppose,further,thatwhathevalues,inparticular,istheepistemicsecurityofmyconﬁdenceinthesyntacticwell-formednessofmyownlanguage.Inthatcase,wecanimaginehimbeingconcernedabouttheepistemicsafetyofotherthings—ofbeliefintheformoftheworld,inparticular.Wecanimaginehimreasoningasfollows:Icanbeconﬁdentofthesyntacticwell-formednessofmylanguage—theonelanguagewhichincludesallmythoughtsandimaginings—buthowcanIbeconﬁdentoftheformoftheworld?HowcanIbeconﬁdentthatwhatseemstobepossibleis,indeed,genuinelypossibleintherealworld?IfthisisWittgenstein’sconcern,whathewillbelookingforisreasontothinkthatmyunshakableconﬁdenceinthecombinatorialpossibilitiesoftheonlylan-guagewhichIunderstandprovidesgroundsforbeingsimi-larlyconﬁdentoftherealityofthepossibilitiesintheworldwhichareco-ordinatewiththem.23Andsuchareason,itseems,canonlybeprovidedbymeansofthefollowingidealistconceptionoftherelationbetweenmylanguageandtheworld:(LWI)Thesyntaxofmylanguagedetermineswhatispossibleintheworld.ItmightbethoughtthatthisidealistviewisnotstrictlyrequiredfortheconﬁdencewhichWittgenstein,onthecur-rentsuggestion,islookingfor.Itmightbethoughtthatall\nSOLIPSISM,IDEALISM,ANDREALISM291thatisreallyrequiredisthatthegapbetweenlanguageandworldshouldbeshrunkenoughtopreventanyfailureofisomorphism.Sowemightinsteadhavesuggestedthisrealistalternative:(LWR)Thesyntaxofmylanguageisdeterminedbywhatispossibleintheworld.ButthisrealistalternativeseemstoundercuttheconﬁdenceIhaveinthesyntacticwell-formednessofmyownlanguage—atleast,asitappearstome.Forsuppose(LWR)weretrue,andtheformoftheworldwererigorouslyindependentofthesyntaxofmylanguage.Inmakingthatindependenceproperlyintelligible,weseemtohavetocountenancethepossibilitythatthesyntaxofalanguagemightseem(toitsspeaker)tobeinorder,eventhoughinfactitwasnot(thatis,thatitmightseemtoaspeakerthatshewasdealingwithsymbols,whenreallyshewasdealingjustwithdeadsigns).Togivefullweighttotheindependenceoftheworldwhich(LWR)requires,weseemtohavetoentertaintheideathatmyownjudgementsofsyntacticallegitimacyarenotaninfallibleguidetowhetherinfactthesyntaxofmylanguageisinorder.Ifwearetoinsistthattheimmunitytodoubtwhichthesyntacticwell-formednessofmyownlanguagepossessesformeisaproperguidetotheactualcombinatorialpossibilitiesofmyownlanguage,weneedtoshrinkthegapbetweenlanguageandtheworldintheotherdirection.Wecannotleavetheworldwhereitis,asitwere,andforcelan-guageclosertoit—forthatriskstakingitfurtherfromwhatwecanbeconﬁdentof.Insteadwehavetobringtheworld,asitwere,closertolanguage,leavingtheindubit-abilityofmyjudgementsofsyntacticwell-formednessintactandunthreatened.Thatistosay,wehavetoadopt(LWI),ratherthan(LWR).Whathasbeensaidsofarprovidesareasonforpreferringtheidealisttotherealistwayofreducingthedistancebetweenmylanguageandtheworld—givenadesiretomaintainourrighttoconﬁdenceinourjudgementsof\n292SOLIPSISM,IDEALISM,ANDREALISMsyntacticwell-formedness.Thatistosay,theidealistwayofreducingthedistancebetweenmylanguageandtheworldgivesusacomfortwhichwewant.Onereasonforadoptingidealismis,then,thatitiscomfortable.Buttheseconsidera-tionsmightbethoughttoprovideamoredirect,andlessdishonest,argumentfortheidealistconception.Foritmightbethoughtthatitwasincoherenttoquestiontheinfallibilityofourjudgementsofsyntacticwell-formedness.Wecanlaytheargumentoutasfollows:(C1)Ifmyjudgementofthesyntacticwell-formednessofmyownlanguagewerenotinfallible,itmightbewrong(forallmycon-fidence);(C2)Ifmyjudgementofthesyntacticwell-formednessofmyownlanguagemightbewrong,Ioughttodoubtit;(C3)IfIoughttodoubtmyjudgementofthesyntacticwell-form-ednessofmyownlanguage,Icandoubtit(giventhat‘ought’,ingeneral,implies‘can’);but(C4)Icannotdoubtmyjudgementofthesyntacticwell-formednessofmyownlanguage;so(C5)Myjudgementofthesyntacticwell-formednessofmyownlan-guagemustbeinfallible;but(C6)Ifrealismweretrue,myjudgementofthesyntacticwell-form-ednessofmyownlanguagewouldnotbeinfallible;so(C7)Realismisnottrue.Mytentativesuggestionisthatitissomesuchargumentasthisthatanimatestheﬁnalparagraphof5.62.Itmaynotbetheonlykindofissueinplayinthediscussionofsolipsism—theneo-Kantianconceptionconsideredinsection6DmaybepartofwhatWittgensteinhasinmind—butitlooksasifthemorenarrowlyepistemicconsiderationsappealedtointhisCartesianargumentareplayingsomepartinWittgenstein’sthought.Evenso,thesuggestionremainstentative,becausethisargumentreliesonepistemicconsiderationswhichseemforeigntothemaincourseoftheTractatus.Theotherreasonforsuggestingadifferentreconstructionoftheargumentof5.62wasthatwewantedtomakesense\nSOLIPSISM,IDEALISM,ANDREALISM293ofWittgenstein’sclaimthatsolipsism‘showsitself’.RecallthatWittgensteindoesnotjustsaythat‘whatsolipsismmeans’cannotbesaid:hefurthersaysthatit‘showsitself’(‘zeigtsich’:5.62).Whatcanthismean?Thenaturalappli-cationsoftheconceptofshowingintheTractatusaretotheconceptofform.Thus,famouslyhemakesthisclaimaboutpicturesormodels:2.172Thepicture,however,cannotrepresentitsformofrepresentation;itshowsitforth[‘esweistsieauf’].Andaboutsentences:Thepropositionsshow[‘zeigt’]thelogicalformofreality.Theyexhibitit[‘Erweistsieauf’](4.121)Butitisnotcrediblethattheuseoftheconceptofshowingin5.62isadirectapplicationoftheconcepttotheconceptofform.‘Whatsolipsismmeans’cannotbetheformoftheworld,becausetheformoftheworldisneutralbetweensolipsismandrealism:theformoftheworldistherangeofpossibilitiesofcombinationpossessedbytheobjects;solip-sism,however,isathesisaboutwhatdeterminesthatrangeofpossibilities.Sowhatdoeshemeanby‘show’(‘zeigt’)here,andhowcouldhethinkthatwhatsolipsismmeans‘showsitself’?Itisworthnotingthattheterm‘zeigt’isusedintheargumentwehavebeentryingtounderstand,inthenextparagraphofthetext:Thattheworldismyworld,showsitself[‘zeigtsich’]inthefactthatthelimitsofthelanguage(the[only]languagewhichIunderstand)meanthelimitsofmyworld.(5.62)Ifthisargumentis—orsomehowinvolves—thebroadlyCartesian(C)argumentIhavejustlaidout,wecanoffera\n294SOLIPSISM,IDEALISM,ANDREALISMparticularinterpretationoftheclaimthatsolipsism‘showsitself’.Itrunsasfollows.Accordingtothethoughtofthe(C)argument,itseemsthattheformoftheworldisevidenttome,injustthatspecialwayinwhichthesyntacticlegitimacyofsentencesofmyownlanguageisevidenttome.The(C)argumentthenprovidesthefollowingunderstandingoftheideathattheformoftheworldshowsitself:Icannotdoubtthattheformoftheworldisasitseemstobe(thatwhatseemtobepossibilitiesare,infact,realpossibilities).Further,ifweattributetoWittgensteinthe(C)argument,wetakehimtoacceptthispremiseinit:(C2)Ifmyjudgementofthesyntacticwell-formednessofmyownlanguagemightbewrong,Ioughttodoubtit.This,combinedwiththefactthatIcannotdoubtthesyntacticwell-formednessofmyownlanguageandtheassumptionthattheformoftheworldisthesameastheformoflanguage,simplyentailsthat,aswellasnotbeingabletodoubttheformoftheworld,Iamactuallyinfallibleaboutit.Sowemightsupposethat,given(C2),myinfallibilityabouttheformoftheworldshowsitself:thatis,isevidenttometosomethingliketheextenttowhichthesyntacticwell-formednessofmyownlanguageisevidenttome.Butthisinfallibilityisitselfduetotheworld’sbeingdependentonme,accordingtothe(C)argument:thatis,itisduetotheworld’sbeingmyworldinthesenserequiredbysolipsism.Oncethereasoninghasbeenworkedout,itmightthenbeclaimedthat‘whatsolipsismmeans’—thatis,thedependenceoftheformoftheworldonwhatIcantaketobeapossiblecombinationofsymbols—showsitself,inthesensethat,onceallthelinksareworkedout,itisevidenttomeinsomethinglikethewayinwhichthesyntacticwell-formednessofmyownlanguageisevidenttome.Sothe(C)argumentprovidesanaccountofwhyWittgensteinmighthavefeltabletoclaimthatsolipsism‘showsitself’.ButthisisatleastascontroversialastheattributiontoWittgensteinofthe(C)argumentitself:itmakestheconceptofshowingastronglyepistemic—\nSOLIPSISM,IDEALISM,ANDREALISM295indeed,Cartesian—concept.Andithasoftenbeenfeltthatthenotionisnotfundamentallyepistemicatall—oratleastnotepistemicinthisway.Wheredoesthisleaveus?Intheﬁrstplace,itseemstomethat,althoughtheﬁrst-personalnatureofourconﬁdenceinthemeaningfulnessorsyntacticwell-formednessofourownlanguagehasrootswhicharesimilartothosewhichcanbefoundinKant’sthoughtthatthe‘Ithink’mustbecapableofaccompanyingallmyrepresentations,thereisanaspectoftheargumentherewhichrunsintheotherdirection.TheKantian(K)argumentcandonomorethanshowthattheworldisaworldforme.Whatweneedissomereasonforthinkingthattheworlddependsonme.Thereisanalter-native,stillbroadlyKantianapproach—whatIhavecalledaformofneo-Kantianism—whichdoesseemtoprovidesomesuitablyidealistview.Butthisseemstogivenospecialplacetotheﬁrstpersonsingular(the‘I’),anditishardtoseeanyreasontobelieveit—whichmeansthatitishardtoseehowwhatsolipsismmeanscanbesaidto‘showitself’.ThelastargumentIhaveconsidered—the(C)argument—seemstopresenttheworldasbeingmyworldinasensewhichbothsupportsaclearlyidealistposition,andgivesasubstantialroletotheﬁrstpersonsingular.Furthermore,the(C)argumentoffersawayofunderstandinghowsolipsismmightbethoughtto‘showitself’.Unfortunately,this(C)argumentrepresentsWittgenstein’s‘solipsism’,likemostformsofidealism,asaresponsetosomeformofscepticism:inWittgenstein’scaseitisscepticismaboutwhethertheapparentlimitsofthepossiblecombinationsofsymbolsareanyguidetothelimitsofwhatispossibleinreality.ThisepistemicemphasisseemstohavelittleplaceintheTractatusasawhole,whichmakesitsattributiontoWittgensteinuncertain,tosaytheleast.Inmitigationofthatuncertainty,itisworthpointingoutthatepistemicconsiderationsdoplaysomeroleintheTractatus—perhapsagreaterrolethanissometimesacknowledged.Aswesawinthepreviouschapter,itseemsthatwehavetoacceptthatthereissomethingepistemic\n296SOLIPSISM,IDEALISM,ANDREALISMaboutthenotionofshowing,asWittgensteinusesitincon-nectionwithlogic:heseemstohavehoped—toputitnomorestrongly—thatlogicwasdecidable,inthespeciﬁcsensethateverylogicaltruthcouldbeshowntobetruebymeansofaﬁnitenumberofstepsinamechanicalprocedure(seeChapter5,section5E,above).Andthishopeisclearlylinkedwithaviewaboutthespecialobviousnessofform—atleastinasuitablenotation.WewillalsoseeinthenextsectionthatepistemicconsiderationsplayaroleinWittgenstein’sargumentfortheclaimthatthesubject‘doesnotbelongtotheworld’(5.631).Furthermore,Wittgensteindoesaddressscepticismexplicitlyintheclosingpagesofthebook(6.51),aswewillseeinChapter7(section7D).And,ﬁnally,itisworthaddingthatintheNotebooksfromwhichtheTractatuswasdrawn,thediscussionofsolipsismgrowsoutofamoregeneralconsiderationofthemeaningoflife(whosetransformationintheTractatuswillbeconsideredinthenextchapter).Andthatgeneralconsiderationofthemeaningoflifebeginswithanepistemicworry:WhatdoIknowaboutGodandthepurposeoflife?Iknowthatthisworldexists.ThatIamplacedinitlikemyeyeinthevisualfield.(NB:72–73)(ThisimageoftheeyeinthevisualﬁeldisrecalledintheTractatus,5.633;wewillconsideritmorefullyinthenextsection.)SotherearereasonstothinkthatWittgenstein’ssolipsismisboundupwithepistemicissues.Forallthat,itishardtobecompletelyconﬁdentthattheargumentof5.62isreallytheepistemicargumentwhichIhavelaidoutas(C).Isthe(C)argumentitselfplausible?Itiscertainlyvalid,butisitsound?Likemanyepistemicargumentsforanti-realistconclusions,itsweaknesscanbetracedtoadistinctivelyCartesianpremise.Inthiscase,thecrucialassumptionis(C2),wherethepossibilityoferroristakentoprovideanobligationtodoubt.Thisisexactlywhatrealiststraditionallydeny:itcanbeirrational,andthereforewrong,todoubt\nSOLIPSISM,IDEALISM,ANDREALISM297something,evenwhen(forallweknow)wemightbemis-taken.Andinthiscase,arealistcanacceptthatwemightbewrongaboutthesyntacticwell-formednessofourownlan-guage,butdenythatthismeansthatweshould(orcould)suspendjudgementaboutitswell-formedness:ofcourse,ourjudgementsmightbewrong,butthatdoesnotstopusbeingcommittedtomakingthem.6FSOLIPSISM,REALISM,ANDTHESUBJECTWittgensteinseemstobecommittedtothestronglyidealistviewthatthenatureoftheworlddependsuponme.Hethenmakestwoclaimswhichmightseemtoconﬂictwiththat:(NS)Thethinking,presentingsubject;thereisnosuchthing.(5.631)(SR)[S]olipsismstrictlycarriedoutcoincideswithpurerealism.(5.64)Whydoeshemaketheseclaims?Thecrucialpointmightseemtobethis:5.632Thesubjectdoesnotbelongtotheworldbutitisalimitoftheworld.ButhereWittgensteinseemstohaveinmindareasonforholdingthatthesubjectdoesnot‘belong’totheworldwhichisindependentof—andperhapsthegroundfor—thethoughtthatthesubjectisa‘limit’oftheworld.Therea-soningseemstoderivefromthesecondparagraphof5.631.Thereasoningofthisparagraph,likemuchofthediscus-sionofsolipsism,isnotimmediatelyclear.Butitlooksasifitreliesonakindofthinkingwhichisstronglyepistemicinthesamewayasthe(C)reconstructionoftheargumentof5.62,whichItentativelyofferedinthelastsection.Accordingtothe(C)reconstructionoftheargumentof5.62,WittgensteinreliesthereonwhatisultimatelyaCartesianassumption.The\n298SOLIPSISM,IDEALISM,ANDREALISMsecondparagraphof5.631suggestsanargumentfortheclaimthatthesubjectdoesnotbelongtotheworld,whichalsohasaCartesianﬂavour.Thecrucialpointofthatparagraphisthis:IfIwroteabook‘TheworldasIfoundit’…of[thesubject]aloneinthisbookmentioncouldnotbemade.ItseemsthatWittgensteinhasinmindsomethinglikethefollowingepistemicargument:(E1)TheonlythingsintheworldarethingswhichImightfind;(E2)Icannotfindmyself;so(E3)Imyselfamnotathingintheworld.Here‘ﬁnd’mustmeansomethinglike:encounterinexperience.Thisargumentisevidentlyvalid:areitspremisesbothtrue?(E1)iscertainlycurious,andwewouldnaturallyrejectitinothercontexts.WhycantheworldnotcontainthingswhichIcannotpossiblyﬁnd—thingswhichceasedtoexistbeforeIwasborn,forexample.Wecanruleoutatleastsomeofthesethingsifwecanrestrictourattentiontothingswhich,liketheobjectsoftheTractatus’smetaphysics,existnecessarily.Anditisnaturaltothinkthatwecandothatwithoutbeggingthequestionaboutthenatureoftheself.Thereasonisthatitishardtoseehowthesubject,inthesenseWittgensteinhasinmindhere,canbeamerelycontingentexistent,inanyordinarysenseof‘contingent’,ifitalsodeterminesthefundamentalnatureoftheworld.Moreover,ifweunderstandthesolipsismoftheTractatusasinvolvingCartesianassumptions,asthe(C)argumentdoes,(E1)becomesextremelynatural:therestrictiontowhatImightﬁndnolongerseemsmuchofarestriction.(E1),then,seemsdeniable,althoughitdoesnotseemaltogetherforeigntothesolipsismoftheTractatus.Whatabout(E2)?ThismightseemtobeanechoofthefamouspassagewhereHumedescribeshisowninabilitytoﬁndhimselfinexperience,24butIsuspectthatitsprovenancehereismoredirectlyKantian(and,ultimately,Cartesian).\nSOLIPSISM,IDEALISM,ANDREALISM299Thekeypoint,Ithink,istheonewenotedinthesection6D,thattheawarenessthatIhaveofmyselfasmyselfisnotempirical:itisnotasaresultofobservingmybehaviourthatIsay‘Ithinksummeriscoming’(ifanyobservationisinvolvedhere,itisobservationoftheweather).ThisshowsthatIamawareofmyselfinawayinwhichIamnotawareofotherthings—inawayinwhichIamnotawareofatleastthebulkoftheobjectsthatIencounterintheworld.ButdoesitshowthatIamnotalsoawareofmyselfinthewayinwhichIcanbeawareofobjectsofexperience,whichiswhat(E2)requires?Wittgensteinappearstothinkso.Heconsidersastrikingcomparison:Yousaythatthiscaseisaltogetherlikethatoftheeyeandthefieldofsight.Butyoudonotreallyseetheeye.Andfromnothinginthefieldofsightcanitbeconcludedthatitisseenfromaneye.(5.633)Thecomparisonmentionedintheﬁrstsentencehereseemsveryapt,andtobeunsettlingforWittgenstein’sview.Icanseetheeyesofotherpeople,unaided.AndifIhaveamirror,Icanseemyowneyes.Inthesameway,someonecanlookatherselfinamirror,orcatchherselfunawaresinashopwindow.Onthefaceofit,itseemsthatinthiswaysomeonecancometohavethekindofknowledgeofherownstateofmindthatshecanhaveofsomeoneelse’sstateofmind—andinthesameway,throughobservationofbehaviour.Thisiswhatis,ineffect,deniedintheﬁnaltwosentencesof5.633:Wittgensteinclaimsthat‘youdonotreallyseetheeye’.Butwhyisthisnotjustobviouslyfalse?Theanswerhastobethatinseeingtheeye(ofanother,orofyourselfinamirror)theeyeisnotpresentedtoyouasyourowneyeispresentedtoyou(asthefocusoftheﬁeldofsight)whenyoulookatotherthings.ButthiscanonlysupportWittgenstein’sclaimhereifitisheldtobeimpossibleforthesamething\n300SOLIPSISM,IDEALISM,ANDREALISMbothtobepresentedasthefocusofyourownvisualﬁeldandtobetheobjectofsight.And,unfortunately,thatisexactlywhatisinquestion.Similarly,thefactthatIampresenttomyselfnon-empiricallydoesnotshowthattheverysamething—I,thesubject—cannotbetheobjectofempiricalobservation(myownoranother’s),unlesswesimplyassumethatitisimpossibleforthesamethingbothtobepresent(tomyself)non-empiricallyandtobetheobjectofempiricalobservation.Butthat,again,isexactlywhatisinquestioninpremise(E2).Itseems,then,that(E2)canbedenied,evenbysomeonewhoacceptsWittgenstein’ssolipsism.Sotheargumentlooksunsound:moreover,itisunsoundinawayinwhichexactlysimilarargumentsabouttheselftobefoundinDescartes’sMeditationsareunsound.25Thereseemstobeastronglyepistemicapproachtotheselfinplayhere—evenifwearehesitantaboutadoptingsuchanapproachtotheargumentof5.62.Interestingly,itlooksasifWittgensteinhadasimplerargumentavailabletohim,onewhichderivesmoredirectlyfromhissolipsism.Thisisbecauseitseemsthatthesubjectmustbea‘limit’oftheworldinaspecialsense,ifsolipsismistrue.Atﬁrst,itmightnotbeobviouswhybeingalimitoftheworldpreventsthesubjectfrom‘belonging’totheworld.Afterall,thesimpleobjectstowhichnamesinelementarysentencesrefermightberegardedasbeinglimitsoftheworld:theyconstituteitssubstance(2.021),andhencedeterminewhatispossible.ButweshouldbecarefulaboutthesenseinwhicheachoftheobjectsoftheTractatus’smetaphysicscanclaimtobealimitoftheworld.Itissimplythateachcarriesaspartofitsessencethepossibilityofcombiningwithotherobjectsincertaindeterminateways;andthesepossibilitiesofcombinationconstitutethebasicformoftheworld.Eachoftheseobjectsis,asitwere,acontributortoacollectivedeterminationofthelimitsoftheworld.Thesubject,however,isalimitoftheworldinamuchgrandersense,ifsolipsismistrue:whatthesubjectcanmakesenseofdetermineseverypossibilityallatonce.Its\nSOLIPSISM,IDEALISM,ANDREALISM301roleisquiteunlikethatoftheobjects,eachofwhichcontainsmerelyitsownpossibilitiesofcombination.ThisseemstorequirethattheselfﬁguresintheTractarianpictureinsomewayotherthanasanobjectintheworld.Hencethesubjectdoesnot‘belong’totheworld:itis,asWittgensteinputsit,ametaphysicalsubject(5.633,5.641).Butjustbecauseitdoesnotbelongtotheworld,whyshoulditfollowthat‘thereisnosuchthing’asthemeta-physicalsubject,as(NS)claims?Wecanexpressstherea-soningasfollows.Supposeweweretoclaim:(1)Thereissuchathingasthesubject.AccordingtotheTractatus’sconceptionoflanguage,thissentence,likeallsentences,canonlybetrueinvirtueofthebasicobjectsoftheTractatus’smetaphysicsbeingcombinedinacertainway.Atbesttherearetwopossibilities.Oneapparentpossibilityisthatthesubjectiscomposite:thesubjectisacombinationofTractarianobjects,and(1)isanalysableastheclaimthatcertainsuchobjectsaresuitablycombined.TheotherapparentpossibilityisthatthesubjectisitselfaTractarianobject,and(1)istrueinvirtueofatruthofsomesuchformasthis:(2)Fa&a=thesubject—where‘a’isthenameofaTractarianobject.But,ﬁrst,thesubjectcannotbecomposite.Afterall,Wittgensteininsists:Acompositesoulwouldnotbeasoulanylonger.(5.5421)And,ofcourse,acompositesubjectwouldexistonlycon-tingently(sincetothinkofitascompositeistothinkofitasacombinationofelementswhichmightnothavebeencombined—thereasoningwehaveseenatworkin2.021),andwehavealreadyseenthatthemetaphysicalsubjectcannotbecon-tingentinanyordinarysense.And,second,wehavealsojustseenthatthemetaphysicalsubjectcannotbeoneoftheobjects\n302SOLIPSISM,IDEALISM,ANDREALISMwhichbelongtotheworldeither.Soitseemsthat(1)cannotbetrue:therereallyisnosuchthingasthemetaphysicalsubject.Ofcourse,ifthereisnosuchthingasthemetaphysicalsubject,thereissomedifﬁcultyinstatingsolipsism:TheIinsolipsismshrinkstoanextensionlesspointandthereremainstherealityco-ordinatedwithit.(5.64)Andthisistheimmediategroundfor(SR),theclaimthatsolipsismcoincideswithrealism.ButitshouldbenotedthatwhatWittgensteinhasprovidedisnotanendorsementofrealism.Realismisnotthethesisthattherealworldexists:itis(roughly)thethesisthatthefundamentalnatureoftheworldisindependentofanysubject.Ifwecannottalkaboutanysubject,strictlyasasubject(whichtheargumentof5.631–5.633purportstoshow),thenwecannotstaterealismanymorethanwecanstatesolipsism.SomemightsuspectthatWittgensteinishereusingatricktoslipoutofacontradictionthathemightseemtohavetrappedhimselfin.Wehaveseenthat,inaway,heendorsessolipsism:‘Infactwhatsolipsismmeans,isquitecorrect’(5.62).And,aswehavenotedbefore,somehavethoughtthatifthemetaphysicsoftheearlysectionsoftheTractatus(1–2.063)istakenliterally,Wittgensteinistherecommittedtoaformofrealism.26Sohemightbethoughttobecom-mittedtoanuglyinconsistency,andhemightbeaccusedoftryingtoevadeitherebydenyingsubstancetoeitheroftheopposingpropositions.Wittgensteiniscertainlyinvolvedinsomekindofinconsistencyhere,butnotthisone.Aswehaveseenalready,themetaphysicsoftheTractatusisitselfneutralonthequestionofrealismandidealism(see,e.g.,Chapter1,section1F,above).ThemetaphysicsoftheTractatusissimplytheconsequenceofinsistingthattheformoftheworldisthesameastheformoflanguage—withafewsupplementaryassumptionsabouttheformoflanguage.Thatsame-formassumptionleavesuswiththethree\nSOLIPSISM,IDEALISM,ANDREALISM303positionswhichweredistinguishedintheﬁrstsectionofthischapter:(A4)Languagecouldnothaverepresentationalblind-spots,becauselanguagesimplyadoptstheformofwhatthereis;(A5)Languagecouldnothaverepresentationalblind-spots,becausewhatthereisisdeterminedbywhatlanguagecandepict;(A6)Languagecouldnothaverepresentationalblind-spots,becausewhatlimitslanguagealsolimitsreality.Aswesawbefore,(A4)isrealist;(A5)isidealist;and(A6)isneutralbetweenthetwo.Anyoneofthemcanbeacceptedcompatiblywithendorsingboththestrongmetaphysicsofthebook’searlysections,andtheconceptionofsentencesasmodelsofreality.SoweshouldnotthinkofWittgensteinashereevadinghiscontradictorycommitmentstobothsolipsismandrealism,becausehewasnevercommittedtorealism.Hisincon-sistencyliessimplyinthefactthathebothstates(andarguesfor)solipsism,andinsiststhatitcannotbestated.Andthedifficultyattachesnotjusttothispoint,buttoWittgenstein’sreasonformakingit.WehaveseenWittgensteininsistingthatthereisnosuchthingas‘thethinking,presentingsubject’(5.631),andthatthisleadshimtodenythestatabilityofanycontrastbetweensolipsismandrealism(5.64).Buthefollowsthatimmediatelywiththisremark:5.641Thereisthereforereallyasenseinwhichinphilosophywecantalkofanon-psychologicalI.Thisseemsﬂatlytocontradicttheremarksonwhichitissupposedtobebased.Itisnotclearthattheproblemsherecanbesatisfactorilyresolved,buttheycanatleastbeclariﬁedbyconsideringthegeneralproblemsfacingWittgenstein’sclaimthatwhatsolipsismmeans‘cannotbesaid’(5.62),soletusturntothosenext.\n304SOLIPSISM,IDEALISM,ANDREALISM6GSOLIPSISMANDWHATCANNOTBESAIDWearenowinapositiontosummarizetheissuesraisedbytheparadoxicalclaimwhichisthecoreofWittgenstein’streatmentofsolipsism:Infactwhatsolipsismmeans,isquitecorrect,onlyitcannotbesaid,butitshowsitself.(5.62)WehavefoundanumberofwaysofinterpretingWittgenstein’sargument(inthefollowingparagraphof5.62)fortheconclusionthat‘whatsolipsismmeansisquitecorrect’.Whyexactlycanitnotbesaid?Infact,theunsayabilityofsolipsism—atleast,thesolipsismoftheTractatus—isoverdetermined.Onereasonforthinkingthatsolipsismisunsayablewehavejustseen.Tostatesolipsism,weneedtotalkaboutthesubject,onwhosecapacitytomakesenseofsentencesthepossibilitiesoftheworlddepend(accordingtosolipsism).Butthesubject,wehaveseen,mustbea‘metaphysical’subject—somethingwhichdoesnotbelongtotheworld.Andametaphysicalsubjectcannotbetalkedabout.Thereis,though,amoregeneralreasonforthinkingthatsolipsismisunsayable.Tobeableeventodescribesolipsism(eithertoacceptitortorejectit),wedonotmerelyhavetotalkaboutthesubject:weneedtobeabletocontemplatethelimitsoftheworldaslimits.Further,weneedtoconsidervariouswaysinwhichthoselimitsmighthavebeendeter-mined,whichlooksasifitrequiresustocontemplatethepossibilityofthoselimitshavingbeenotherwisethantheyare.ButthisissomethingwhichWittgenstein’sconceptionoflanguageandlogicrulesout.Thereasonswereconsideredindetailinsection6Babove;theyaresummarizedmetaphoricallyatthispointinWittgenstein’stext:5.61Logicfillstheworld:thelimitsoftheworldarealsoitslimits.Wecannotthereforesayinlogic:Thisandthisthereisintheworld,thatthereisnot.\nSOLIPSISM,IDEALISM,ANDREALISM305Forthatwouldapparentlypresupposethatweexcludecertainpos-sibilities,andthiscannotbethecasesinceotherwiselogicmustgetoutsidethelimitsoftheworld:thatis,ifitcouldconsidertheselimitsfromtheothersidealso.Whatwecannotthink,thatwecannotthink:wecannotthereforesaywhatwecannotthink.Wittgensteinthenwrites:Thisremarkprovidesakeytothequestion,towhatextentsolipsismisatruth.(5.62)Althoughthenumberingindicatesthattheremarkreferredtohereas‘thisremark’is,strictlyspeaking5.6,ratherthan5.61,itissurelythroughthethirdandfourthparagraphsof5.61thatweunderstandhow5.6providesthekeytotheextenttowhichsolipsismistrue.Thekeyisthatsolipsismrequiresustocontemplate—andthereforestate—some-thingwhichcannotbecontemplatedorstated.Sosolip-sismcannotstrictlybecontemplatedorstated.Thismeans,ofcourse,thatsolipsismcannotstrictlybedeniedeither;andconsequently,realismcannotstrictlybecontemplatedorstated,whichgivesus(SR),thethesisofthecoincidence—asfaraswhatcanbestatedgoes—ofsolipsismandrealism.Thesetworoutestotheunstatabilityofsolipsism(orrea-lism)arereﬂectedinthetwofaultswiththediagramofthevisualﬁeldwhichWittgensteindrawsin5.6331.Onefaultisthatthediagramportraystheeyeasoccurringwithinthevisualﬁeld:thisisliketheerror(asWittgensteinseesit)ofthinkingthatthesubjectbelongstotheworld.Theotherfaultisthatthediagramdrawsalinearoundtheextentoftheﬁeldofvision,therebymarkingoutaregionasoutsideit,beyonditslimits:thisisliketheerror(asWittgensteinseesit)oftryingtocontemplatewhatisnotpossible—theerrorwhichishighlightedinthethirdparagraphof5.61.Theﬁrstoftheseroutestotheunsayabilityofsolipsism\n306SOLIPSISM,IDEALISM,ANDREALISMdependsontheparticularnatureofthesubject:ineffect,itsbeinga‘metaphysical’subject.Thesecondroute,however,restssimplyonthecentralclaimofthepicturetheoryoflanguage,thattheformoflanguageisthesameastheformoftheworld.Assuch,itbelongswiththeparticularreasonprovidedbythattheoryforsaying‘No’tothequestionweconsideredinsection6Babove:(Q)Mightlanguagehaverepresentationalblind-spots?Wittgenstein’streatmentofsolipsismasultimatelyunsay-ablerepresentsawayofapproachingthewholerangeofissuesraisedbyaKantianapproachtophilosophy.Kant’sowntranscendentalidealismwillbecomeunsayable,onthisapproach,aswillthewholerangeofmorerealistandmoreidealistpositions.TheTractatusmightseemtoofferapecu-liarlysophisticatedresponsetothosepositions,whichwemightwanttoembraceourselves.ButitisimportanttoseethatthisapproachtothoseKantianissuesdoesnotsimplyexploitanincoherenceinternaltoallthevariousmetaphysi-calpositionsbetweenwhichwemightbeaskedtochoose.ItdependscruciallyonthephilosophyoflanguagewhichtheTractatuspresents(aswellascontroversialassumptions—perhapsincluding(C2)—aboutthenatureofthesubject).Thekeypremiseisthatlanguagehasthesameformastheworld,thattherearethesamepossibilitiesofcombiningsymbolsin(afullyanalysed)languageasthereareofcombiningobjectsintheworld.Thatassumptionforcesustochooseoneoftheanswers(A4),(A5),and(A6)toques-tion(Q),andthesearewhatmakeanylarge-scalemeta-physicalpositionunstatable.Ifweabandonthesame-formassumption,however,wecanchooseoneofthesealternativepositions:(A1)Languagemighthaverepresentationalblind-spots,andthatpossibilityisstatable;(A2)Languagemighthaverepresentationalblind-spots,butthatpossibilityisnotstatable;\nSOLIPSISM,IDEALISM,ANDREALISM307(A3)Languagecouldnothaverepresentationalblind-spots,becausethereisnoconstraintatallonwhatcanberepresentedinanygivenmedium.Only(A2)heremakeslarge-scalemetaphysicslookunsta-table(thoughforreasonswhichdifferfundamentallyfromthatofferedbyWittgensteinin5.61,despitethesuperﬁcialsimilarity).Moreover,theapparentsophisticationofWittgenstein’sresponseisslightlycomplicatedbytwothings.Firstthereisthefactthathearguesforhisposition,whileeventoarguefortheposition—thatitisimpossibletocontemplatewhatisimpossible—requireshimtodowhathehimselftherebyarguesisimpossible.And,second,thereisthatoddremarkwenoticedattheendofthelastsection:in5.641heseemstothinkthereisawayoftalkingaboutthemetaphysicalsubject—inphilosophy.Itisonthiskindofissuethatinterpretationsofthetreat-mentofsolipsismintheTractatustendtodivide.Iremarkedattheoutsetthatthedramaticclaimof5.62seemstocommitWittgensteintothreethings:(i)‘Whatsolipsismmeansisquitecorrect’;(ii)‘Whatsolipsismmeans’cannotbesaid;(iii)‘Whatsolipsismmeans’‘showsitself’.(iii)iscurious,inthecontextoftheunderstandingnaturallygivento‘showing’moregenerallyintheTractatus;butbeyondthatitraisesnospecialproblems.ThemajordivisionisbetweeninterpretationswhichunderstandWittgensteinasreallyasserting(i),inspiteof(ii),andthosewhichtakehimnottobeasserting(i),becauseof(ii).27TherearethosewhothinkthatWittgensteinreallyissomekindofidealist,andthosewhothinkthatin(ii)hehasmanagedtoavoidanycommitmentontheissuebetweenidealismandrealism,andhasactuallysucceededindissolvingtheproblem.Myownpreferenceisfortheformeroftheseviews:IthinkWittgensteinisunambiguously,ifparadoxically,committedtoboth(i)and\n308SOLIPSISM,IDEALISM,ANDREALISM(ii).Otherswillthinkthatthereisawayofunderstandinghimasavoidingparadoxhere.Thediscussionofsolipsismoverallhasadoublesig-niﬁcance.First,itseemstolinktheTractatusunambiguouslybacktotheKantiantradition,withitslargequestonsofrea-lismandidealism.ThestandwetakeonthesefewsectionsaffectsourunderstandingofthewholeoftheTractatus.And,second,itisoneofthemostobviousplaceswheretheparadoxoftheTractatusmanifestsitself—beforeweencounteritinconnectionwiththegeneraldifﬁcultyofdoingphilosophyattheendofthework.HereweseeWittgensteinclearlysayingthings—orseemingtosaythings—whichhetherebydeclarestobeunsayable.Inthecaseofsolipsism,theparadoxicalityseemsparticularlybla-tant,without(asitseemstome)dampingWittgenstein’senthusiasmforsayingthethingswhichareparadoxical.Inthenextchapterwewilllookathisapproachtopara-doxicalityinmoredetail;thisshouldhelpusdecidewhichweshouldfavourofthetwogeneralapproachestothetreatmentofsolipsismthatIhavejustdistinguished.\n7METAPHYSICS,ETHICS,ANDTHELIMITSOFPHILOSOPHY7ATHEPROBLEMOFTHEPOSSIBILITYOFMETAPHYSICSDavidHume’sﬁrstEnquiryendswiththisfamousparagraph:Whenwerunoverlibraries,persuadedoftheseprinciples,whathavocmustwemake?Ifwetakeinourhandanyvolume;ofdivinityorschoolmetaphysics,forinstance;letusask,Doesitcontainanyabstractreasoningconcerningquantityornumber?No.Doesitcontainanyexperimentalreasoningconcerningmatteroffactandexistence?No.Commititthentotheflames:foritcancontainnothingbutsophistryandillusion.(Hume1777:XII,iii)Inthesecondparagraphofapaperwhichwasstronglyinﬂu-encedbyWittgenstein’sTractatus,RudolfCarnapwrites:Inthedomainofmetaphysics,includingallphilosophyofvalueandnormativetheory,logicalanalysisyieldsthenegativeresultthattheallegedstatementsinthisdomainareentirelymeaningless.(Carnap1956:60–61)\n310METAPHYSICS,ETHICS,LIMITSOFPHILOSOPHYAndlestanyoneshouldbeinanydoubt,Carnapinsists:Insayingthattheso-calledstatementsofmetaphysicsaremean-ingless,weintendthiswordinitsstrictestsense.(Carnap1956:61)The‘principles’whichleadtoHume’sresultunderlieCarnap’sconclusiontoo.Humeinsiststhatallknowledgeeitherfallswithintheprovinceof‘demonstration’oriscon-cernedwith‘matteroffact’:thisistheprincipleknownasHume’sFork.Carnapholdsthatallstatementsareeither(i)‘truesolelybyvirtueoftheirform’,(ii)negationsofthese(whicharethereforecontradictory),or(iii)empiricalstate-ments(trueorfalse)(Carnap1956:76).SincetheﬁrsttwoofCarnap’scategoriesofstatementfallwithinwhatHumecountsastheprovinceof‘demonstration’,itisclearenoughthatCarnapiscommittedtosomethingverylikeHume’sFork.ItisbecausestatementsofmetaphysicsfallintononeoftherelevantclassesofpossiblestatementsthatHumeandCarnapdismissthemas‘sophistryandillusion’,orsimplymeaningless.WhatHumeandCarnaparehererulingoutisthepossi-bilityoftheclassofstatementswhichKantcalledsyntheticapriori,whichhetooktobecentraltophilosophy,aswellastomathematics.Hume’sprovinceof‘demonstration’broadlycoincideswiththeclassoftruthswhichKantcounted‘ana-lytic’(togetherwiththenegationsofanalytictruths)—thatis,thenon-synthetic;andheinsiststhattruthsconcerning‘matteroffactandexistence’canonlybeknownbyexperi-ence—thatis,aposteriori.WehavealreadyseenthatWittgensteinalsorejectedthepossibilityofsyntheticaprioritruths.Itshouldthereforecomeasnosurprisetoﬁndhimrejectingmetaphysics.Norshoulditsurpriseusthatthisrejectionisbroadened(likeCarnap’s)toincludeethics(Humesimplyregardedmoralityasnotbeingaproperobjectofreasonatall).ButthecharacterofWittgenstein’srejectionofmetaphysicsseemsquitedifferentfromCarnap’sorHume’s:wheretheyseemkeentopushpastmetaphysics\nMETAPHYSICS,ETHICS,LIMITSOFPHILOSOPHY311andgetonwithscience,Wittgenstein’sattitudeseemsmorepoeticandcontemplative.Partofthedifferenceofapproachhereisadifferenceinthesephilosophers’attitudetotheirownwork.Ifwerejectmetaphysicsonthegroundthatalltruthsareeitheranalyticoraposteriori,weseemboundtobeinsomedifﬁcultyoverthatrejectionitself.Supposewe‘takeinourhand’Hume’sﬁrstEnquiry,andaskwhetheritcontainsany‘abstractreasoningconcerningquantityornumber’,orany‘experi-mentalreasoningconcerningmatteroffactandexistence’.WeseemboundtoanswerNo,inwhichcase,accordingtoHume’sownprinciples,hiswork‘cancontainnothingbutsophistryandillusion’.Similarly,itishardtoseehowwecanclaimthatCarnap’sstatementthatallstatementsareeither(i)analytic,(ii)negationsofanalytictruths,or(iii)empirical,isitselfeitheranalytic,anegationofananalytictruth,orempirical.SoitseemsthatCarnap’sownstatementmustbecountedasmeaningless,inthestrictestsenseoftheword,byitsownlights.Therejectionofmetaphysicsonanysuchgroundsastheseseemsboundtobeparadoxical.NeitherHumenorCarnapseemstobeawareofanydif-ﬁcultyhere:theyseemconcernedsimplytodismisscertaintypesofworkfromwhichtheythinktheycanclearlydis-tinguishtheirown.Wittgenstein,however,seemstoseetheproblemquiteclearly:Mypropositionsareelucidatoryinthisway:hewhounderstandsmefinallyrecognizesthemassenseless,whenhehasclimbedoutthroughthem,onthem,overthem.(6.54)ThetaskofthischapteristoexplainWittgenstein’sreason-inginmoredetail,andtotrytomakesenseofhisresponsetotheparadoxwhichseemstobeinvolvedinrejectingmetaphysics.Iwillapproachthesetwoaspectsofthetaskinthatorder,thoughitshouldbemadeclearthatthisalreadyinvolvestakingastandontheinterpretationofWittgenstein’sapproachtotheparadox.Therearesomeinterpretersofthe\n312METAPHYSICS,ETHICS,LIMITSOFPHILOSOPHYTractatuswhoendorsewhatWittgensteinsaysin6.54,andconcludethat(atleastthebulkof)thesentencesoftheTractatusareindeednonsense.Theseinterpretersmusthavesomedifﬁcultyinmakingsenseofthereasoningwhichleadstotheconclusionthatanyattempttosaysomethingmeta-physicalwillendinnonsense,andthereforeendupsuppos-ingthattheconclusionisreachedinsomeotherway.Thisinterpretationstrikesmeasclearlywrong—thoughIwillpostponetheargumentforthatclaimuntilweaddresstheparadoxexplicitly.IthinktheTractatuscontainsargumentsfortheconclusionthatanyattempttosaysomethingmeta-physicalmustresultinnonsense.Ourﬁrsttaskistotrytounderstandthem.7BNECESSITYANDLAWSOFNATURERememberWittgenstein’sviewoflogic:6.1Thepropositionsoflogicaretautologies.ThekeyKantiannotionofanalyticityisintroducedintheverynextremark:6.11Thepropositionsoflogicthereforesaynothing.(Theyaretheanalyticalpropositions.)Inthelightofthat,thefollowingcanbeseenasWittgenstein’sversionofHume’sFork:6.3Logicalresearchmeanstheinvestigationofallregularity.Andout-sidelogicallisaccident.‘Regularity’isapoortranslationoftheGermanwordhere(‘Gesetzmässigkeit’):‘law-governedness’wouldbebetter.1Thethoughtseemstobesomethinglikethis:everygenuinelaw(‘Gesetz’)involvesnecessity;‘thereisonlylogicalnecessity’(6.37);soanythingwhichcannotberepre-sentedas‘logical’canonlybeaccidental.Given6.11,6.3is\nMETAPHYSICS,ETHICS,LIMITSOFPHILOSOPHY313therejectionofnon-analytic—thatis,synthetic—necessarytruths.ThisprovidesoneangleonWittgenstein’srejectionofmetaphysics,oneinwhichhisviewseemslargelytocoincidewithHume’s.Metaphysicsisconcernedwithwhatisneces-saryintheworld:howtheworldmustbe.Humethoughtthatnecessitycouldnotbeexperienced.Nordidhethinktherewasanygenuinenecessityrevealedbyinduction(rea-soningfromcaseswehaveobservedtothosewehavenot).2Heconcluded(toputthematteralittlecrudely)thatneces-sity—atleasttheonlykindofnecessitywecaneverbeconcernedwith—isnotreallyintheworld.3Heendedup,ineffect,rejectingnaturalnecessity,thenecessityofcausa-tionandofnaturallaws.ThereremainssomesenseforHumeinwhichwecanspeakofnaturalnecessity—asanexpressionofafeelingofpsychologicalcompulsioninourexpectationofoneeventhavingexperiencedanother—butthistalkismisleading,becausetheonlynecessityhere(apsychologicalcompulsion)isnotthenecessitywethinkwearedescribing(whichwouldbebetweeneventsintheworld).KantthoughtthatHume’sreasoningwouldalsosufﬁcetoundermineallnecessity(notjustnaturalnecessity),andthereforethatithadtoberejectedifweweretomakesenseofmathematicsandphysics—aswell,ofcourse,asmeta-physics.WecanseeWittgenstein,inthe6.3s,defendingtheHumeanpositionagainstKantianandotherobjections.Ineffect,hehastorejectanyclaimwhichcannotbeplacedunambiguouslywithinoneorotherofhistwocrucialcate-gories,thelogicalandtheaccidental.AndheisatleastasﬁrmasHumeinhisrejectionofnaturalnecessity.Hisclaimthat‘Thereisonlylogicalnecessity’followsthisremark:Anecessityforonethingtohappenbecauseanotherhashappeneddoesnotexist.(6.37)Wittgenstein’sexaminationof‘law-governedness’beginswithinduction:\n314METAPHYSICS,ETHICS,LIMITSOFPHILOSOPHY6.31Theso-calledlawofinductioncannotinanycasebealogicallaw,foritisobviouslyasignificantproposition.—Andthereforeitcannotbealawapriorieither.Whatisthis‘lawofinduction’?Perhapsitissomethinglikethis:(I)IfallobservedFsareG,allFsareG.Whyisthis‘obviouslyasigniﬁcantproposition’(obviouslyasentencewithsense—‘sinnvoller’)?Presumablybecauseitisobviousthatitmightbefalse.Sothesupposed‘law’ofinductionisonlyaccidentallytrue.Why,then,shouldwebesoinclinedtomakeinductiveinferences,tomakejudge-mentsonthebasisofexperience?Wittgensteinrespondstothisquestionbyredescribingtheprocessofinduction,andthengivingaHumeanaccountofit:6.363Theprocessofinductionistheprocessofassumingthesimplestlawthatcanbemadetoharmonizewithourexperience.6.3631Thisprocess,however,hasnologicalfoundationbutonlyapsychologicalone.Itisclearthattherearenogroundsforbelievingthatthesimplestcourseofeventswillreallyhappen.Theinterestingthinghereistheredescriptionofthepro-cessofinduction.Ifweformulateinductionassomethinglikealaw,inthemannerof(I),weseemtobelookingforsomeconnectionofnecessitylinkingtheantecedent(‘allobservedFsareG’)andtheconsequent(‘allFsareG’).Thesamegoesforanyrepresentationoftheprocessofinductionasaprocessofinference.Wittgenstein,however,representsinductionasamatterofassumingoracceptingalaw.Inthecaseofthekindofinductionwhichwetriedtorepresentin(I),thelawisthis:(L)AllFsareG.\nMETAPHYSICS,ETHICS,LIMITSOFPHILOSOPHY315Andtheprocessofinductionissimplytheprocessofassuming(L)whenalltheobservedFsareG.Whatisstrik-ingaboutthisisthatWittgenstein’sHumeantreatmentofinductioninvolvestheassumptionoflaws.Itiscrucialtohisviewthatlawsareinvolved.How,then,doesWittgensteindealwithlaws?Thekeyremarkhereisthis:6.32Thelawofcausalityisnotalawbuttheformofalaw.Whatisthe‘lawofcausality’?Presumablyitisthis:(Cau)Everyeventhasacause.Thisisaprinciplewhichhasadistinguishedhistory.Humethoughtthattherewasnoreasontobelieveit—thoughheseemsnottohavebeenabletostopbelievingit.Kantthoughtthatitstruthrequiredtheadoptionofhistranscen-dentalidealism,including,inparticular,thethoughtthattheverynotionofcausationisdependentonwhatwebringtotheworld,ratherthanjustonwhatisthereanyway,intheworldasitisinitself.4WhereHumeandKantagreeisinthinkingthat(Cau)iscontentiousandinneedofsomekindofsupport.Strikingly,itseemsthatitisjustthisthatWittgensteindenies.Wittgensteinoffersanotherinterpretationofthesigniﬁcanceofthe‘lawofcausality’alittlelateron:Iftherewerealawofcausality,itmightrun:‘Therearenaturallaws’.(6.36)Whatwenoticein6.32and6.36isthatWittgensteinimpli-citlydistinguishesbetweentwokindsof‘law’.First,therearesuchlawsasthe‘lawofcausality’:these,accordingto6.32,arenotreallylawsatall;letuscallthemhigher-orderlaws,inordertoremainasneutralaspossibleabouttheirstatus.Second,therearethelawswhoseformissupposedlygivenby‘laws’oftheﬁrstkind.Followingthehintgivenby\n316METAPHYSICS,ETHICS,LIMITSOFPHILOSOPHY6.36,letuscalllawsofthislatterkindnaturallaws.Itisplausiblethatnaturallawswilllooklike(L).Ifso,then6.32claims,ineffect,thatthe‘lawofcausality’(forexample)istheformofalawlike(L)—orperhapsbetter,theformoflawslike(L).5Butwhatcouldthatmean?FormintheTractatusiscon-cernedwithpossibility:theformofanobjectisthewaysitcancombinewithotherobjects;theformofasentenceisthepossibilityofitselementsbeingarrangedinthewaytheyare.Thissuggeststhatthecentralclaimof6.32isthis:(CauL)(Cau)means:foreveryeventeitispossibletoclassifyebymeansofsomepredicate‘F’,andalsobymeansofsomeotherpre-dicate‘G’whichdescribeseventsintermsoftheircauses,forwhichpredicates‘AllFsareG’holds.Ifthisistheclaimof6.32,andthisclaimcanitselfproperlyreformulatedastheclaimthat‘therearenaturallaws’(6.36),thenwhatWittgensteinwantstosayaboutitisthis:Butthatclearlycannotbesaid:itshowsitself.(6.36)Whateverelsethismeans,itsurelyrequiresthat(Cau)turnout,onthisinterpretation,tobesomethingthatcouldnotpossiblybefalse—assomethingthat,ineffect,needsnojustiﬁcation.Howcan(CauL)removethepossibilityoffalsehoodfrom(Cau)?Itcanonlydothatifthereisalmostnorestrictiononthepossiblechoicesofpredicates‘F’and‘G’:ithastobeclearthattherearesimplyboundtobesomepredicateswhichmeettherequirementthatallFsareG.Crucially,thiswillrequirethatweareveryliberalinwhatwecountasadescriptionofanevent‘intermsofitscause’.Onesugges-tionmightbethatwecountadescriptionofanevent‘intermsofitscause’asbeing,bydeﬁnition,nomorethan:amaximallyexplanatorydescriptionofthatevent.Allwewillthenneedfor(Cau)tobetruewillbethepossibilityof\nMETAPHYSICS,ETHICS,LIMITSOFPHILOSOPHY317classifyinganyeventintwoways:inamaximallyexplana-toryway(forthepredicate‘G’inlawsoftheformof(L)),andinalessthanmaximallyexplanatoryway(forthepre-dicate‘F’insuchlaws).Onthisinterpretation,then,(Cau)amountstonomorethanthis:(Cau*)Everyeventcanbedescribedintwoways—amaximallyexplanatoryway,andalessthanmaximallyexplanatoryway.Effectively,whathashappenedhereisthatwehaveletthenotionof‘cause’bedeﬁnedinsuchawayastoensurethat(Cau)cannotbefalse.Whatstatusdoesthisgivetothetwodifferentkindsof‘law’whichwedistinguishedbefore?Interpreting(Cau)as(Cau*)doesindeedseemtomakesenseofthefollowingclaimabouthigher-orderlaws:Laws,likethelawofcausation,etc.,treatofthenetworkandnotofwhatthenetworkdescribes.(6.35)Thesehigher-orderlawsarethelawswhichitisnaturaltoregardasnecessary:wecanseeherethatWittgensteinholdsthattheydonotreallytellusanythingabouthowtheworldis—rather,they‘treatofthenetwork’.So,despiteﬁrstappearances,theydonotencourageustothinkthatthereareanysyntheticaprioritruths.Wewillconsidertheirstatusfurtherinamoment,butletusturnnexttolawsoftheotherkind,thenaturallaws(lawslike(L)).Theseseemtobestraightforwardlyempirical.Althoughitisperhapsapriorithatitispossibletodescribeanyeventinthetwowaysrequiredfor(Cau*),itisanempirical(aposteriori)matterwhatthemaximallyexplanatorywayofdescribinganeventmaybe.Furthermore,itlooksasifthiscanharmlesslybecountedascontingent,aswellasbeingaposteriori.Soitseemsinsomewaynecessaryandapriorithattherearelawsofnature,butwhichlawsdescribetheactualworldisbothaposterioriandcontingent.\n318METAPHYSICS,ETHICS,LIMITSOFPHILOSOPHYCantheinterpretationwhichIhaveofferedof(Cau)as(Cau*)bemadetosquarewiththisremark?6.371Atthebasisofthewholemodernviewoftheworldliestheillu-sionthattheso-calledlawsofnatureareexplanationsofnaturalphenomena.Wittgensteinapparentlyholdsthatitisanillusiontothinkthatnaturallawsexplainnaturalphenomena,andyetIhavesuggestedthatnaturallawsare,ineffect,‘maximallyexpla-natory’descriptions.Thereisnodeeppuzzlehere,Ithink.Allweneedtosayisthat‘maximallyexplanatory’descrip-tionsdonotprovidethekindofexplanationwhich‘thewholemodernviewoftheworld’takeslawsofnaturetoprovide.Thenaturalwaytounderstandthisistosupposethat‘thewholemodernview’takeslawsofnaturetobenecessary—justas‘theancients’tookGodtobeanecessarybeing—whereas,infact(onWittgenstein’sview),thoselawswhichwerecountedasnaturallaws,onourearlierclassiﬁcation,arecontingent,andthosethingswhichwerecalledhigher-orderlawshavearatherdifferentstatus(whichwewillreturntoinamoment).The‘maximallyexplanatory’descriptionswhicharepositedin(Cau*)neednotinvolveanynecessitation:theymightbejustusefullyinclusive.Letusnowreturntothediscussionofinduction,wherewebeganthediscussionoflaws.Wecanseethatitisnaturallaws,inoursense,ratherthanhigher-orderlaws,whichareinvolvedininduction.OnWittgenstein’saccount,thepro-cessofinductionistheprocessofassumingthesimplestnaturallawwhichﬁtstheevidence.Thelawwhichishereassumedneedbenomorethanauniformity:itissimplyaccidental—ageneralstatementwhichhappenstosucceedindescribingtheworld.ThereisthereforenosurpriseinthefactthatWittgensteindevelopsabroadlyHumeanapproachtoinduction,whichgoeswitharejectionofnaturalneces-sity,asinvolvingtheassumptionoflaws—sincethelawsinquestiondonotimportanynaturalnecessity.\nMETAPHYSICS,ETHICS,LIMITSOFPHILOSOPHY319RecalltheremarkwhichIsaidearlieramountedtoWittgenstein’sversionofHume’sFork:6.3Logicalresearchmeanstheinvestigationofall[law-governedness].Andoutsidelogicallisaccident.Amongsigniﬁcantsentencesthereare,ontheonehand,sentencesoflogic,aboutwhichWittgensteinholdsthis:6.1Thepropositionsoflogicaretautologies.And,ontheotherhand,thereareempiricalsentences,sen-tenceswhichdescribetheworld.Butwheredosuchthingsashigher-orderlawsﬁthere?OnWittgenstein’saccounttheyseemtobeneithertautologiesnorempiricalstatements.Doeshe,then,afterall,assignthemanintermediatestatus,likethatofKant’ssyntheticapriorijudgements?HecertainlydoesdescribetheminawaywhichisconsciouslyindebtedtoKant:6.34Allpropositions,suchasthelawofcausation,thelawofcon-tinuityinnature,thelawofleastexpenditureinnature,etc.etc.,alltheseareaprioriintuitionsofpossibleformsoftheproposi-tionsofscience.Thisnotionofan‘aprioriintuition’isjustwhatisneededtomakesenseofsyntheticaprioritruths—truthswhicharebothapriori,andyetsomehowconcerntherealworld.ButthisKantiandescriptionissurelyundercutbywhatWittgensteinsayselsewhereabouthigher-orderlaws.Hereiswhathesaysin6.342:SotoothefactthatitcanbedescribedbyNewtonianmechanicsassertsnothingabouttheworld.Andrememberwhathesaysaboutthe‘lawofcausality’:6.36.Iftherewerealawofcausality,itmightrun:‘Therearenaturallaws’.\n320METAPHYSICS,ETHICS,LIMITSOFPHILOSOPHYButthatclearlycannotbesaid:itshowsitself.‘Showing’hereemergesasWittgenstein’sreinterpretationoftheKantian‘aprioriintuition’,butitissurelymorethanareinterpretation:itisadeﬂation.Kant’saprioriintuitionwassupposedtoprovideuswithameansofaccesstosome-thingwhichisoftherightkind,broadlyspeaking,tobeseen,butwhichhappenstobe,asitwere,inthewronglocation.What‘showsitself’,however,seemstobethewrongkindofthingtobesaid.InredescribingwhatKantwoulddescribeasaprioriintuitionsasthingswhichcanbeshown,butnotsaid,Wittgensteinis,ineffect,insistingthattheseso-calledaprioriintuitionsarenotintuitionsatall.WhatemergeshereisthatthethingswhichKantwouldhavecountedassyntheticaprioriarenotcounter-examplestoWittgenstein’sversionofHume’sFork:theyarenotcasesof‘law-governedness’whichlogicsomehowfailstoaccom-modate.Rather,theyarenotreallylawsatall:infact,theyarenotevenmeaningful,notevensentences.Theyareattemptstosaywhatcannotbesaid.Sothereremainjustthetwocategoriesofsigniﬁcantsentences:thosedealtwithbylogic(tautologiesandcontradictions),andempiricalsen-tencesabouttheworld.Thethingswhichseemtoexpresssyntheticaprioritruthsarenotreallysentencesatall.7CETHICSWittgensteinbeginshisdiscussionofethicswithwhatlookslikeadeliberatelycontroversialformulationofhisview:6.4Allpropositionsareofequalvalue.Thislooksasifitissayingthatnostateoftheworldisanybetterorworsethananyotherstateoftheworld.Canthisreallybewhathemeans?Thepuzzlehereisthat,followingonfromthediscussionoflawsofnature,andinthecontextofmoregeneralconsiderationsofnecessity,weareexpectingWittgensteintomakesomemeta-ethicalclaim—some\nMETAPHYSICS,ETHICS,LIMITSOFPHILOSOPHY321claimaboutthestatusofethicsandstatementsofethics.But6.4seemstobeanormativeclaim:itdoesnottalkaboutvalue;itmakesavaluestatement(andaveryoddoneatthat).Infact,itlooksasiftheseremarks(roughlythe6.4s)expressbothameta-ethicalview(aboutthestatusofethicsassuch)andaparticularethicalapproachtolife,andtheseareintertwinedinacomplicatedway.6.41,whichisostensiblyacommenton6.4,isunambiguouslymeta-ethical:Thesenseoftheworld[roughly:themeaningoflife]mustlieout-sidetheworld.Thereisnovalueintheworld,Wittgensteinclaims;rather,Itmustlieoutsidetheworld.6.41alsoapparentlycontainsanargumentforthisclaim,whichwecouldsummarizeasfollows:(V1)Valueisnon-accidental;(V2)Everythingintheworldisaccidental;so(V3)Valueisnotintheworld.(V2)shouldbefamiliarenoughbynow:itisaHumeanrejectionofnaturalnecessity(see,forexample,6.37).Themoreobviouslystrikingclaimis(V1):whyshouldvaluebenon-accidental?WhatWittgensteinisclaiminghereseemstoamounttothis:anythingwhichisgood(orbad)isessentiallygood(orbad).Thatistosay,ifitisreallygood,itcouldnotbuthavebeengood;anythingwhichwasnotgoodwouldhavebeenadifferentthing.Onthefaceofit,thislooksstraightforwardlyfalse.Supposethatyoudosomethingwhichturnsouttohelpsomeoneelse.Supposethatwhilewalkingalongyouidlykickastoneoffapath—notforanyrealreason,justasaplayfulkick.Andthensupposeachildcomestearingalongthepathonabicycle,andgoessafelyby—thoughshewouldhavecrashedpainfullyifthestonehadstillbeenonthepath.Wemightsay:\n322METAPHYSICS,ETHICS,LIMITSOFPHILOSOPHY(1)Itwasagoodthingyoukickedthatstoneoffthepath.Nowitisnaturaltothinkthatthekickwouldhavebeenthesame,evenifithadnothadthatfortunatelybeneﬁcialeffect;thesamekickmighthavedonenogood,mightevenhavedoneharm.HowcanWittgensteincopewiththat?Hehastothinkthat(1)canbeanalysedintoaconjunction,oneconjunctofwhichisevaluative,whiletheotherisnot.Itmightlooklikethis:(1a)Yourkickingthestoneoffthepathhadeffecte,andeffecteisgood.Theclaimwouldbethatin(1a)wereachsomething(effecte)whichis,indeed,non-accidentallygood.Ifwecanprovideananalysislikethisineverycase,andcanclaimthattheanalysisshowswherethevalueisreallylocated,thenitlooksasifwemightbeabletoclaimthatwhateverreallyhasvaluehaswhatevervalueithasnon-accidentally.ThisalreadyinvolvesWittgensteintakingastandinnor-mativeethics,ratherthanjustinmeta-ethics.Hemustalreadybeopposedtofamiliarformsofconsequentialism.Familiarformsofconsequentialism(utilitarianismistheobviousexample)aretheoriesofthevalueofacts.Theyassumethatactsdoreallyhavevalue,andtheyclaimthatthevaluetheyhaveisdeterminedbytheirconsequences(roughly:theendalwaysjustiﬁesthemeans).Butitisacontingentmatterthataparticularacthastheparticularconsequencesitdoes(itiscertainlycontingentaccordingtoanyview,likeWittgenstein’s,whichdeniestherealexistenceofnaturalnecessity).Soitmustbecontingentthataparti-cularacthasthevalueitdoes.SincethisisexactlywhatWittgensteindeniesinaccepting(V1),hemustrejectfamil-iarformsofconsequentialism.Andthisisexactlywhathedoesin6.422:Butitisclearthatethicshasnothingtodowithpunishmentandrewardintheordinarysense.Thisquestionastotheconsequencesofanactionmustthereforebeirrelevant.\nMETAPHYSICS,ETHICS,LIMITSOFPHILOSOPHY323NotethattheitalicshereshowthatWittgensteinisrejectingtheviewthatthevalueofanactionliesinitsconsequences,butnottheideathatactionshavevalue.Butifanactionhasvalue,andthatvaluedoesnotresideinitsconsequences,itseemsevidentthatitsvaluemustlieintheintention,orwill,withwhichitisperformed.ButatthispointitlooksasifWittgensteinhasanother,moreorlessindependent,reasonforasserting(V2),thatvalueisnotintheworld.Forheinsists:6.423Ofthewillasthesubjectoftheethicalwecannotspeak.Andthewillasaphenomenonisonlyofinteresttopsychology.Thiscontrastbetween‘thewillasthesubjectoftheethical’and‘thewillasaphenomenon’isreminiscentofasimilarcontrast,whichweencounteredinthelastchapterinthediscussionofsolipsism:ThephilosophicalIisnottheman,notthehumanbodyorthehumansoulofwhichpsychologyspeaks,butthemetaphysicalsub-ject,thelimit—notapartoftheworld.(5.641)ItisnaturalthentothinkthattheIwhowills—thesubjectwhoisourconcerninethics—isthemetaphysicalsubject,whoisnotintheworld.IftheIwhowillsisnotintheworld,thennothingdonebytheIcanaffecttheworld.ThisissomethingwhichWittgensteinhasalreadyclaimedinexplainingoursenseoftheinexorabilityoflawsofnature:6.373Theworldisindependentofmywill.6.374Evenifeverythingwewishedweretohappen,thiswouldonlybe,sotospeak,afavouroffate,forthereisnologicalconnexionbetweenwillandworld,whichwouldguaranteethis,andtheassumedphysicalconnexionitselfwecouldnotagainwill.Andhemakesthepointagaininthediscussionofethics:\n324METAPHYSICS,ETHICS,LIMITSOFPHILOSOPHYIfgoodorbadwillingchangestheworld,itcanonlychangethelimitsoftheworld,notthefacts;notthethingsthatcanbeexpressedinlanguage.(6.43)Thisisapuzzlingremarkifwetakethe‘limitsoftheworld’heretobewhattheyusuallyareintheTractatus:thelimitsofwhatispossible.Itishardtoseewhatsensecouldbemadeoftheclaimthatgoodorbadwillingchangeswhatispossible,inthesenseofmakingpossiblewhathadpre-viouslybeenimpossible,orimpossiblewhathadpreviouslybeenpossible.Ifgoodorbadwillingchangeswhatispossi-ble,theonlychangetowhatispossiblewhichitseemscap-ableofeffectingisachange,crudelyspeaking,inthewaywhatispossiblefeelstous.ThisisnaturallyconnectedbackwithwhatWittgensteintakestobetheproperapplicationinethicsofthenotionsofrewardandpunishment:Theremustbesomesortofethicalrewardandethicalpunishment,butthismustlieintheactionitself.(Andthisisclearalsothattherewardmustbesomethingacceptable,andthepunishmentsomethingunacceptable.)(6.422)Itlooksasifgoodwillingwillmaketheworld,whichonecannotchange,acceptable,andbadwillingwillmakeitunacceptable.Wittgensteinthenclaims:Theworldofthehappyisquiteanotherthanthatoftheunhappy.(6.43)Wecanreadthisintwoways,compatiblywithacceptingthatthesubjectcannotchangetheworld.Bothwaysinvolvetakingthedifferencebetweenthehappyperson’sworldandthatoftheunhappypersontobeamatterofhowthesameworldseemstothatperson.Ontheﬁrstinterpretation,exactlythesamepossibilitiesareevidenttoboththehappy\nMETAPHYSICS,ETHICS,LIMITSOFPHILOSOPHY325personandtheunhappyperson:thedifferenceliesintheiracceptanceofthosepossibilitiesastheonlypossibilities.Onthesecond,thehappypersonisawareofadifferentrangeofpossibilitiesfromthoseofwhichtheunhappypersonisaware.(Onewouldlikethehappypersontobeawareofmorepossibilitiesthantheunhappyperson,orelsehappi-nesswouldseemtodependonaformofdelusion,whichseemsclearlyforeigntothespiritoftheTractatus.)Itisnoteasytodecidebetweenthesetwointerpretations,althoughmyownpreferenceisfortheﬁrst:thisseemsclosertothekindofreconciliationtoone’sfatewhichWittgensteinseemstohaveachievedonthefrontline.Howeverthismaybe,itseemsclearthatWittgenstein’sconceptionofethicsinvolvessomekindofremovaloftheethicalsubjectfromtheworld.Andthisprovideswhatseemstobeanindependentsourceof(V3),theclaimthatvalueisnotintheworld.ItisalsowhatleadsWittgensteintosay:Ethicsistranscendental.(6.421)Hethenaddsastrikingparenthesistothatlastremark,asifinexplanationofit:(Ethicsandaestheticsareone.)Tounderstandthis,weneedtolooktothosesectionsintheNotebookswheresomeoftheseideaswereﬁrstsketchedout.Thesefourremarks,inparticular,arehelpful:Theworkofartistheobjectseensubspecieaeternitatis;andthegoodlifeistheworldseensubspecieaeternitatis.Thisistheconnexionbetweenartandethics.(NB:83)(Thethoughtforcesitselfuponone):Thethingseensubspecieaeter-nitatisisthethingseentogetherwiththewholelogicalspace.(NB:83)\n326METAPHYSICS,ETHICS,LIMITSOFPHILOSOPHYAesthetically,themiracleisthattheworldexists.Thatthereiswhatthereis.(NB:86)Isittheessenceoftheartisticwayoflookingatthings,thatitlooksatthingswithahappyeye?(NB:86)TheseremarksfromtheNotebooksarenaturallyputbesidewhatwehavealreadyfoundintheTractatus—andalsothis:6.45Thecontemplationoftheworldsubspecieaeterniisitscon-templationasalimitedwhole.Thefeelingoftheworldasalimitedwholeisthemysticalfeeling.(‘View’wouldbebetterthan‘contemplation’asatranslationof‘Anschauung’here:itisanattitude,ratherthananactivity.)Whattheseremarksallsuggestisaparticularnormativeethics,whichwecanexplainrathercrudelyasfollows.Thereisasingleethicalimperative,whichistoviewtheworldinacertainway.Thisistheartist’swayofviewingtheworld,awayoflookingatthings‘withahappyeye’,anoutlookwhichﬁndsitamiraclethattheworldexists.Viewingtheworldinthiswayisviewingitsubspecieaeternitatis—fromthepointofviewofeternity—removedfromitanddisinterested.Whatweseewhenweviewtheworldlikethisiseachthing‘togetherwiththewholelogicalspace’:withaconsciousness,thatis,ofwhatispossible,ofthewaysinwhicheachthingcanbecombinedwithotherthings.Thiswayofviewingtheworld,theartisticway,mayalsobedescribedasmysticism:6.44Nothowtheworldis,isthemystical,butthatitis.Whattheartistdelightsinisnotthefactsbeingoneparti-cularwayratherthananother,buttherebeinganyfactsatall—ineffect,therebeingthepossibilitiesthereare.\nMETAPHYSICS,ETHICS,LIMITSOFPHILOSOPHY327SomethinglikethisinterpretationoftheethicsoftheTractatusseemsunavoidable,onceweputtheseremarksinthecontextofthepassagesintheNotebooksfromwhichtheyoriginallyarose.Whateverthegeneralmeritsoftheoutlookwhichishererecommended,itseemsbizarre—mad,even—toregardthisassummarizingallofethics.Itisnotimplausible,however,toattributethisoddethicstotheeffectsofbeingonthefrontintheFirstWorldWar,whichiswherethelogicaltreatisewhichWittgensteinwascomposingspreadouttoencompassthequestionofthemeaningoflife.Itwouldnotbesurprisingifthatkindofexperienceledtosomethingalittleunhinged.AndcertainlyRussellremarkedonthechangewhichhadcomeoverWittgenstein,whenhemethimfortheﬁrsttimeafterthewar:Ihadfeltinhisbookaflavourofmysticism,butwasastonishedwhenIfoundhehasbecomeacompletemystic.HereadspeoplelikeKierkegaardandAngelusSilesius,andheseriouslycontemplatesbecomingamonk.(Monk1997:568).AndthereisaconnectionwithSchopenhauer,whomWittgensteinobviouslyreadfromearlyinhislife.Hereisapassagewhichhasastrikingresonance,inthelightofthefactthatWittgenstein’sexperienceatthefrontclearlychangedhimquitedeeply:Fromthefirstappearanceofhisconsciousness,manfindshimselftobeawillingbeing,andhisknowledge,asarule,remainsinconstantrelationtohiswill….Itisalwaysanexception,whensuchalifesuf-fersaninterruptionthroughthefactthateithertheaestheticdemandforcontemplationortheethicaldemandforrenunciationproceedsfromaknowledgeindependentoftheserviceofthewill,anddirectedtothenatureoftheworldingeneral.6Finally,letuslookbackattheremarkwithwhichthediscussionofethicsbegins:\n328METAPHYSICS,ETHICS,LIMITSOFPHILOSOPHY6.4Allpropositionsareofequalvalue.Isaidbeforethatthisseemedtosaythatnoonestateofaffairsisbetterorworsethananyother,whichlookslikeavalueclaim,ofsorts,ratherthanaclaiminmeta-ethics.ItnowseemsthatthisispreciselywhatWittgensteinmeanstosay.Thethingswhichhaverealvaluearenotfacts,notanythingintheworld.Whathasrealvaluearejust:acertainkindofoutlook,combinedwiththeactionofadoptingthatoutlook;andwhatthatoutlookﬁndsinlookingattheworld.Whatisreallygood,itseems—whattheartist’seyedelightsin—isnotthefactsbeinganyparticularway,butsimplytheirbeingsomeway.77DMETAPHYSICSANDPHILOSOPHYInthe6.5sWittgensteinturnsfromethicstophilosophyingeneral—andphilosophyconceivedofinthelargestpossibleway.Thekeytohisapproachcanbeseeninthisremark:6.52Wefeelthatevenifallpossiblescientificquestionsbeanswered,theproblemsoflifehavenotbeentouchedatall.Ofcoursethereisthennoquestionleft,andjustthisistheanswer.First,weshouldnotetheconceptionofphilosophywhichisinvolvedhere.Itisconcernedwithquestions(ifthereareany)whichremainuntouchedbyanypossiblescientiﬁcadvance.Theseareboundtoseemmorefundamentalthananythingthatsciencecantellus.Inthelaymind—themindofthosewhoarenotprofessionalphilosophers—thesequestionsseemtoconcernthemeaningoflife(what-everexactlythatphrasemightitselfmean).6.52showsthatWittgensteinthinksofthequestionsofphilosophyinjusttheseterms:theyconcern‘theproblemsoflife’.Insomesense,itseems,Wittgensteintakestheproblemsofphilosophytobeconcernedwithathreattothemeaningoflife.Andhereheofferssomereassurance,thoughonewhichpeoplemayﬁndithardtoaccept:itturnsoutthatthereisno\nMETAPHYSICS,ETHICS,LIMITSOFPHILOSOPHY329threatatall.Thereisnogenuinequestionwhichremainsuntouchedonceallpossiblescientiﬁcquestionshavebeenanswered;thereisnorealproblemofthemeaningoflife.Inhiswords:Thesolutionoftheproblemoflifeisseeninthevanishingofthisproblem.(6.521)ItisinthiscontextthatWittgensteinaddressesscepticismexplicitlyfortheﬁrst(andonly)timeinthebook(thoughwefoundthattheargumentforsolipsismin5.62washardtounderstandexceptasaresponsetoaformofscepticism):6.51Scepticismisnotirrefutable,butpalpablysenseless[unsinnig:nonsense],ifitwoulddoubtwhereaquestioncannotbeasked.Fordoubtcanonlyexistwherethereisaquestion;aquestiononlywherethereisananswer,andthisonlywheresomethingcanbesaid.WhydoesWittgensteinconsiderscepticismhere?Whatisthelinkbetweenscepticismand‘theproblemsoflife’?Wecanbringouttheconnectionbyconsideringascenariowhichisfamiliarindiscussionsofutilitarianism.Someclassicalversionsofutilitarianismclaimthatallthatmatters,ulti-mately,isthemaximizationofpleasure,andminimizationofpain.Thissuggeststhatanideallifecouldbeachievedifeveryonewerehookeduptoa‘pleasuremachine’,whichensuredthattheirliveswerespentwithmaximumpleasureandminimumpain.Ofcourse,pleasureisalwayspleasureinsomething,sowecouldonlyfeelpleasureifwethoughtthatcertainnicethingswerehappening.Sothepleasuremachinewouldhavetoengendercertainkindsofillusioninus.Wewouldspendourlivesinastateof(apparently)blissfulhallucination.Whatwouldbewrongwiththis?Well,itseemsthatinthiscircumstanceeveryone’slifewouldbeanemptysham:ourpleasurewouldnotbeproperlygrounded,woulddependonalie,wouldbe,inasense,pathetic,empty,andfutile.If\n330METAPHYSICS,ETHICS,LIMITSOFPHILOSOPHYanylifeisalifewithoutmeaning,thislifewouldbe.Itisjustthisthreatofmeaninglessnesswhichscepticismraises.Scepticisminvitesustowonderwhetherthereisanythingreallythere:whetherourthoughtsrelatetoanyreality,whetheranythingwethinkreallymeansanything.AnditisjustthisthreatofthecompleteemptinessofourthoughtsthatWittgensteinthinkshecandismiss.HerewecanreturntothekindofthinkingwhichItentativelysuggestedlaybehindWittgenstein’sargumentforsolipsism(inChapter6,section6E).Icannotdoubtthatmylanguageissyntacticallywellformed.Butifmylanguageissyntacticallywellformed,then,accordingtotheaccountoflanguageprovidedbytheTractatus,thepossiblecombinationsofitssymbolsmustbeco-ordinatewithgenuinepossibilities.Andforthesetobegenuinepossibilities—ratherthanmerelyimaginedpossi-bilities—theremustbearealworldforwhoseconstituentseverygenuinepossibilityisapossiblewayofbeingarran-ged.Andthatrequiresnotjustarealworld,butrealobjectswhoseformistherangeofpossibilitiesofcombinationwhichconstitutesthewholeofgenuinepossibility.(Thisobviouslyrecallsthesubstanceargumentof2.021–2.023,discussedinChapter1,section1D.)Thatis,asitwere,thestraightanswertoscepticismwhichWittgenstein’saccountoflanguagesuggeststhatwegive.But,aswesawinthecaseofsolipsism,Wittgensteindoesnothim-selfgivethisanswer.Inthediscussionofsolipsismhewrote:Wecannotthereforesayinlogic:Thisandthisthereisintheworld,thatthereisnot.Forthatwouldapparentlypresupposethatweexcludecertainpos-sibilities,andthiscannotbethecasesinceotherwiselogicmustgetoutsidethelimitsoftheworld:thatis,ifitcouldconsidertheselimitsfromtheothersidealso.(5.61)Andweseemtohavethesamekindofthinkinghere,in6.51.Fortoentertainscepticism,wewouldhavetoentertainthepossibilitythatourlanguageisnotsyntacticallywell\nMETAPHYSICS,ETHICS,LIMITSOFPHILOSOPHY331formed.Andthiswouldrequireustoframe,asagenuinepossibility,somethingwhichwecannotacceptis,infact,possible.ButtheTractatus’sconceptionoflanguagerulesthatout:thatconceptionrequiresacoincidencebetweenwhatisconceivable(framable,picturable)andwhatispossible.Itturnsout,infact,thatthesameappliestoallofphilo-sophyasisappliedheretoscepticism.ThisgenerallessonisdrawninoneofthemostfamousremarksintheTractatus:6.53Therightmethodofphilosophywouldbethis.Tosaynothingexceptwhatcanbesaid,i.e.thepropositionsofnaturalscience,i.e.somethingthathasnothingtodowithphilosophy:andthenalways,whensomeoneelsewishedtosaysomethingmetaphysi-cal,todemonstratetohimthathehadgivennomeaningtocer-tainsignsinhispropositions.Thismethodwouldbeunsatisfyingtotheother—hewouldnothavethefeelingthatwewereteachinghimphilosophy—butitwouldbetheonlystrictlycor-rectmethod.WhatdoesWittgensteinmeanby‘philosophy’here?Apparently,hemeansthesameashemeansby‘meta-physics’,sincesayingsomethingmetaphysicalseemsheretobethesameassayingsomethingphilosophical.Andwhateverhemeansby‘philosophy’and‘metaphysics’seemstoincludetheTractatusitself,sinceinthenextremarkhewrites:Mypropositionsareelucidatoryinthisway:hewhounderstandsmefinallyrecognizesthemassenseless[unsinnig:nonsense],whenhehasclimbedoutthroughthem,onthem,overthem.(6.54)ThenaturalinterpretationisthatforWittgensteinphiloso-phy(ormetaphysics)includespreciselywhatithastradi-tionallybeentakentoinclude:whatitwastakenbyKanttoinclude,forexample.Itisconcernedwiththepossibilitiesoftheworld:itsbusinessishowtheworldmustbe,howitmightbe,howitcannotbe.8ItsprovinceistheﬁeldofthosetruthswhichKantcountedsyntheticapriori.\n332METAPHYSICS,ETHICS,LIMITSOFPHILOSOPHYWhatensuresthatanyattempttosaysomethingphiloso-phicalwillendupasnonsense?Theconclusionmightseemtobeoverdetermined:atleast,itlooksasifitcanbereachedbymoreandlessdirectroutes.Butthecorethoughtistheonewhichisexpressedintheargumentfortheinexpressibilityofsolipsism:Whatwecannotthink,thatwecannotthink:wecannotthereforesaywhatwecannotthink.(5.61)Theconceptionofsentencesasmodels—indeed,ofallrepresentationasmodelling—makesitimpossibletorepresentanimpossibility:becausethepossibilitiesofcom-binationofsymbolsarethesameasthepossibilitiesofcombinationofobjects,nocombinationofsymbolscanrepresentanimpossiblecombinationofobjects.ThisistheﬁrstofthreeprincipleswhichwesawinthelastchapterthatWittgensteiniscommittedto:(SP)Itispossibletostatethatponlyifitispossiblethatp.(SPN)Itispossibletostatethatponlyifitispossibletostatethatnot-p.(SPP)Itispossibletostatethatitispossiblethatponlyifitispos-sibletostatethatp.Alittlereﬂectionshowsthat,withtheseprinciplesinplace,itwillbeimpossibletostatethatsomethingisimpossible,thatsomethingispossible,orthatsomethingisnecessary.(TheargumentswereelaboratedmorefullyinChapter6,section6B.)Sincethebusinessofphilosophy(ormetaphysics),onthenaturalinterpretationIhavesuggested,ispreciselytosaywhatisnecessary,orpossible,orimpossible,intheworld,thesethreeprinciplesmeanthatnothingphilosophical(ormetaphysical)canbestated.WiththecoreassumptionoftheTractatus’stheoryoflanguage—thatsentencesandrealityhavethesameform—inplace,similarreasoningattachestoallofthemoreformalremarksintheTractatus.Theproblemaffectsthe\nMETAPHYSICS,ETHICS,LIMITSOFPHILOSOPHY333philosophyoflanguageandlogicasmuchasitaffectsattemptstosaysomethingabouthowtheworldmustbe.Thisisbecause,withthetheoryoflanguageinplace,thephilosophyoflanguageandlogicwillitselfbeconcernedwithwhatispossible(withwhatsymbols,orcombinationsofsymbols,arepossible,forexample).ThisproblemwithsayinganythingmodalisconnectedwithwhatWittgensteinsaysaboutform,sinceformisexplainedintermsofpossibility.Itis,infact,thenon-metaphoricalexplanationofthisclaimaboutapictureanditsform:2.172Thepicturecannot,however,representitsownformofrepresentation;itshowsitforth.AndWittgensteinthenattachesthisdifﬁcultytoawholerangeofphilosophicalterms.2.172concernspicturesormodelsingeneral.Wittgenstein,ofcourse,isconcernedwithsentencesinparticular.Theapplicationofthegeneralpointof2.172totheparticularcaseofsentencesisfoundinthisremark:Propositionscanrepresentthewholereality,buttheycannotrepre-sentwhattheymusthaveincommonwithrealityinordertobeabletorepresentit—thelogicalform.(4.12)Thesecondremarkofferedasacommentonthisbeginsasfollows:Wecanspeakinacertainsenseofformalpropertiesofobjectsandatomicfacts,orofpropertiesofthestructureoffacts,andinthesamesenseofformalrelationsandrelationsofstructures.(4.122)Andthisisthebasisoftheintroductionofthenotionofaformalconceptin4.126.Itshouldthenfollowthatnothingcanberepresented,nothingcanbesaid,usingaformalcon-cept,sinceanyattempttouseaformalconcepttosay\n334METAPHYSICS,ETHICS,LIMITSOFPHILOSOPHYsomethingwillbeanattempttospeakaboutwhatispossible.And,indeed,thisisexactlytheconclusionWittgensteindrawsaboutvarioussuchattempts,in4.1272and4.1274.Itseems,then,thatthebasicreasonwhynothingphilosophicalcanbesaid,accordingtotheTractatus,isthatphilosophyattemptstomakemodalclaims(claimsaboutwhatisnecessaryorpossible),andnosigniﬁcantmodalclaimcanreallybemade,given(SP),(SPN),and(SPP).Butinthatcase,theproblemattachesevento6.54.ForWittgensteindoesnotheremerelymakeaconjecture,orofferanempiricalobservation:hetellsuswhatwouldbetherightmethodinphilosophy;hetellsustoconﬁneourselvestowhatcanbesaid;heassumesthatitisinevitable,capableofdemonstration,thatanyonewhoattemptstosaysomethingmetaphysicalwillhavefailedtogivemeaningtocertainsignsinthesen-tencesheproduces.6.54isitselfmodal:ittellsuswhatmustbedone,andwhatcannotbedone.Itisitselfapieceofphiloso-phy,ormetaphysics.TheTractatus’sconceptionoflanguageliesbehindthe(philosophical)claimof6.54,thatnothingphilosophicalcanbesaid.Itisalsoimplicatedintheparticularformwhichthatclaimtakes.NotethatWittgensteindoesnotmerelysaythatanyattempttosaysomethingphilosophicalwillleadtononsense:hesays,inparticular,thatanyonewhotriestosaysomethingphilosophicalwillhave‘givennomeaningtocertainsignsinhispropositions’.Thismeansthatwhatisofferedasaphilosophicalstatementwillbemeaningless,inwhatCarnapcalled‘thestrictestsense’oftheword:thatistosay,itisplainnonsense.Butitmeansmorethanthat.Carnapthoughtthatthereweretwodifferentkindsofmean-inglessness,evenin‘thestrictestsense’oftheword.Inaddi-tiontomeaningless‘sentences’—whichhecalled‘pseudo-statements’—which‘containameaninglessword’,Carnapthoughtthattherewereother‘pseudo-statements’which‘consistofmeaningfulwords,butthewordsareputtogetherinsuchawaythatneverthelessnomeaningresults’.9Butthis,ofcourse,issomethingwhichWittgensteinhastoreject,aswesawinChapter4,indiscussing5.4733(see\nMETAPHYSICS,ETHICS,LIMITSOFPHILOSOPHY335section4C).Hehastorejectit,becauseitisincompatiblewiththeconceptionoflanguagepresentedintheTractatus.TheTractatusinsiststhattheelementsofarepresentationcanbecombinedinexactlythesamewaysastheobjectsinrealitywithwhichtheyarecorrelated:thisisthecommon-formassumptionattheheartofhisconceptionoflanguage.Asentence—orpseudo-sentence—whichconsistedofmeaningfulwords‘puttogetherinsuchawaythatneverthelessnomeaningresults’wouldbeasentencewhichrepresentedthings(thecorrelatesofthosewords)asbeingarrangedinwaysinwhichtheycouldnotbearranged.Thatis,wewouldhaveapossiblearrangementofwordstowhichnopossiblearrangementofobjectscorresponded.AndthatisexactlywhattheTractatus’stheoryoflanguagerulesout.Itseems,then,thatweareforcedintotheparticularwayinwhichWittgensteinclaimsthatanyattempttosaysome-thingphilosophicalendsupinnonsenseonlybytheparti-cularphilosophywhichheendorsesintheTractatus.Thismakestheworkseemtightlyparadoxical.IfthephilosophicalclaimsoftheTractatusaretrue,it—andthey—arenon-sense.AnditisonlyifthephilosophicalclaimsoftheTractatusaretrue,thatit—andthey—arenonsenseintheparticularwaythatWittgensteinclaimstheyare.Thisparadoxwillbeourconcerninthenextsection.Itisimportanttocomparethisapparentlytightlypara-doxicalconclusionwiththeremarkswhichWittgensteinmakesearlierinthebook,inthe4.1s(remarkswhosedis-cussionwasnotpursuedinChapter4).Thefollowingsectionisparticularlysigniﬁcant:4.112Theobjectofphilosophyisthelogicalclarificationofthoughts.Philosophyisnotatheorybutanactivity.Aphilosophicalworkconsistsessentiallyofelucidations.Theresultofphilosophyisnotanumberof‘philosophicalpropo-sitions’,buttomakepropositionsclear.Philosophyshouldmakeclearanddelimitsharplythethoughtswhichotherwiseare,asitwere,opaqueandblurred.\n336METAPHYSICS,ETHICS,LIMITSOFPHILOSOPHYWhatisrecommendedherehasseemedtomanytobesimi-larinspirittothecharacterofphilosophyasitispracticedinWittgenstein’slaterwork.Butwhateverwesayaboutthelaterwork,weshouldbeclearthatthispassageintheTractatusisnotitselfphilosophicallyinnocent.Thesucceed-ingremarksofparallelimportanceareinextricablyboundupwiththewholetheoryoftheTractatus:4.113Philosophylimitsthedisputablesphereofnaturalscience.4.114Itshouldlimitthethinkableandtherebytheunthinkable.Itshouldlimittheunthinkablefromwithinthroughthethinkable.4.115Itwillmeantheunspeakablebyclearlydisplayingthespeakable.4.116Everythingthatcanbethoughtatallcanbethoughtclearly.Everythingthatcanbesaidcanbesaidclearly.Herethenotionof‘limit’isexactlytheonewhichisinplay,forexample,inthediscussionofsolipsism,andwhichistheresaidtobeunstatable.Soalthough4.112advocatesthereplacementoftheideaofphilosophyasatheory,withthatofphilosophyasanactivity,anddeclaresthatphilosophyisnotconcernedtoproduce‘philosophicalpropositions’—nevertheless,4.112seemsitselftobeasequenceofphiloso-phicalpropositions,andtheactivitywhichisrecommendedthereseemstobeanactivityundertakenforareason,andthereasonitselflooksasifitisboundtobesomethingwhichisstatableinaphilosophicalproposition.4.112needstobeconsideredalongsidewhatlooklikethemostobviouslyparadoxicalsectionsoftheTractatus.Beforeaddressingtheissueoftheapparentparadoxicalityofthebook,however,itseemsappropriatetogiveabriefrecapitulationofitsprincipalphilosophicalachievements.InthePrefaceWittgensteinwrites:Ontheotherhandthetruthofthethoughtscommunicatedhereseemstomeunassailableanddefinitive.Iam,therefore,oftheopinionthattheproblemshaveinessentialsfinallybeensolved.(29)\nMETAPHYSICS,ETHICS,LIMITSOFPHILOSOPHY337The‘problems’herearethosedescribedas‘theproblemsofphilosophy’onthepagebefore.WhenWittgensteinclaimsthattheyhave‘ﬁnally’beensolved,heisclaimingtohaveputanendtoanancienttradition.WhatancientproblemshasWittgensteinsolvedhere,ifwetakehimathisownword?Ifwetakehimathisword,hehassolvedthequestionofsolipsism,idealism,andrealism:solipsismis,inasense,correct,butcannotbesaid.HehassolvedtheproblemswhichmotivatedKanttointroducethecategoryofsyntheticaprioritruths:whatsuchtruthswouldattempttostatecannot,infact,besaid.Hehassolvedtheproblemofethics,andthestatusofethics:herecommendsaparticular,aes-theticethicalview,whileinsistingthatnothingethicalcanbesaid.Hehasunderminedscepticism,showingthatitattemptstoraisequestionsthatcannotberaised,becausetheiranswerscannotbestated.Hehasunderminedallattemptstosaysomethingaboutthemeaningoflife:nosuchthingcanbesaid.And,ofcourse,hehas,hethinks,explainedtherelationbetweenthought,languageandtheworld,anddealtwiththestatusoflogicandofmodality;though,again,noneofthiscanstrictlybesaid.TheTractatusisashortwork:thisisanimpressiverangeofproblemstohavetackledinit.Thesolutiontotheproblemisineachcasethesame:thesolutionoftheproblemisseeninthevanishingoftheproblem(see6.521).Thereisonepuzzlethatremainsinthe6.5s—thereap-pearancethereofmysticisminthediscussionofphilosophy:6.522Thereisindeedtheinexpressible.Thisshowsitself;itisthemystical.Thepuzzleisthis:ismysticisminthesameboatasphiloso-phy—ismysticismnonsensetoo?Ithasoftenbeenassumedthatitis,thattherejectionofphilosophyalsoincludesarejectionofmysticism.10Butourconsiderationofethicsinthelastsectionmakesthislookwrong.ItseemsveryclearthatWittgensteinisthererecommendingtheadoptionofamysticalattitude,theattitudewhichhe\n338METAPHYSICS,ETHICS,LIMITSOFPHILOSOPHYdescribedintheNotebooksasaestheticorartistic.11Andinfactthewordingof6.522makesmostsenseifwesupposethatmysticismisheredistinguishedfromphilosophy.Thedifﬁcultywithphilosophyisthatitattemptstosaywhatcannotbesaid.Butthisisnotwhatmysticismdoes:itsattentionisdirectedtothattheworldis(6.44),thatthereisanythingatall,nottohowtheworldis(whichiswhatcanbesaid).Itdoesnotattempttosayanything:itisaview(‘Anschauung’,6.45)oftheworld,awayoffeelingtheworld(‘Gefuhl’,6.45).Thesequenceofthoughtfrom6.5mightbeputlikethis.Philosophyattemptstoraiseques-tionswhicharenotrealquestions(6.5).Scepticism(akindofpanicattheabsenceofananswer)attemptstoraiseaques-tionwhichcannotberaised(6.51).Philosophyattemptstoanswerthequestionswhichremainoncescienceissettled;buttherearenosuchquestions,andhencethereisnoplaceforphilosophy(6.52).Butthisdoesnotmeanthat,asitwere,thereisnothingthere(‘Thereisindeedtheinexpres-sible’,6.522;myitalics),butwhateveritiscannotbesaid:‘Thisshowsitself’(6.522).Seeninthislight,mysticismlooksasifitistheattitudethatshouldbeadoptedinplaceofphilosophy,oncewehaveseenthatphilosophy,withitsambitiontosaythingsthatcannotbesaid,cannotbedone.127ETHEPARADOXOFTHETRACTATUSOneofthecentraldifﬁcultiesinunderstandingtheTractatusisraisedbythisremark:Mypropositionsareelucidatoryinthisway:hewhounderstandsmefinallyrecognizesthemassenseless[unsinnig:nonsense],whenhehasclimbedoutthroughthem,onthem,overthem.(6.54)Weneedﬁrsttobeclearaboutthenatureoftheparadoxwhichthisinvolves.Itseemsthatif(thebulk,atleast,of)theTractatusistrue,thenitisnonsense.Butifitisnon-sense,itcannotbetrue.Soif(thebulk,atleast,of)the\nMETAPHYSICS,ETHICS,LIMITSOFPHILOSOPHY339Tractatusistrue,itisnottrue.Conversely,itseemsthat(thebulk,atleast,of)theTractatusisonlynonsenseinthewayitclaims(orseemstoclaim)thatitis,ifitistrue:itisonlytheparticularphilosophyoflanguageoftheTractatuswhichleadsustothinkthatWittgensteinmusthave‘givennomeaningtocertainsignsinhispropositions’(6.53).Thatistosay,ifitisnottrueinthewayitseemstoclaimthatitisnottrue,thenitistrue.Thisisaseriousproblem,butonitsownitwouldnotobviouslybeaproblemofinterpretation.Itisworthcom-paringtheTractatuswithHume’sﬁrstEnquiryorCarnap’s‘EliminationofMetaphysics’onthispoint.HumeandCarnapbothpresentpositionswhichareparadoxicalinwayswhicharequitesimilartothatinwhichtheTractatusisparadoxical,buttheirpresentationshaveacertaininnocenceaboutthem:theyseemnottobeawareoftheparadox.ButthereisnosuchinnocenceabouttheTractatus:6.54showsveryclearlythatWittgensteinknewthat(thebulk,atleast,of)theTractatuswasself-refuting.Andthatisourproblem:ifheknewthat,whatdidhethinkhewasuptoinwritingthework?Itishardtoseehowhecanhavethoughthewasengagedinanythingotherthanasillygame,unlesshethoughthehadsomewayofavoidingtheparadoxwhichIhavejustdescribed.Whatcouldthatwayhavebeen?Tworesponsestothisquestionarewidespreadinthelit-erature.13Theﬁrst,whichIshallcalltheIneffable-TruthsView,isthemoretraditional.14Accordingtothisview,althoughWittgensteinrecognizedthatthestatementofanythingphilosophicalwasimpossible,heneverthelessthoughtthattherewerephilosophicaltruths,andthatthesetruthscouldsomehowbecommunicatedwithoutbeingstated.Thesetruthswouldbeunstatableorineffable,becauseanyattempttostatethemwouldbenonsense.TheIneffable-TruthsView,assuch,needhavenoparticularviewaboutthemechanismbywhichtheseineffabletruthsaresomehowcommunicated,althoughtwoparticularideasonthisareoftenassociatedwiththeIneffable-TruthsViewbyits\n340METAPHYSICS,ETHICS,LIMITSOFPHILOSOPHYopponents.OneisthatWittgensteinusesthecontrastbetweensayingandshowinginasimplewaytoindicatehowhethinksthattheineffablecanbeappreciated:ordinaryempiricaltruths,onthisview,aresaid,whereastheineffabletruthsofphilosophycanonlybeshown.Theotherviewofthemechanismbywhichineffabletruthsmightbecommu-nicatedwhichisoftenattributedtotheIneffable-TruthsViewisthis:ineffabletruthsarecommunicatedbynon-sensicalcombinationsofwords;thesenonsensicalcombina-tionsrepresentimpossiblecombinationsofthings;weseethetruthoftheineffabletruthswhenweseethattherepresentedcombinationsareindeedimpossible.15WeshouldbeclearthatneitherofthesesuggestionsisessentialtotheIneffable-TruthsView.ItiscertainlyclearthatthecontrastbetweensayingandshowingwasimportanttoWittgenstein.Indeed,hesuggeststoRussellthatitisthekeytothewholework:NowI’mafraidyouhaven’treallygotholdofmymaincontention,towhichthewholebusinessoflogicalprop[osition]sisonlyacorollary.Themainpointisthetheoryofwhatcanbeexpressedbyprop[osition]s–i.e.bylanguage–(and,whichcomestothesame,whatcanbethought)andwhatcannotbeexpressedbyprop[osition]s,butonlyshown:which,Ibelieve,isthecardinalproblemofphilosophy.(CL:124)Butthisdoesnotmeanthatwhatcanonlybeshownisakindoftruth.AndintheTractatus,Wittgensteinseemsgenerallytorestricthisuseofthenotionofshowingtothings(sotospeak)whicharenotordinarilythoughtofastruthsatall:forexample,thelogicalrelationsbetweensen-tences,andtheformoftheworld.Thereisjustoneunam-biguouscasewherewhatissaidtobeshownisalsotakentobeatruth—thefamousclaimaboutsolipsism:Infactwhatsolipsismmeans,isquitecorrect,onlyitcannotbesaid,butshowsitself.(5.62)\nMETAPHYSICS,ETHICS,LIMITSOFPHILOSOPHY341Andthisformspartofanargumentwhich,itseemstome,iseccentricinthecontextoftheTractatusinanumberofways(forexample,ininvolvingaparticularkindofepistemicconsideration,ifthesuggestionofsection6Eofthepreviouschapterwasright).NodoubtthosewhoholdtheIneffable-TruthsViewwillthinkthatshowingplayssomekindofroleinthecommunicationoftheineffabletruthswhichtheytakeWittgensteintobelievein,buttheyneednotthinkthatitissimplythattheseineffabletruthsareshown.Again,thereisnoreasonwhytheIneffable-TruthsViewneedattributetoWittgensteinaviewofnonsensewhichheclearlydenied.ItcanacceptthatforWittgensteinthereisnosuchthingasnonsensewhichisnonsensethroughbeinganillegitimatecombinationofmeaningfulwords;thatforhimtheonlykindofnonsenseisnonsensewhosenonsensicalityisduetooneormoresignsnotbeinggivenmeaning.(5.4733).TheIneffable-TruthsViewneednotthinkthatthesupposedineffabletruthsarecommunicatedbymeansofnonsensicalcombinationsofmeaningfulwordswhichareusedtorepresentimpossiblecombinationsofobjects.TheIneffable-TruthsViewcanperfectlyeasilyholdthattheapparentsentencesoftheTractatusarethemselvesnonsense—plainnonsense—andforthereasonwhichtheTractatusitselfseemstorequirethemtobein6.53.Forallthat,theIneffable-TruthsViewisproblematic,becauseitseemsthattheveryideaofineffabletruthsrunscountertothepointofmuchofwhatWittgensteinwantstosayaboutphilosophy.ThosewhothinkWittgensteinbelievesinineffabletruthswillbeinclinedtocomparewhatWittgensteindoesintheTractatuswithFrege’streatmentofhisdifﬁcultywiththecon-cepthorse,whichwelookedatinChapter2.16Thedifﬁcultywasthatthefollowingsentencecannotbetrue,iftakenliterally:(F)Theconcepthorseisnotanobject.Forifthephrase‘theconcepthorse’ismeaningfulatall,itfunctionsasasingularterm,andhenceasanexpressionwhichreferstoanobject,notaconcept,sinceconcepts,in\n342METAPHYSICS,ETHICS,LIMITSOFPHILOSOPHYFrege’ssense,areessentiallypredicative.Fregesaysofsuchcases:Byakindofnecessityoflanguage,myexpressions,takenliterally,sometimesmissmythought;Imentionanobject,whenwhatIintendisaconcept.IfullyrealizethatinsuchcasesIwasrelyingonareaderwhowouldbereadytomeetmehalf-way—whodoesnotbegrudgeapinchofsalt.(Frege1892b:204)Thewholecharacterofthisremark—ratherweaklyplead-ingforareader’sindulgence—strikesmeaswhollyunlikeanythinginWittgenstein.Andthatdifferenceincharactercorrespondstoadifferenceinview,Ithink:whereFregeseemstotrytositonthefence,Wittgensteinisquiteclearthatphilosophysimplycannotbestated.Appealingtoineffabletruthsisafudge,andWittgensteinisnotinclinedtofudge.Moreimportantly,Wittgenstein’streatmentofphilosophyrequireshimpreciselytorejecttheideaofineffabletruths.Thekeytexthereisaremarkwelookedatintheprevioussection:17Fordoubtcanonlyexistwherethereisaquestion;aquestiononlywherethereisananswer,andthisonlywheresomethingcanbesaid.(6.51)Anineffabletruthwouldbeananswerwhichcannotbesaid;theexistenceofsuchananswerwouldmeanthat,afterall,therewasaquestiontowhichitwastheanswer.Andiftherewereaquestiontowhichanineffabletruthwastheanswer,thenWittgensteinwouldnotbeabletosaythis:Thesolutionoftheproblemoflifeisseeninthevanishingofthisproblem.(6.521)Giventhisclearrejectionoftheideaofineffabletruths,wecanhardlysaveWittgensteinfromparadoxbyadoptingtheIneffable-TruthsView.\nMETAPHYSICS,ETHICS,LIMITSOFPHILOSOPHY343AquitedifferentwayofavoidingtheparadoxisofferedtoWittgensteinbyamorerecenttraditionofscholarship,sometimesdescribedaspresentinga‘newWittgenstein’,andsometimesasofferinga‘resolute’readingofthetext.18ThosewhoofferthiskindofinterpretationareoftenconcernedtomakecertainconnectionswithWittgenstein’slaterwork,butforourpresentpurposeswecandescribethecoreoftheirtreatmentoftheparadoxasembracingaNot-All-NonsenseView.WhereastheIneffable-TruthsViewhasWittgensteinavoidtheparadoxbygivinghimaresting-placeabovethetext,asitwere,inalandoftruthswhichcannotbestated,theNot-All-NonsenseViewgiveshimaresting-placeinapartofthetextitself.Theideawillbethatsomeofthetext—sometimescalledthe‘frame’—is(heldbyWittgensteintobe)meaningfulandtrue,andthispartcommentsontherest,whichissimplynonsense.Itwillbeclaimedthatallofthesubstantivephilosophyofthework—whatseemstobeametaphysics,atheoryoflanguage,atreatmentofsolipsismandtherest—allthisisjustnonsense.Theonlypartswhicharemeaningfulwillbethosewhichsayjustthat(together,perhaps,withafewscatteredremarkswhichmightnotbeoffensive).Therearetwobasicproblemswiththisview.Theﬁrstisthattheclaimthatallphilosophyisnonsense,ormustbenonsense,isitselfaphilosophical—indeed,ametaphysical—claim.Itisaclaimwhichisgeneral(allphilosophy)andmodal(mustbenonsense);itisaclaimabouthowtheworldmustbe.Thisisnotjustaremarkaboutanyparticularscholarwhomightbeinclinedtodismissphilosophy:itrelatesto6.53itself,asweobservedintheprevioussection.6.53tellsuswhatwould—thatis,inevitably—betheonlycorrectmethodinphilosophy.Itsayswhatweshouldalwaysdo,whensomeonewantstosaysomethingphilosophical.Thismeansthatthepartofthetextwhichissupposedtobepartofthe‘frame’—thepartwhichismeaningful,andmeaningfullytellsusthattherestisnonsense—isitselfasmuchnonsenseastherestofthetext.Thetextisall\n344METAPHYSICS,ETHICS,LIMITSOFPHILOSOPHYnonsense,ifanyofitis,sotheNot-All-NonsenseViewmustbewrong.ThesecondproblemfortheNot-All-NonsenseViewisthattheclaimthatmuchofthetextisnonsensebecomesquiteunmotivated,ifwedetachitfromthesubstantivephi-losophywhichthetextappearstocontain.Itiseitherdisin-genuousornaïvetoclaimthatsentenceswhichseemperfectlymeaningfulcanbeshowntobenonsenseinanywayotherthanonthebasisofsomesubstantialmetaphysi-calview—someviewofhowthingsmustbe.Wehavejustseenthat.Itthenseemsodd,tosaytheleast,tosupposethatthesubstantialmetaphysicalviewwhichdoestheworkheremightbeanyviewotherthanthatwhichappearsinthetextoftheTractatus.And,infact,aswehaveseen,thedetailoftheclaimthatattemptingtosaysomethingphilo-sophicalleadsusintononsenseseemstorequiretheveryparticulartheoryoflanguagewhichweﬁndintheTractatus.Itisonlyifweacceptthecommon-formassumptionwhichliesattheheartoftheTractatus’sconceptionoflanguagethatwehaveanyreasontosupposethattryingtosaysomethingphilosophicalwillgoastrayfortheveryparticularreasonthatthepersonmakingtheattemptwillhave‘givennomeaningtocertainsignsinhispropositions’.SoitseemsthattheNot-All-NonsenseViewrequiresthatpartofthetextwhichitclaimstobesimplynonsensetohavesenseafterall.TheseproblemsalsoinfectanyattempttoreadearlierpassagesintheTractatuswhichseemtostandbackandcommentgenerallyonthenatureofphilosophy.Themoststrikingoftheseis4.112,whichwelookedatbrieﬂyintheprevioussection.Again,theclaimsmadeherearegeneral—itisnotjustakindofphilosophywhichisunderconsidera-tion—andmodal(forexample:‘Aphilosophicalworkcon-sistsessentiallyofelucidations’).AndtheirmotivationclearlycomesfromthegeneraltheoryoftheTractatusitself(asthefollowingsequenceofremarks,4.113–4.116,clearlyshows).4.112cannotbekeptclearofbeingnonsenseanymorethantheﬁnalremarksofthewholebookcan.\nMETAPHYSICS,ETHICS,LIMITSOFPHILOSOPHY345IfneithertheIneffable-TruthsViewnortheNot-All-NonsenseViewcanprovideasatisfactoryaccountofhowWittgensteinmighthavethoughtheavoidedtheparadoxoftheTractatus,isthereanythingelsewecansuggest?Thereisanotheroption,whichappearswhenwenoticeanassumptionwhichiscommontobothoftheviewswehavejustconsidered.BothoftheseviewstrytoﬁndawayinwhichWittgensteincanavoidparadoxwhilestillcommu-nicatingsometruthaboutphilosophy.Thatistosay,bothviewssharethisassumption:(T)ThepurposeoftheTractatusistocommunicatetruths.With(T)inplace,itisveryhardtoseeanywayofallowingWittgensteintoavoidtheparadoxoftheTractatusotherthanthosesuggestedbytheIneffable-TruthsViewandtheNot-All-NonsenseView.Butmighttherebeanotheroptionifwereject(T)?Ithinktheremight.19Iwillcallaviewwhichrejects(T)aNo-Truths-At-AllView.ItisnaturaltoattributetoWittgensteinthefollowingthought:(P)Therightphilosophicaltheoryentailsthatanyattempttosaysomethingphilosophicalresultsinnonsense.(P)isnaturallyattributedtoWittgensteinonthebasisof6.53:thusfartheattributionseemsunproblematic.(P)isnotonlynaturallyattributabletoWittgenstein:itseemscentraltotheTractatus.Soitlooksasifwecansaythefollowing:(TP)IfthepurposeoftheTractatusistocommunicateanytruths,itsbusinessistocommunicatethetruthof(P)inparticular.(P),ofcourse,isparadoxical:ifitistrue,then,asanattempttosaysomethingphilosophicalitself,itmustbenonsense,whichmeansthatitcannotbetrue.If(P)isparadoxical,and(TP)istrue,thenitseemsthatifthepurposeoftheTractatusistocommunicatetruths,as(T)claims,that\n346METAPHYSICS,ETHICS,LIMITSOFPHILOSOPHYpurposeisboundtobefrustrated:thereisnorealtruthheretobecommunicated,becausethekeyapparenttruthsunderminethemselves.Nowitisnaturaltothink,onthebasisof6.54,thatWittgensteinwasawareofthat;thatistosay,thatheacceptedthis:(PP)(P)isparadoxical.Andbeingawareofthat,andof(TP),hemusthavebeenawarethatifthepurposeoftheTractatusweretocommunicatetruths(as(T)claims),thatpurposewouldbeboundtobefrustrated.SoitisnaturaltothinkthatincarryingonwiththepublicationoftheTractatus,despiterealizingallthis,hecannothavebeenmeaningtocommunicateanytruthsinthework:thatis,itisnaturaltothinkthat(T)mustbefalse.Ifwearetomakethisreallycredible,therearetwothingsweneedtomakesenseof.First,if(T)isfalse,andtheTractatuswaspublishedforsomepurpose,thereneedstobesomepurposewhichitisplausibletoattributetoWittgenstein,andwhichdoesnotdependonanytruthsbeingcommunicatedinthework.And,second,ifhegoesaheadwiththeTractatusforthisotherpurpose,asaresultofaccepting,insomesense,both(P)and(PP),thereneedstobesomesenseinwhichhecanbesaidtoacceptboth(P)and(PP),evenif—ashemust,inthesamesense,accept—thereisnorealtruthheretobeaccepted.And,ofcourse,ifthereissomesenseinwhich(P)isaccepted,theremustalsobesomesenseinwhichitisacceptedthatacertainphilosophicaltheoryisright,andconsequentlysomewayinwhichitcanbecountedright(bysomeonewho,inthatsense,acceptsit),eventhough—accordingtotheverytheorywhichishere,asitwere,accepted—thereisnorealtruthhereatall.Letusaddressthissecondissueﬁrst:given(P),howcanwemakesenseoftherebeingacertainphilosophicaltheorywhichis,insomesense,right—andhowcanwemakesenseofsomeone,asitwere,acceptingit,eventhoughheknows(asitwere)thatitcannotreallybetrue?Onthislatterpoint,ﬁrst,itisimportanttobeclearthat,ifthe\nMETAPHYSICS,ETHICS,LIMITSOFPHILOSOPHY347generalaccountIhavebeenofferingsofarisanythinglikeright,Wittgensteinisnotunambiguouslycommittedtotheviewthatthe(apparent)sentencesoftheTractatusarenonsense.Thisisbecausehisreasonforthinkingthattheyarenonsenseisthatsomeofthem,atleast,aretrue.Sohedoesnotthinktheyarenonsenseanymorethanhethinkstheyaretrue—although,ofcourse,itisalsothecasethathedoesnotthinktheyaretrueanymorethanhethinkstheyarenonsense.Thepositionseemsbestdescribedbysayingthat,forWittgenstein,the(apparent)sentencesoftheTractatusareinanunstableposition,whichwecancharacterizeasthatofbeingbothnonsenseandtrue,orelseassuccessively(andendlessly)non-senseandtrue.Thisdoesnotstopthembeingplainnon-sense,insofarastheyarenonsense.Nordoesitmaketheirtruth—insofarastheyaretrue—ineffable.Rather,theyareboth(orsuccessively)plainnonsenseandstatablytrue.Itfollowsfromthisthatwhatever‘accepting’the(appar-ent)sentencesoftheTractatusamountsto,itcannotbeunambiguouslyeitherthekindofacceptinginwhichoneacceptssomethingoneunderstandsoramerepsychologicalappearanceofacceptance,whichisthestateofsomeonewhoseemstoacceptsomethingwhichis,infact,nonsense.‘Accepting’the(apparent)sentencesoftheTractatushastobeanambivalentkindofstate,whichwecannotresolveintoanythingmorefamiliar.Andthesamewillgoforthe‘acceptance’of(P),orof(PP),andalltherest.Whatweneednowtodo,then,isexplainthesenseinwhichWittgensteinmightbethoughttoholdthattheTractatuswas,somehow,right,eventhoughitis(also)nonsense.Theissuecanbegivenasharpfocusbyaskingthisquestion:whyisthefactthatiftheTractatusistrue,itisnonsense,andsonottrue,notareductiooftheTractatus?WhydoesthisnotjustshowthattheTractatusisfalse?Forthefollowingreason,onWittgenstein’sview,Ithink.IftheTractatuswerefalse,thentherewouldbesomeotherphilosophicaltheory—somethingwhichentailedthenegationofsomecentralclaimoftheTractatus—whichwouldbetrue.ButitseemsclearthatWittgensteinthinksthatnoothertheorycouldbetrue.\n348METAPHYSICS,ETHICS,LIMITSOFPHILOSOPHYThisisnotyetenough,however.Sofar,weseemsimplytohaveastand-offbetweentheTractatusandeachsupposedrival.Thiswill,nodoubt,endupbeingparadoxicalinitself:ifeveryphilosophicaltheoryisfalse,thatwillapplyequallytothephilosophicalviewthateach(andevery)philosophicaltheoryisfalse.ButwestillhavenoreasontoprefertheTractatustoanyofthesupposedrivals.Ifallofthesethe-oriesareeitherfalse,ormeaningless,howcananyofthembeanybetterorworsethananyother?IsuggestthatthereisasimplereasonwhyWittgensteinpreferredtheTractatustoanypossiblerival.ThesuggestionisthatWittgensteinthoughtthateveryrivalwasalreadyobviouslywrong,evenbeforeitsapplicationtoitselfwasconsidered.ThedistinctivethingabouttheTractatus,then—onWittgenstein’sview—isthatthefollowingistrueofit,anditalone:itisonlywhenitisappliedtoitselfthatitbecomesproblematic.IfWittgensteinthoughtthis,wecanunderstandwhyhemighthavemadethefamousclaimofthePreface:Ontheotherhandthetruthofthethoughtscommunicatedhereseemstomeunassailableanddefinitive.(TLP,p.29)Itisunassailableanddeﬁnitiveuntilitisappliedtoitself,somethingwhich,onWittgenstein’sview,canbesaidofnoothertheory.ThenexttaskistoexplainwhatpurposeWittgensteinmighthavehadinwritingandpublishingtheTractatus—apurposewhoseachievementdoesnotdependonanytruthsbeingcommunicatedinit.Inawell-knownlettertothepublisher,LudwigvonFicker,Wittgensteinwrote:[T]hebook’spointisethical.Ioncemeanttoincludeintheprefaceasentencewhichisnotinfacttherenow,butwhichIwillwriteoutforyouhere,becauseitwillbeakeyforyou.WhatImeanttowritethenwasthis:myworkconsistsoftwoparts:theonepresentedhereplusallIhavenotwritten.Anditispreciselythissecondpartthatistheimportantone.Fortheethicalgetsitslimitdrawnfromtheinside,as\nMETAPHYSICS,ETHICS,LIMITSOFPHILOSOPHY349itwere,bymybook;andIamconvincedthatthisistheONLYrigor-ouswayofdrawingthatlimit.Inshort,Ibelievethatwheremanyotherstodayarejustgassing,Ihavemanagedinmybooktoputeverythingfirmlyintoplacebybeingsilentaboutit.(WSP:94–95)Ifthepointofthebookisethical,ourconsiderationoftheethicsoftheTractatus,insection7Cabove,allowsustounderstandsomethingofwhatWittgensteinmighthavehadinmind.Itseemsclearthathethinksthatwhatethicsrequiresistheadoptionofamysticalorartisticoutlookontheworld,anoutlookwhichseestheworld‘togetherwiththewholelogicalspace’(NB:83).ThissuggeststhatthepenultimateremarkofthebookexpresseswhatWittgensteinhopesfor:Hemustsurmountthesepropositions:thenhewillseetheworldrightly.(6.54)‘Seeingtheworldrightly’would,then,beviewingtheworldasthemysticviewsit,‘asalimitedwhole’(6.45).ButifWittgensteinisnotaimingtocommunicatetruthsintheTractatus—becausetherearenonetobecommu-nicated—thereisanimportantrestrictiononthewayinwhichthepurposeofgettingthereadertoadoptthemysticalattitudecanbeachieved.ItcannotbeachievedbythereaderﬁrstrecognizingthetruthoftheTractatus,andthendecid-ingtoadoptamysticaloutlookforthatreason.Forthiswayofbecomingamysticdependsontherebeingtruthstobecommunicated.And,ofcourse,WittgensteindoesnotdescribethewayinwhichtheTractatusissupposedtoworkasbeinglikethis.Hereisthewholeof6.54:6.54Mypropositionsareelucidatoryinthisway:hewhounderstandsmefinallyrecognizesthemassenseless,whenhehasclimbedoutthroughthem,onthem,overthem.(Hemustsotospeakthrowawaytheladder,afterhehasclimbeduponit.)Hemustsurmountthesepropositions;thenheseestheworldrightly.\n350METAPHYSICS,ETHICS,LIMITSOFPHILOSOPHYWhatprocessdoesWittgensteinhaveinmindhere?IsuggestitissomethingwhichcanbemostsimplyexplainedbyrecallingagainFrege’ssituationwiththecon-cepthorse.Icharacterizedtheproblemasarisingoverthissentence:(F)Theconcepthorseisnotanobject.Wecan(tryto)putthepointwhich(F)triestocapturelikethis.Fregeanconcepts,asthereferentsofpredicates,areessen-tiallypredicative,whereasFregeanobjects,asthereferentsofsingularterms,areessentiallynon-predicative.Wesupposethatthephrase‘theconcepthorse’describesthepredicativeconceptwhichisthereferentofthepredicate‘xisahorse’.What(F)triestosayisthatthispredicativeconceptisnotanythingnon-predicative.Thatoughttobesimplyandobviouslytrue.Unfortunately,aswehaveseen,thephrase‘theconcepthorse’functionsasasingularterm(forFrege,atleast).Butthatmeansthatifitmeansanythingatall,itsreferentmustbeanobject,ratherthananythingessentiallypredicative.Sowecannotget(F)tosaywhatwewantittosay.Nowsupposethatweacceptthispoint:(F)iseithermeaninglessorfalse.Butwestillhaveanideaofwhatwearetryingtoexpressin(F).Wehavenotlostoursenseofthecontrastbetweenthepredicativeandthenon-predicative.Whathappensisthattheefforttomakesenseof(F)leavesuswithoursenseofthatcontrastintact—indeed,perhaps,reinforced—eventhoughitisnotsomethingwhichcouldbestated,oraboutwhichtherecould,inprinciple,beanytruths.Itis,asitwere,asiftheattempttoexpressthedif-ferencebetweenthedifferentkindsofreferentsofwordshasbeenwipedaway,andweareleftsimplywiththereferentsthemselves,simplybeingdifferent.IsuggestthatitissomesuchprocessasthiswhichWittgensteinhasinmindinhisdescriptionofclimbing‘outthrough[thesentencesoftheTractatus],onthem,overthem’.IfthisishowWittgensteinhopestheTractatuswillwork,thenwecanunderstandhowhemighthavethoughthecould\nMETAPHYSICS,ETHICS,LIMITSOFPHILOSOPHY351achievethepurposeofgettinghisreaderstoadoptamysticaloutlookwithoutacceptingtheTractatusastrue.TheideawillbethatworkingthroughtheTractatuswillitselfgiveusasenseoftheshapeofthings—oftheformofreality—andthatthiswillremainoncetheattempttoexpressitinsentenceshasbeenwipedout.InthiswayitmightbehopedthattheTractatusworksdirectlytogiveusthatsenseoftheformofreality,withoutrequiringusactuallytobelievethatitistrue.Itseemstomethatthisprovidesuswithagenuinealter-nativetotheIneffable-TruthsViewandtheNot-All-NonsenseView,anditcertainlyseemstochimewithsomeofthespiritofthetext.Inparticular,itallowsustogiveduepoeticweighttotheclosingsentenceofthebook:7Whereofonecannotspeak,thereofonemustbesilent.20Theaimhereisclearlynottoconveysometruth(astheIneffable-TruthsViewholds);norcanitbesimplytodismissphilosophy(astheNot-All-NonsenseViewthinks).Thecadenceofthelineanditspositioninthetextbothshowittohaveanotherpurposeentirely:tocarryoneforward(inasense)beyondthekindsofconcernswithwhichthebookhasbeenoccupied.Therearetwothings,however,whichmightmakeonepausetoembracetheNo-Truths-At-AllViewasaninter-pretation.TheﬁrstisthePreface—andinparticulararemarkwehavelookedatalready:Ontheotherhandthetruthofthethoughtscommunicatedhereseemstomeunassailableanddefinitive.(TLP,p.29)WehaveseenhowWittgensteinmightprefertheTractatustoanyotherphilosophy,butcanwereallymakesenseofhimwritingthat,ifheheld—asisnowbeingsuggested—thatnotruthsatallwerecommunicatedintheTractatus?Infact,thePrefaceisproblematicforanyinterpretation.Thepreviousparagraphbeginsasfollows:\n352METAPHYSICS,ETHICS,LIMITSOFPHILOSOPHYIfthisworkhasavalueitconsistsintwothings.Firstthatinitthoughtsareexpressed…(TLP,p.29)AndtheIneffable-TruthsView,liketheviewIamnowsuggesting,holdsthat,accordingtoWittgenstein,nothingatallisreallyexpressedintheTractatus.NorcantheNot-All-NonsenseViewregardthePrefaceaspartofanunparadoxical‘frame’.Considerthisparagraphforexample:Thebookwill,therefore,drawalimittothinking,orrather—nottothinking,buttotheexpressionofthoughts;for,inordertodrawalimittothinkingweshouldhavetobeabletothinkbothsidesofthislimit(weshouldthereforehavetobeabletothinkwhatcannotbethought).(TLP,p.28)Wittgensteinhereusesaphrase‘drawalimittothinking’,whichhethencorrects,asbeingparadoxical.Butthecorrec-tionhasapeculiarstatus:itisnotasifhesimplyerasestheparadoxicalphraseinthetext,leavingusonlywithanunparadoxicalformulation.Rather,heleavestheparadoxicalformulationthere,and,further,elaboratelyexplainsitsparadoxicality.Sothephraseisleft,whenitcannot,itseems,reallysayanything;andtheexplanationofthephrase’sparadoxicalityseemsinevitablytofacethesameparadox—requiringustotrytothinkwhatcannotbethought.Sothewholeparagraphisparadoxicalinitsownterms.WhatthismeansisthatwehavetobeabitlessinnocentinourconsiderationofthePreface,whateverinterpretationwechoose.ThePrefaceisitselfpartofthetext,andnolessparadoxicalthantherestofit.Thefactthatitcontradicts—orseemstocontradict—somethingwhichseemstobesaidinthetextdoesnotsetitapartfrommanyotherpartsofthetext.ThepointofthePrefaceisnottobesomethingoutsidethetextwhichcantellushowtoreadthetext(paceDiamond(1991)),buttobeapartofthetextwhichindicatesthepointofthewhole,aswellasanticipatingsomeoftheproblemswhichwillbeelaboratedmorefullyintherest.\nMETAPHYSICS,ETHICS,LIMITSOFPHILOSOPHY353TheotherdifﬁcultywithacceptingtheNo-Truths-At-AllViewisinmakingsenseofWittgenstein’streatmentofphiloso-phicalproblemsonhisreturntothesubject,inthefaceofques-tioningbyFrankRamsey,andlater.Intheperiodafterhereturnedtophilosophy,andbeforehechangedhisapproachtophilosophyquiteradically,hestillseemstohavetakenphiloso-phicalproblemsseriously,andtohavearguedoverphilosophicalpointswithasmuchearnestnessandconcernforrigourasanyanalyticphilosopher.21Surely,heshouldjusthaveabstainedfromphilosophyaltogether?Howcanwemakesenseofthis?Inpart,wecanrespondbysayingthatthecoreoftheinter-pretationbeingsuggestedhereisthatWittgensteinthinksthatthephilosophyoftheTractatusisbetterthananyother.Hestillneedstothinkthisifheistobeabletoconclude,onthebasisofthephilosophyoftheTractatus,thatanyattempttosaysomethingphilosophicalmustresultinnonsense.Sohemaintainsasimpleinterestingettingthephilosophyright—inthesenseofremovingfromitanyfaultsotherthantheparadoxeswhicharisewhenitisappliedtoitself.Butthishardlyseemstocapturethetoneofthediscussionsofthisinterveningperiod.ItmaybethatthebestthatcanbesaidisthatsomeoftheheatoftheﬁrewithwhichtheTractatuswascomposed,intheimmediatecontextofservingonthefrontoftheFirstWorldWar,hadcooledbythelate1920s.Ontheotherhand,wecanadducesomehistoricalevidencewhichmightbethoughttosupportthesuggestionthatWittgensteinwastryingtogetustoadoptanon-philosophical,mysticaloutlook.RudolfCarnapwaspresentattheearlymeetingsofWittgensteinwiththethennew‘ViennaCircle’,andrecalled:Hispointofviewandhisattitudetowardpeopleandproblems,eventheoreticalproblems,weremuchmoresimilartothoseofacreativeartistthantothoseofascientist;onemightalmostsay,similartothoseofareligiousprophetoraseer.22Andinhisown‘EliminationofMetaphysics’hedescribesmetaphysicsasattempting,inamuddledway,todowhatit\n354METAPHYSICS,ETHICS,LIMITSOFPHILOSOPHYisthebusinessofarttodo.Thepointofmetaphysics,accordingtoCarnap,istoexpress‘thegeneralattitudeofapersontowardslife(‘Lebenseinstellung,Lebensgefühl’)’.Heholdsthat‘metaphysicsisasubstitute,albeitaninadequateone,forart’,whoseconcernproperlyistoexpressthis‘basicattitude’tolife(Carnap1956:78–80).ItisnaturaltoseeCarnaphereofferingusaprojectwhich,onseeingWittgenstein,hetookWittgensteintobeengagedin.Thereis,perhaps,nocompletelysatisfactorytreatmentoftheparadoxoftheTractatus.TheIneffable-TruthsViewandtheNot-All-NonsenseViewseemclearlytobeunacceptable.Thepresentalternative,theNo-Truths-At-AllView,seemstomakesense(afterafashion)ofmoreoftheworkthanthese,butisstillnoteasytoacceptasaninterpretation.23Thisdoesnot,however,diminishthevalueoftheworkasawhole.Whenweceasebeingjustinterpreters,andconsiderwhatcanbelearnedfromtheTractatusforourownphilo-sophy,westillhavetwowaysofrespondingtoit.Wecantreatit,ifwehavethestomachto,inthewaywhichtheNo-Truths-At-AllViewencouragesusto:wecanreadtheworkasadevicetoworkusintoamysticalviewoftheworld.Orwecantreattheparadoxasprovidingareductioofthephi-losophyatitscore.ThislatteroptionistheonewhichIwouldprefer,philosophically,butitisnoeasyoption.ThetheoryoftheTractatusprovidesuswithtwothingswhichmostphilosopherswouldliketohave.First,itprovidesuswithanaccountoftherelationbetweenlanguageandtheworldwhichexplainshowitispossibleforwordstobecor-relatedwithitemsintheworld.Andsecond,itexplainshowtherecanbesomenecessityandpossibilityintheworld,whichwecanknowabout,withouttherebeinganysuchthingasasyntheticaprioritruth.Itisnosimplematterprovidinganotherwayofsecuringthesedesirablethings,withoutlapsingintoparadoxatsomeotherpoint.\nAPPENDIXTHESUBSTANCEARGUMENTWittgenstein’sargumentfortheexistenceofsubstance—thenecessarilyexistentobjectswhicharecommontoeverypossibleworld—iscontainedinthesesections:2.02Theobjectissimple.2.0201Everystatementaboutcomplexescanbeanalysedintoastatementabouttheirconstituentparts,andintothosepro-positionswhichcompletelydescribethecomplexes.2.021Objectsformthesubstanceoftheworld.Thereforetheycannotbecompound.2.0211Iftheworldhadnosubstance,thenwhetherapropositionhadsensewoulddependonwhetheranotherpropositionwastrue.2.0212Itwouldthenbeimpossibletoformapictureoftheworld(trueorfalse).Therealcoreoftheargumentiscontainedinthelasttwosectionshere.InterpretationsdifferasaresultoftheirdifferentviewsofwhatWittgensteinhasinmindwhenhesays‘whetherapropositionhadsensewoulddependonwhetheranotherpropositionwastrue’.Whatotherpropositionishethinkingof?Accordingtoabroadtraditionofinterpretations,theotherpropositionistantamounttothepropositionthatthecomplex,whichastatementisapparentlyabout,exists.Forthecomplextoexistwillbeforitsconstituentpartstobearrangedinacertainway.Forexample(theexampleisWittgenstein’sown,fromthePhilosophicalInvestigationsI:§60),forabroomtoexistisforacertainbrushandacertainbroomsticktobearrangedinacertainway.Fromthispointwecandistinguishbetweentwodistinctinterpretations.\n356APPENDIXTheﬁrstinterpretationtakestheargumenttobeconcernedprimarilytoarguethattheremustbeanendtoanalysis:callthis,then,theend-to-analysisinterpretation.Thepointoftheargumentistakentobetosupport2.02,inthelightof2.0201:itisthesimplicity,inthesenseoffurthernon-analysability,ofobjectswhichiscrucial.Fogelinelaboratestheargumentasfollows:Ifanalysisalwaysgeneratesnamesthatareintheirturnnamesofcomplexes,thenthecriterionofsenselaiddownin2.0201wouldforeverremainunsatisfied.(Fogelin1987:14)Theargumenthereseemstodependonanumberofquitegeneralassumptionsaboutlanguage.Theﬁrstisthis:(N1)Everylanguagemustcontaineithernames,oratleastthepos-sibilityofnames.Thecautiousqualiﬁcationisinsertedheretoallowforthepossibilityofalanguagenoneofwhoseexistingexpressionswerenames,butwhichcontainedquantiﬁersandvariables.Suchalanguagewouldatleastneedittobepossiblefortheretobenameswhichmightreplacethevariablesofquantiﬁcation.(This,Ithink,isthepointof3.23–3.24:seeChapter4,section4E.)Thesigniﬁcanceof(N1)isgivenbyaconceptionofnames:(N2)Ifthereisnoobjecttowhichanamerefers,thensentenceswhichincludethatnamehavenosense.(N2)expressesanaturalconceptionofnames,andonewhichitisplausibletoﬁndbothinWittgensteinandinhisphilo-sophicalpredecessors,FregeandRussell(seeChapters2and4).1Iftherearenosimpleobjects,thentheonlynamesalanguagecouldcontainwillbenamesofcomplexes.Howwillwedealwithasentencecontaininganameofacomplex?2.0201maybethoughttosuggestthefollowingview:\nAPPENDIX357(N3)Asentencecontaininganameofacomplexcanbeanalysedasbeingequivalentinmeaningtosomesentenceinwhichtheonlythingsnamedarethecomponentpartsofthecomplex.(N1)–(N3)exhaustthegeneralassumptionsaboutlanguagewhichtheend-of-analysisviewcannaturallyappealtoinitsinterpretation.Unfortunately,itisdifﬁculttousethemtoconstructacredibleargumentfortheconclusionthattheremustbesimpleobjects.Itmightreasonablybethoughtthat(N1)and(N2)togetherrequiresomethinglikethis:(EA1)Iftherearenoobjectstowhichthe(possible)namesofalan-guagerefer,thennosentenceinthatlanguagehasanysense.Andreﬂectionon(N3)mightsuggestthefollowing:(EA2)Iftherearenosimpleobjects,thentherecanonlybeobjectstowhichthe(possible)namesofalanguagereferifeverysentencecontaininganamecanbegivenaninfiniteanalysis.Buttogetfromthesepremisestosomethinglikethecon-clusionWittgensteinneeds,weclearlyneedthefollowingfurtherpremise:(EA3)Nosentencecanbegivenaninfiniteanalysis.Buttheideathatasentence‘canbegivenaninﬁniteanalysis’isambiguous.Itmightmeaneitherofthesetwothings:(i)Foreachstageofanalysis,thereisafurtherstageofanalysiswhichcan,inprinciple,beprovided;(ii)Itispossibletocompleteaninfiniteseriesofanalyses.Itisonlyoninterpretation(ii)that(EA3)isatallobvious.But(EA2)isonlyplausibleonthelessdemandinginter-pretation(i).\n358APPENDIXThismeansthattheargumentofferedtoWittgensteinbytheend-to-analysisinterpretationlooksfallacious.Andthereareotherreasonsforquestioningitasaninterpretation.First,itisunclearwhetheranyonewhothoughtthattherewerenosimpleobjectsneedaccept(N3):theideaofthiskindofanalysisseemsdesignedpreciselytoensurethattheonlythingsnamedaresimpleobjects.Second,theend-to-analysisinterpretationgivesastrangeover-readingof‘whetherapropositionhadsensewoulddependonwhetheranotherpropositionwastrue’.Ittakesittomean:whetherapropo-sitionhadsensewoulddependonwhetheraninﬁnitenumberofotherpropositionsweretrue.Third,itleavesunexplainedtheintroductionoftheideaofapicturein2.0212:whydidWittgensteinnotjustsaythatthatwouldmakeitimpossibleforanysentencetohavesense?And,fourth,itmisunderstandsthewholedirectionofthepassage.Ittakesthepointofthepassagetobeconcernedwithana-lysis,onthebasisofthefactthatanalysisismentionedin2.0201.Buttheargumentclearlydoesnotrunonthenotionofanalysis,butonthenotionofsubstance:2.021explicitlysaysthatitisbecauseobjectsformthesubstanceoftheworldthattheycannotbecompound.2.0201ismostnatu-rallyunderstoodasexplaininghow2.02canbetrue,despitethefactthatmostoftheexpressionsinourordinarylan-guageswhichlooklikenamesarenotnamesforsimpleobjects.Theend-to-analysisinterpretationbeginsfromtheideathatthe‘otherproposition’,whosetruthisrequiredforanoriginalpropositionPtohavesense,ineffectstatesthatthecomplexwhichPisaboutexists.Butitisnottheonlyinterpretationwhichbeginsfromthatstarting-point.AnotherisofferedbyIanProops(2004):wemightcallittheplenitude-of-truth-valueinterpretation.Onthisinter-pretation,thecoreofWittgenstein’sargumentissomethinglikethis:(PT1)Ifitcanbetruethatanobjectexists,itiscontingentthatitexists;\nAPPENDIX359(PT2)Ifitiscontingentthatanobjectexists,thereisapossibleworldinwhichitdoesnotexist;(PT3)Anysentencewhichcontainsanameofanobjectwillhavenotruth-valueinanypossibleworldinwhichthatobjectdoesnotexist;(PT4)Nosentencecanfailtohaveatruth-valueinanypossibleworld;so(PT5)Nosentencecancontainthenameofanobjectwhichcantrulybesaidtoexist.Ifweaccept(N1),asbefore,thisargumentwillshowthatalanguage’shavingsenseatallrequiressomeobjectstoexistnecessarily.Necessarilyexistentobjectswillhavetobesimple:todescribethemascompoundispreciselytoimaginethepossibilityoftheirnotexisting(invirtueoftheirele-mentsnothavingbeencombined).Sotheargumentshowsthattheremustbesimpleobjects.Liketheend-to-analysisinterpretation,theargumentofferedhererestson(N2):itis(N2)whichissupposedtounderlie(PT3).Thisargumenthasthevirtuethatitmakesthesimplicityofobjectsdependupontheirconstitutingthesubstanceoftheworld,onanaturalinterpretationofWittgenstein’snotionofsubstance(whatremainsconstantacrossallpossiblevariations).Butitisnotwithoutdifﬁcultiesofitsown.Oneisthatthereisnoobviousreasontoaccept(PT3).ConsiderBillythebookcase,whichonlyexistsinworldsinwhichitspartsareassembled.Inonepossibleworld—worldW—Billy’spartsarenotassembled,soBillydoesnotexist.Somesentencescontainingthename‘Billy’seemtohaveatruth-valuequiteunproblematicallyinW:‘Billyexists’,forexample,looksunproblematicallyfalseinW,and‘Billydoesnotexist’unproblematicallytrue.Andothersentencesmaybeassignedtruth-valueseithernaturallyorarbitrarily:‘Billyistwometrestall’,forexample,wemightcountfalseinW(sinceithasnotbeenassembledinW),whereas‘Billyisabookcase’mightbecountedtrueinW(sinceBillyisanon-existentbookcaseinW,ratherthan,forexample,anon-existenthorse-race).\n360APPENDIXTheproblemherelooksasifitderivesfromaconfusionbetweentheworldatwhichtheinterpretationofasentenceisﬁxedandtheworldwithrespecttowhichthetruth-valueofthatsentence,onthatinterpretation,isdecided.2Aswenaturallyunderstandtheissueshere,weareconsideringasentencesuchas‘Billyexists’ontheinterpretationofitwhichisgivenintheactualworld—whereBillyexiststobenamed,andhasbeenassembled—butweareconsideringwhetherthatsentence,onthatinterpretation,istrueinsomeotherworld(suchasW).Onthisunderstanding,‘Billyexists’istrueintheactualworld(whichishowithassense,given(N2)),butfalse,onthatinterpretation,inW.But(PT3)isonlyplausibleontheunnaturalreading,whichtakestheworldatwhichtheinterpretationisﬁxedtobetheworldinwhichtheobjectdoesnotexist.Andonthisreading(PT4)isimplausible:itiseasyforasentencetofailtohaveatruth-valueinaparticularworld,ifitfailstohaveatruth-valueinthatworldbyfailingtohaveaninterpretationinthatworld.So,onceagain,thisinterpretationgivesWittgensteinaweakargument.Andtherearefurtherreasonsforbeingscepticalaboutitsplausibilityasaninterpretation.Oneisthat,althoughitdoesmakethesimplicityofobjectsdependonthethoughtthatobjectsformthesubstanceoftheworld,as2.021says,itseemsnottotakeaccountofWittgenstein’sreasonforthinkingthatsubstanceisimportant.WhatmattersforWittgensteinaboutthenotionofsubstanceiscontainedinthenextremark:2.022Itisclearthathoweverdifferentfromthereal[i.e.,theactual]worldanimaginedworldmaybe,itmusthavesomething—aform—incommonwiththerealworld.Andtheconnectionwithobjectsisestablishedintheremarkafterthat:2.023Thisfixedformconsistsoftheobjects.Thenotionofformdoesnotenterintothereasoningpre-sentedbytheplenitude-of-truth-valueinterpretationatall;\nAPPENDIX361soitishardtoseehowitcanberegardedasdoingjusticetoWittgenstein’sconcerns.Moreover,asinthecaseoftheend-to-analysisinterpretation,thisinterpretationcanﬁndnoclearreasonwhyWittgensteinshouldhaveexpressedhispointin2.0212intermsofthenotionofa‘picture’:hemightjustaswellhavesaidjustthatitwouldthenbeimpossibleforanypropositiontohavesense.AstrikingalternativeapproachhasrecentlybeensuggestedbyJoseZalabardo(Unpublished).I’llcallittheRussellian-forminterpretation.ThisreadingisinspiredbythefollowingremarkfromtheNotebooksaboutRussell’sconceptionofform(ItouchedonthisremarkmyselfinChapter1,section1D,inmyaccountoftheargumentfortheclaimItherecall(FO)):Ithoughtthatthepossibilityofthetruthofthepropositionuawastiedupwiththefact(9x,u).ux.Butitisimpossibletoseewhyuashouldonlybepossibleifthereisanotherpropositionofthesameform.uasurelydoesnotneedanyprecedent.(Forsupposethatthereexistedonlythetwoelementarypropositions‘ua’and‘wa’andthat‘ua’werefalse:Whyshouldthispropositiononlymakesenseif‘wa’istrue?)(NB:17)ThepointhereisparticularlydirectedtoRussell,whothoughtthatthegeneralformofsentencesinvolvingaone-placepredicatewasgivenbythesentence‘(9x,u).ux’(Russell1984:129).3Sentencesinvolvingaone-placepre-dicatehavesensebecausethatsentence,‘(9x,u).ux’,istrue.Wittgensteinseemstohavethoughtthiswasabsurdforthefollowingreason:thesentence‘(9x,u).ux’canonlybetrueinvirtueofsomeparticularsentence,say‘ua’,beingtrue.Soasentencesuchas‘ua’onlyhassensebecausesomesentenceofthatform—either‘ua’itself,oradifferentone,suchas‘wa’—istrue.Aswehaveseen,Wittgensteinthoughtthatthisshowedthatitwaswrongtoregardtheformofasen-tenceasitselfanothersentence:ratherithadtobesome-thingwhichwas‘already…givenbytheformsofitscomponentparts’(NB:23).Andthismeans,ineffect,that\n362APPENDIXtheformoftheworldmustresideinobjects.Onthisinter-pretation,the‘otherproposition’referredtoin2.0211iseithersomeutterlygeneralpropositionlike‘(9x,u).ux’,oranotherpropositionofthesameform(as‘wa’hasthesameformas‘ua’).Zalabardo’sRussellian-forminterpretationﬁtswellwiththenotionofsubstancewhichisactuallyinplayinthepas-sage,anditlinksthatnotionappropriatelytothenotionofform.Butitstillfacesanumberofdifﬁculties.Theﬁrstisthatitdoesnotreallygettothepointoftheworryaboutoneproposition’shavingsensedependingonanotherpro-position’sbeingtrue.Intheﬁrstplace,itisnotobviousthattheonlyalternativetoWittgenstein’sownview(thatformresidesinthecomponentpartsofaproposition,andhence,ultimately,intheobjects)isRussell’s:Russell’swasjustaparticularviewwhichWittgensteindisagreedwith—whyshouldhehavethoughtthatunlesshewereright,Russell’sviewwouldhavetobeaccepted?Second,itisnotobviousthatRussell’sview,asWittgensteinunderstandsit,hastheconsequencethatoneproposition’shavingsensedependsonanotherproposition’sbeingtrue.ThiswouldbereasonableifwestuckwithRussell’saccount,andsupposedthat‘(9x,u).ux’couldbetrue,withoutanyparticularinstanceofit,like‘ua’,beingtrue:thentheinstance’shavingsensewoulddependupontherebeingthatform,andtheformwouldbeamatteroftheutterlygeneralpropositionbeingtrue.ButWittgensteinseemspreciselytohavedisagreedwiththatsuggestion:heseemstohavethoughtthattheutterlygen-eralpropositioncouldonlybetrueifithadatrueinstance.NowsupposethatWittgensteinisrightinthis,andsuppose,asbefore,thatthepropositionwhosesenseweareconsider-ingissomeparticularpropositionlike‘ua’.Doesthispropo-sition’shavingsensedependonsomeotherproposition’sbeingtrue,onWittgenstein’srevisedversionofRussell’stheory?Thatdependsonwhether‘ua’itselfistrue:ifitistrue,thennoothertruepropositionofthesameformisneeded.Furthermore,Wittgenstein’sviewseemstohavebeenthatRussell’sviewwasobviouslyabsurdinitself.Iftheproblem\nAPPENDIX363raisedbysayingthatoneproposition’shavingsensewoulddependonanotherproposition’sbeingtrueistheproblemwhichWittgensteinisconsideringinthepassageinNB:17,theproblemseemstobejustthatoneproposition’shavingsensedependsonanotherproposition’sbeingtrue.ButthatisnothowWittgensteinconsidersitintheTractatuspas-sage.IntheTractatuspassage,heclearlythinksthatoneproposition’ssensedependingonanotherproposition’struthisproblematicforadifferentreason—thereasonthatitwouldmakeitimpossibletoformapictureoftheworld(2.0212).AndthisRussellian-forminterpretationshareswithalltheotherinterpretationsconsideredsofarthedifﬁ-cultythatitcannotaccountforWittgenstein’sdecisiontoexplainthepointof2.0212intermsofthenotionofapic-ture:hecouldjustaseasilyhavemadethepointjustintermsofaproposition’shavingnosense.TheinterpretationofferedinChapter1abovediffersfromalloftheseintakingthe‘otherproposition’of2.0211tobeapropositionwhichstatesthatagivenpropositionhassense.Andtheargumentthatnosuchpropositioncanhaveasenseinadvanceofthepropositionwhosehavingsenseitassertsdependsontheconceptionofpropositionsaspictureswhichisadvancedinthe4s.SoitaccountsforWittgenstein’suseoftheword‘picture’in2.0212asnoneoftheotherinterpreta-tionsdoes.ButitshareswiththeRussellian-forminter-pretationthevirtuesofmakingtheargumentdependonthefactthatobjectsformthesubstanceoftheworld,andofmakingwhatisimportantaboutthesubstanceoftheworldbethatitistheformoftheworld.Nointerpretationofthesedifﬁcultlinescanbeentirelyuncontroversial,butIsuggestthatthisonedoesbetterthantheexistingalternatives.\nNotes1THENATUREOFTHEWORLD1McGuinness(1988:299)aptlydescribesthisas‘asortofcreationmyth’.2E.g.,White(2006:23);butthisisacommonview.3IthinkitisimportanttodistinguishWittgenstein’sconcernssharplyfromthoseofcertaincontemporaryphilosophers,whobelievein‘truthmakers’.(ThemostfamousoftheseisDavidArmstrong:see,e.g.,his(1997).)‘Truthmaker’theor-istsacceptacertainformofthecorrespondencetheoryoftruth.Theircentralclaimissomethinglikethis:(TM)Foreverytruth,thereisanentitywhoseexistencemakesittrue.Thiskindofviewexcitestwokindsofdebate:first,anontologicaldebate,aboutwhatkindsofentitythereare;andsecond,aformaldebate,aboutwhether(TM)canbemaintained,giventherestrictionsonontologyemergingoutofthefirstkindofdebate.Neitherdebate,Ithink,hasanyseriousconnectionwiththeTractatus.Wittgensteindoeshaveconcernsaboutontology,inthemodernsense,butthesearerootedinconcernsaboutthekindsofthingwecanhaveacquaintancewith,orintuitionsof.Andhisconcernsaboutthekindsofthingwecanhaveacquaintancewith,orintuitionsof,arenotrootedingeneralphi-losophicalprejudicesaboutthekindsofthingsthereare(apreferenceformedium-sizeddrygoods,say),butinthestatusofthetruthswhichdependonthem.Heisconcernedinparticulartopreventlogicandarithmeticdependingonanyacquaintancewiththeworld,andisconsequentlyconcernedtoavoidmakinglogicandarithmeticdependonanyobjectsofacquaintance.Hisotherconcernsaboutontologyarereallyconcernsaboutlogicalform,Ithink.Ithinkhewouldnotcareatallaboutwhethertherearesuchentitiesasfacts(say),wereitnotforthedifficultieswhichhistheoryoflanguagepresentsoverrefer-ringtosuchentities.Similarly,Ithinkheisnotsqueamishabouttheexistenceofpossiblefacts—except,ofcourse,thathewillwanttoinsistthattheyarenotallactual.Hewouldhavenoproblemabouttalkingaboutsuchpossibilia,wereit\nNOTES365notforthegeneraldifficultieswhichhistheoryoflanguagepresentsfortalkingaboutpossibility.(ForsomethingoftheflavourofthekindofdebatewhichIthinkWittgensteinisnotconcernedwith,seeQuine(1961).)And,ofcourse,withoutanontologicaldebateofthekindwhichtruthmakertheoristsarecon-cernedwith,thereislittlefortheformaldebatetogetagripon.Formoreonthegeneraldebateabout‘truthmakers’,seeBeebeeandDodd(2005).4IntheAristotleliantradition,themostbasicentitiesaresubstances.Ihavenotusedtheterm‘substance’here,becauseWittgensteinhimselfreservesthattermforsomethingwhichmeetsadifferentoneoftheAristotelianconditionsforbeingabasicentity—whatIcall(Sub)(seesection1Dbelow).5IntheAristoteliantradition,(Ind)isoneofthecharacteristicmarksofsub-stances,asthatnotionisunderstoodinthattradition,andtheviewsofLeibnizandSpinozawhicharementionedherearecouchedintermsofthenotionofsubstance.6AndinthelettertoRussell,Wittgensteincontinues:‘Tatsache[fact]iswhatcorrespondstothelogicalproduct[conjunction]ofelementaryprop[osition]swhenthisproductistrue’(CL,p.125).Infact,thiscannotbequiteright,sinceitleavesoutwhatheelsewhere(TLP2.06)calls‘negative’facts,i.e.,factsthatsuchandsuchisnotthecase.7TheideathatthingshaveessencesisfamouslyquestionedinQuine(1975).8Theclassic(thoughextremelydifficult)discussionisinAristotle’sMetaphysicsZ.9Kant(1781/87:A20/B34);notethat2.0141appearsintheTLPbutnotinPT,althoughthenotionofformasusedinthesubstanceargumentofTLP2.021–2.0212doesappearthere.10Thenotionofmaterialpropertiesbelongswiththegeneralcontrastbetweenmatterandform,whichisAristotelianinorigin,andisexploitedbyKant(1781/87:A20/B34).11Thetermtranslatedas‘circumstance’hereis‘Sachlage’,whichOgdentrans-latesas‘stateofaffairs’at2.014.12Kant(1781/87:A24/B38–39).13Thetermtranslatedas‘stateofaffairs’hereis‘Sachlage’,translatedas‘cir-cumstance’at2.0122.14ThisisoneoftwokeycomponentsofthetraditionalAristoteliannotion,theotherbeingtheconditionidentifiedas(Ind)insection1Babove.Ineffect,whatWittgensteindoesispullthesetwocomponentsapart:(Ind)istakentocharacter-izeatomicfacts,and(Sub)—oravariantofit,(Sub*)—tocharacterizeobjects.15Thetermtranslatedas‘real’hereis‘wirklichen’;Iarguebelow(inconnectionwith2.06and2.063)thatitshouldbetranslatedas‘actual’:thecontrastisbetweenwhatispossibleandwhatisactual.16ArelatedpointismadeatNL,p.94:WhenwesayAjudgesthatetc.,thenwehavetomentionawholepropo-sitionwhichAjudges.Itwillnotdoeithertomentiononlyitsconstituents,oritsconstituentsanditsform,butnotintheproperorder.Thisshowsthatapropositionitselfmustoccurinthestatementthatitisjudged;\n366NOTEShowever,forinstance,“not-p”maybeexplained,thequestionwhatisnegatedmusthaveameaning.17ThishasbeenpointedoutbyJoséZalabardo(Unpublished).18SeeRussell(1984:114).19Infact,theviewistobefoundinWittgensteinhimselfalittlebeforetheworkofRussell’scitedinthelastfootnote:inaletterfromWittgensteintoRussellofJanuary1913(CL,pp.24–25).20ThispointismadeexplicitlyatNB,p.17.Zalabardo(Unpublished)takesittobethepointof2.0211:hisinterpretationofthesubstanceargumentisdiscussedintheAppendix.21PeterSullivanhelpedmetoseethispoint.22Itisimportantnottogetdistractedherebyananachronisticontologicalsqueamishnessover‘negativefacts’(forthegeneralirrelevanceofthiskindofontologicalsqueamishness,seen.3above).AllWittgensteinhasinmindissomethinglikethis.Supposethat‘abc’isabasicsentence:ifithadbeentrue,itwouldhavebeenafactthatabc,andsincethesentenceis(byhypothesis)basic,thatfactwouldhavebeenanatomicfact.Butsupposethesentence‘abc’isactuallyfalse.Thatmeansthat‘~abc’istrue,whichmeansitisafactthat~abc.Thisisanegativefact.23Thisassumptionappearstobemade,forexample,byBlack(1964:7),Pears(1987:9,27–28),andMcGinn(2006:135).24E.g.,byMcGinn(2006),thoughnotPears(1987).25BothPears(1987)andMcGinn(2006)seemclosetothisassumption.2THELEGACYOFFREGEANDRUSSELL1ItisplausibletoassociatetheformerpositionwithRussell,andthelatterwithFregeandWittgenstein(atleast,bythetimeoftheTractatus:previouslyWittgensteinwasclosertoRussell’sview).2ItisadelicatequestionwhetherDavidson’sapproachtolanguage(throughouthis(1984))iscommittedto(Corr).Hedoesnotthinkthateithersentencesor(atleastmany)sub-sententialexpressionsarecorrelatedwithextra-linguisticentitiesinthemannerof(Corr).ButhedoesseemtoacceptthecentralassumptionoftheTractatus’sconceptionoflanguage:seeChapter4,section4B,below.Sowemighthopetoformulatesomelessexplicitlyontologicalver-sionof(Corr)whichwouldcapturehiscommitments.Amoreobviouspersonwhomightbethoughttodisagreewith(Corr)isWittgensteinhimself,inhislaterphilosophy:see,especially,theopeningsectionsofPI.3FormoreonthecontributionofFregeandRusselltothephilosophyoflan-guage,asthatisstudiedtoday,seeMorris(2007).4ItisnotatallclearhowmuchFregeWittgensteinhadactuallyreadbythetimeofwritingtheTractatus:itseemslikelythathisacquaintancewithmuchofFrege’sworkwasindirect—mediatedbyRussell’sreactiontoit.Formoreonthisissue,seeGoldfarb(2002).\nNOTES3675See,mostobviously,Frege(1884:§12);Russell(1903:Ch.52).6ThekeyfactorherewasWittgenstein’sownreadingofSchopenhauer(whowasinspiredbyKant),whichseemstohavebeenindependentofFregeandRussell,andtohavebeenrooted,rather,intheintellectualmilieuoftheViennainwhichWittgensteingrewup.7NotethatthisdoesnotunderminethelegitimacyofinterpretingFregeintermsofanotionofcorrelationwhichischaracterizedby(C):ofcourse,insomesenseitwillmatterforoneaspectofthemeaningoflinguisticexpressionsthattheyarecorrelatedinonewayratherthananotherwiththerelevantentityintheworld—thatiswhereFregean‘sense’comesin.Butthisdoesnotmeanthatthebasictaskofbeingcorrelatedwiththesameextra-linguisticentitydependsonthatparticularmodeofcorrelation.8Inthispassagewehavereplacedthetranslator’s‘meaning’withthemorenatural‘reference’(RussellwroteinGerman,andthewordtranslatedis‘Bedeutung’).9ThemostfamouscriticismsaretobefoundinKripke(1980).Itremainsadis-putedquestionwhethertheproblemofthinnessofmeaningisbesthandledwithinabroadlyRusselliantheory(anexampleofthisapproachisSoames(2002)),orwithinaformofFregeantheory(forwhich,see,e.g.,McDowell(1984)).10Russellhimselfseemstohavebeenmovedbysimilarconsiderations:thepro-positionneedstobetheactualobjectofjudgement(Russell1910:152).11GrahamStevensemphasizesthattherewereotherreasonsforrejectinghisearlypropositional-objecttheory,whichrelatedtotheparadoxesthatseemedtobecreatedbyit(Stevens2005:Ch.2).12‘Ineffect’,becausewemightdoubtwhetherRussellhimselfwasconcernedexplicitlywiththeunityofsentences,consideredassuch.Hewasobviously,throughoutthisperiod,concernedthathistheoryshouldgenerateaunityofacertainkind;andthisunitythathewantedhistheorytogenerateisatleastexpressedintheunityofsentences—inthecontrastbetweenasentenceandalist.Sohistheorydidinevitablyprovideanexplanationoftheunityofsentences(ofthecontrastbetweenasentenceandalist).Buthehimselfcertainlythoughtthattheunityhewasdealingwithwasamerereflectionofadeeperunity,inthenatureofthings,orinjudgement.13IrefertothesecondeditionofWhiteheadandRussell’sPrincipiaMathematica,sincethatisthemosteasilyavailable:itdoesnotdifferinthesecrucialrespectsfromthefirsteditionof1910.14The‘completeness’ofthis‘completemeaning’is,ofcourse,thecounterpart,atthelevelofmeaning,tothecompleteness(orunity)ofasentence,whichdis-tinguishesitfromamerelist.15Thisissometimesreferredtoasthe‘narrowdirectionproblem’:seeStevens(2005:92).16Russellneverthelesstoyedwiththisidea,foratime:hesupposedthatthejud-gingrelationalwayshada‘sense’ordirection(Russell1910:158).17Thisissometimesreferredtoasthe‘widedirectionproblem’:seeStevens(2005:95–96).\n368NOTES18ItisdifficulttobeclearhowconsciousRussellhimselfwasthathewaspro-posingatheorywhichwasincompatiblewiththemultiple-relationtheory.TherearesomeindicationsthathethoughtofhimselfasproposingsomethingnewwhenhewrotetheTheoryofKnowledgemanuscript(Russell1984).Themanu-scriptwaswrittenbetween7Mayand7June1913.On20May,ashetoldOttolineMorrell,Wittgensteinproduceda‘refutationofthetheoryofjudgementwhichIusedtohold’(RusselltoMorrell#782;1984:xix):thisisnaturallytakentobetheargumentwhichappearsatNL96andTLP5.5422,andthe‘theoryofjudgementwhichIusedtohold’isthereforenaturallytakentobethemultiple-relationtheory.ThiscriticismseemsnottohavedisturbedRussell’sprogressunduly,whichmakesitlookasifhenolongerthoughtofhimselfasholdingthemultiple-relationtheory.On25May,hewasapparentlyworkingonthesection(1984:II,iii)wherewhatlookstometobeanewtheoryofjudgementissetout.ThefollowingdayhesawWittgensteinandshowedhima‘crucialpartofwhatIhavebeenwriting’,andreportedthatWittgensteinhadsaiditwas‘allwrong,notrealizingthedifficulties—thathehadtriedmyviewandknewitwouldn’twork’(RusselltoMorrell#787;1984:xix).ItakethiscriticismtobeacriticismofwhatIthinkisreallyanewview,andtobewhatWittgensteinlaterreformu-latedinthetermsquotedlaterinmytext.Thistimethecriticismreallydoesseemtohavehurt,andinfacttohavecrippledRussell’sproject.ButitisnotatalleasytobeclearaboutwhatRussellthoughthewasdoing,sincetherearequitestrongsignsofatheoryverylikethemultiple-relationtheory,eveninpartsoftheTheoryofKnowledgemanuscriptwhichareclosetotheplaceswherewhatlookstomelikeadifferenttheoryisbeingproposed.At(1984:109)Russellclaimsthat‘apropositionis…an“incompletesymbol”’,whichisoneofthecentralclaimsofthemultiple-relationtheory(thecompletionbeingeffectedbyanactofmind);andat(1984:129)hespeaksofan‘understanding-complex’whichlooksatleastsimilartothecomplexcreatedbytheactofjudgementonthemultiple-relationtheory.Andtheuseofthenotionofacquaintanceincon-nectionwith‘pureforms’(1984:99;129),seemstogiveusjustanotherversionofthemultiple-relationtheory(thoughwithformsasextraconstituents,inadditiontothefamiliarconstituentsoftheoldmultiple-relationtheory).Inthelightofthis,itmightbesuggestedthatRussellthoughthewasstickingtosomeversionofthemultiple-relationtheory,eveninthe1913manuscript,andthepartsofthetextwhereheseemstoofferanewtheoryarereallyintendedjusttodealwiththeproblemofordering—theso-called‘narrowdirectionproblem’—eveniftheyseeminevitablytohavewiderconsequences.19Russell’suseoftheword‘proposition’becomesexplicitlylinguisticearlyinthe1913manuscript:see(1984:80,fn.1),althoughthisislatermodified(1984:105–07).20Infact,itwasinordertodealwiththeproblemofordering(theso-called‘narrowdirectionproblem’),thatRussellintroducedthistheory,whichIthinkisreallyanewtheoryofjudgement,inthefirstplace—thoughpossiblywithoutrealizingthatitwasanewtheory.21Russellhimselfseemstohavethoughtthattheproblemonlyaroseinthecaseofsentencesinwhichtheorderofsingulartermsmattered;butitlooksasifhis\nNOTES369newtheoryofjudgementalsohasworktodo,ifitistodealwiththeotherproblemswhichfacethemultiple-relationtheoryofjudgementwithoutfallingbackintotheproblemswhichbesettheoldpropositional-objectsaccount.22Russellhimselfwrites:‘[A]natomicpropositionmay,forthepresent,bedefinedasonewhoseverbalexpressionisofthesameformasthatofanatomiccom-plex’(Russell1984:110).ItisunclearwhatrevisionRussellmighthavesug-gested,afterthe‘present’referredtohere,butsomerevisionisnecessary,sinceitlooksasif,onRussell’snewtheory,noverbalexpressionhasthesameformasthatofanatomiccomplex.23ThispointisurgedbyStevens(2005:102–05).24Weshouldnot,however,assumethattheincompletenessofpredicatesconsistsintheirbeingintelligibleonlyinthecontextofasentence,ratherthaninisola-tion.Fregeheldthatallexpressionsareintelligibleonlyinthecontextofasen-tence,andtendedtoemphasizethisprincipleparticularlyinthecaseofsingularterms(his‘propernames’).25WiththehindsightprovidedbyDavidson(1984a),wemightgivethefollowingaccountofthereferenceofthepredicate‘xisahorse’:(H)Thepredicate‘xisahorse’istrueofanobjectifandonlyifthatobjectisahorse.ItmightbearguedthatFregehimselfofferedthiskindofaccountoftherefer-enceofthehorizontal‘—’inFrege(1893:§5)(IamgratefultoPeterSullivanfordrawingthispassagetomyattention).Butitisworthnotingthatneitherinthatplace,norin(H),istheconceptofreferenceusedinrelationtothepre-dicate,and,indeed,itisunclearthatanaccountlike(H)wouldevensuggestthatpredicateshavereference,orindeed,thatsentencesrefertotruth-values.26Theideathat(Corr)itselfpresupposesrealismisputforwardbyPears(1987).27Fortheissuehere,seeJohnston(2007b)andChapter4,section4C,below.Ithinkitisimportantthatifweadoptthispicture,thestagesaresuccessive—thatis,theestablishmentofagrammarprecedesthecorrelationwithaworld.OtherwisetheTractatuswillnotprovidetheresponsetotheKantianproblemovernecessityintheworldwhichItaketobeoneofitscentralpoints.ForthisresponseseetheIntroduction,above,andChapter5,section5E,below.28ThisistheKantofKant(1781/87).29Itisworthremarkingthatalthoughthisthirdviewisclearlyidealist,itseemsthatitcannotitselfstateitsownidealism.Forinordertostateitsownidealism,ithastoconsiderapossibility—thattheworldistheworldinitselfisasitissupposedtobeonthesecond,Kantian,view—whichitmustregardasunin-telligible.ThiskindofdifficultyhoversinthebackgroundofWittgenstein’streatmentofsolipsismintheTractatus:seeChapter6below.30Frege(1884:x).31Frege(1884:73).32TheissueiswhatstrengthofcontextprincipleFregeneedsforhisclaimthatnumbersareobjects.Thatclaimisdiscussedbrieflyinsection2H,below.For\n370NOTESmoreontheconnectionbetweenthisclaimandthecontextprinciple,seeWright(1983).33Thoughofcoursethiswillingeneralbeaderivedcorrelation,resultingmerelyfromthefunctionreferredtobythepredicatebeingappliedtotheobject(s)namedbythesingularterms(s).34Russell(1984:97–98):notethatthemeaningof‘proposition’seemstoshifthere,fromsentenceinthefirstclause,toobjectivecorrelateofasentenceinthesecond.35Russell(1984:98):itisclearthat‘proposition’heremeans,unambiguously,objectivecorrelateofasentence.36ThisechoestheviewofformtobefoundinaletterfromWittgensteintoRussell(CL,pp.24–25).37Fregealsohadareferentialconceptionofthelogicalconstants:forexample,hetookthenegationsigntorefertoa‘concept’(Frege1893:§6).38SomehavealsothoughtthatWittgensteinisconcernedtoopposeadistinctively‘generalist’conceptionoflogicwhichhefoundinRussell:logicaltruths,onthisconception,aresimply‘maximallygeneral’truthsabouttheworld.Theattribu-tionofsuchaviewtoRusselliscontroversial,however:seeGoldfarb(1989);Sullivan(2000);Proops(2007).39AhelpfulexampleinofferinginformalexpressionsofthePeanoaxioms,aswellasotherrelatedmatters,isprovidedbyGrahamPriest(1998).Peanohimselfcounted1,ratherthan0,asthefirstnaturalnumber.40ForauseofthistermbyFrege,see(1980:141).41Frege’soriginalconstructionislaidoutinhis(1884);itisdevelopedmorerig-orouslyandformallyinFrege(1893).ForagoodintroductiontoFrege’saccountofarithmetic,seePotter(2000:Chs2and4).Foramorethoroughtreatment,seeDummett(1991).42Themostobviousoftheseistheso-calledAxiomofInfinity,whichassertsthatthereareinfinitelymanyindividuals(theobjectsatthelowestlevelofthehier-archyofclasses).ThefinalversionofRussell’stheory(withthe‘ramified’theoryoftypes)alsorequiredtheintroductionofafurtheraxiom,theAxiomofReducibility.TheAxiomofReducibilityisnoteasilystatedwithoutintroducingthetechnicalterminologyofRussell’stheory,butitspointcanbeconveyedinformally:itistorecoversomethingofwhatRussell’sparadoxforcedhimtoremovefromFrege’ssystem;ineffect,whatitdoesisallowhimtoclaimthateverysignificantpredicatedefinesaclass.FormoreonRussell’saccountofarithmetic,including,inparticular,theAxiomofReducibility,seePotter(2000:Ch.5).3.THEGENERALTHEORYOFREPRESENTATION1Though,asInotedinthepreviouschapter,itisnotclearthatitisacceptedbyDavidson(1984),anditseemstoberejectedlater(inPI)byWittgensteinhimself.2Ofcourse,asnotedinrelationtoChapter2,section2F,above,wemightadoptaDavidsoniansolutionandsuggestthatwespecifywhatthepredicate‘xisahorse’,forexample,referstobymeansofsomethinglikethis:\nNOTES371(H)Thepredicate‘xisahorse’istrueofanobjectifandonlyifthatobjectisahorse.AnditisarguablethatFregehimselfpresentsthiskindofaccountofthehor-izontal‘—’at(Frege1893:§5).But,aswasnotedinconnectionwith2F,thiskindofaccountdoesnotitselfusetheconceptofreferenceinrelationtothepredicate,sothatitbecomesunclearthatitreallymakesuseoftheideathatpredicatesrefertoanythingatall.3Ofcourse,inFrege’scase,thecorrelationswillbewhatIcalledderivedcorrela-tions,inChapter2,section2A,above:itisnotasifFregesupposedthatthemeaningofsentencescouldbefixedbyexplicitlyanddirectlycorrelatingwholesentenceswithtruth-values.HereitisimportanttorecallthecharacterizationofthenotionofcorrelationIofferedin(C)ofsection2Aabove.4AswellasotherdifficultiesdiscussedbyStevens(2005:Ch.2).5Seethebriefdiscussionoftheissueofrealismandidealisminsection2F,above.6Ofcourse,itonlystruckhimbecausehewasreadytobestruckbyit.Asiswellknown,oneofthethingswhichpreparedthewayforthisviewwasHertz(1894).StrikinglyrelevantsectionsareHertz(1894:§§418–28),ondynamicalmodels.7Compare:Amaterialsystemissaidtobeadynamicalmodelofasecondsystemwhentheconnectionsofthefirstcanbeexpressedbysuchcoordinatesastosatisfythefollowingconditions:(1)Thatthenumberofcoordinatesofthefirstsystemisequaltothenumberofthesecond;(2)Thatwithasuitablearrangementofthecoordinatesforbothsystemsthesameequationsofconditionexist;(3)Thatbythisarrangementofthecoordinatestheexpressionforthemagnitudeofadisplacementagreesinbothsystems.(Hertz1894:§418)8NotethatStenius(1960:98)usestheterms‘depict’and‘represent’intheoppositeways:unnaturally,asitseemstome.9AndOgdenhimselfuses‘imagine’totranslatethesameconstructionat3.001—unhelpfully,infact(thoughfollowingWittgenstein’sownsuggestion)—see3E,below(andn.25).10Wittgensteinmakeswhatis,ineffect,exactlythispointinconnectionwiththetranslationof3.001.Seethenoteonthediscussionof3.001insection3E,below(n.25).11Compare:‘Therelationofadynamicalmodeltothesystemofwhichitisregardedasthemodel,ispreciselythesameastherelationoftheimageswhichourmindformsofthingstothethingsthemselves’(Hertz1894:§428).12Ihereuse‘formofdepiction’,inplaceofOgden’s‘formofrepresentation’,totranslatetheGerman‘FormderAbbildung’.13Again,Iuse‘formofdepiction’inplaceof‘formofrepresentation’.\n372NOTES14Again,‘formofdepiction’replacesOgden’s‘formofrepresentation’.15Here‘depicting’replacesOgden’s‘representing’totranslate‘abbildende’.16Again,‘depicting’replaces‘representing’.17Compare:‘Asystemisnotcompletelydeterminedbythefactthatitisamodelofagivensystem.Aninfinitenumberofsystems,quitedifferentphysically,canbemodelsofoneandthesamesystem’(Hertz1894:§421).18Thedifferencebetween‘already’and‘thereby’interpretationswillbeconsidered,forthecaseoflanguage,inChapter4,section4C,below.19Here‘depict’replaces‘represent’,and‘depiction’replaces‘representation’.20Notethathere,surprisingly,‘represent’and‘representation’areclosetransla-tionsoftheGerman(‘stellt’and‘Darstellung’).21Despitethegeneralimportanceofdistinguishingbetween‘depict’and‘represent’,Icanseenodifferencebetweenaformofdepictionandaformofrepresentation.22Here‘depiction’replaces‘representation’.23ItissignificantthatWittgenstein’streatmentoftautologiesin4.46–4.4661isconsistentwiththisrevisedprinciple,butinconsistentwiththePrincipleofBipolarity,asoriginallyformulated.24ThisremarkisdealtwithinChapter7,section7C,below;ofcrucialimportancealsoaresections5and6oftheTractatus,whicharediscussedinChapter5,sections5Dand5F,below.25ThepreferenceisWittgenstein’sown,ratherthanOgden’s,thoughWittgensteinchosethistranslationinordertobringoutpreciselythepointImakeinthetext.HereiswhathesaidtoOgdenabout3.001:Idon’tknowhowtotranslatethis.TheGerman‘WirkönnenunseinBildvonihmmachen’isaphrasecommonlyused.Ihaverendereditby‘wecanimagineit’because‘imagine’comesfrom‘image’andthisissome-thinglikeapicture.InGermanitisasortofpunyousee.(LOp.24)(IamverygratefultoPeterSullivanforpointingthisouttome.)Theproblemisthatthenoun‘image’ismoredeeplylostintheverb‘imagine’thanthenoun‘Bild’isinthephrase‘einBildmachen’.ThisisinpartareflectionofaverygeneralfactaboutthedifferencebetweenGermanandEnglishetymology;butitisalsoduetoacontrastbetweenthisparticularGermanidiomandtheparti-cularEnglishwordwhichWittgensteinuseshere—theGermanusesanouninacompoundphrase,whereinEnglishthenounistransformedintoaverbalform.26Atleast,thatisthecasewhere‘p’isanelementarysentence.Nothingyetmakes(5)inadmissible,if‘p’itselfhastheform,e.g.,‘p&~p’.4.SENTENCESASMODELS1Atleast,itlooksasifitdoes.Itmightbethoughtthat4.04involvesacommit-menttothepossibilityofanalysiswhichisnotpresentin(M3):afterall,ituses‘distinguishable’,ratherthanmerely‘distinguished’.Afinaldecisiononthis\nNOTES373pointwouldneedtotakeaccountofWittgenstein’sconceptionoftherelationbetweensentencesofordinarylanguageandelementarysentences(whicharewhatanalysiswouldreach):seesection4Ebelow.Myviewisthatanydifferencebetween‘distinguished’and‘distinguishable’willturnoutnottomatter,onceweareclearwhathappensinanalysis.Ordinarylanguagesentenceswillturnoutonanalysistobeeithersimplepropositional-logiccompoundsofelemen-tarysentences,orelse(inatleasttheoverwhelmingmajorityofcases)quanti-fiedsentences,whoseinstanceswouldbeelementarysentences.Inthefirstcase,Ithink,theelementsarealreadytheretobedistinguished,andnotmerelydistinguishable.Andinthesecondcase,theyarenotevendistinguishable,sincequantifiedsentencesarenotmerelylogicalsumsorlogicalproductsofele-mentarysentences,onWittgenstein’sview(seeChapter5,section5C,below).2ThereferenceseemstobetoHertz(1894:§418),whereonesystemissaidtobeadynamicalmodelofanotheronlyif‘thenumberofcoordinatesofthefirstsystemisequaltothenumberofthesecond’.3Othersmightincludethetendencytothinkofexpressionswhich‘mention’acomplex(3.24:discussedinsection4E,below)asfunctioninglikenames;and,ingeneral,beingdeceivedaboutthecomplexityofeverydaylanguage(seesec-tion4E,below);andthefactthatthesamewordineverydaylanguageisoftendifferentsymbols(3.323;discussedin4C,below).4Ihaveused‘depicted’and‘depiction’hereinplaceofOgden’s‘represented’and‘representation’totranslatetheGerman‘abbilden’and‘Abbilden’.ForthegeneralpointseeChapter3,section3B,above;andthischapter,section4C,below.5NotethathereWittgensteinuses‘darstellen’(‘represent’),wherewemighthaveexpectedhimtouse‘abbilden’(‘depict’).6Ihereuse‘showitforth’inplaceofOgden’s‘exhibitit’,inordertopreserveinEnglishtheparallelbetweentheGermanofthispassageandthatof2.172.‘Represent’,quiteproperly,translates‘darstellen’.7Onceagain,‘represent’translates‘darstellen’.8Wittgenstein’sviewoflanguagehereseemstoanticipatetheconceptionmadepopularbyW.V.Quine(1960:Ch.2)andDonaldDavidson(1984a).QuineandDavidsonmakeradicaltranslationorinterpretationcentraltotheirunderstandingoflanguage.Translationorinterpretationisradicalifitiscarriedoutonthebasisofassumingnomoreaboutthelanguagetobetranslatedorinterpretedthanhastobeassumedforthelanguagetobecountedasalanguageatall.Aradicalinter-preterwillapproachalanguagesheknowsnothingabout,andsimplyonthebasisofwhatshecanobserveaboutspeakersandtheworldfromthatpositionofignorance,shefollowsrationalproceduresinordertoendupinapositiontostate,inherownlanguage,themeaningofanysentenceofthelanguagebeinginterpreted.QuineandDavidsonholdthatitisinradicalinterpretationthatwereallyseelanguageforwhatitis.Theyaretherebycommittedtothisthesis:(RI)Thereisnothingaboutthemeaningofthewordsofanylanguage,whichisdiscoverableatall,whichisnotdiscoverableinprinciplebysomeonewhobeginsfromevidencewhichisavailablewithoutunderstandingthat\n374NOTESlanguage,andproceedsbymeansofakindofrationaltheory-constructionwhichisalsoavailablewithoutunderstandingthatlanguage.ThisisveryclosetothecentralcommitmentofWittgenstein’sclaimthatanylanguagewhichcanrepresenttheworldmusthavethesameformastheworld.(IdonotmeantosuggestthattherearenodifferencesbetweenQuineandDavidsonthemselvesoverradicalinterpretation,ofcourse.Theyseemtodiffer,inparticular,intheirunderstandingofthestartingpoint—intheirconceptionofthekindofobservationoftheworldfromwhichinterpretationbegins:thisispartofthepointofDavidson(1984b),andIthinkDavidsonshowshimselfheretobeclosertoWittgensteinthanQuineis.)9TheseremarksaretakentobeclearindicationsofrealismbyJohnston(2007b),thoughhemaynotbetakingrealismtobedefinedby(R).10ItisattentiontothisthatmakesWittgensteinlookclosertoDavidson(see,especially,his(1984b))thantoQuine.11SeeChapter3,section3B,above.12ForFrege’snotion,seeChapter2,section2C,above;andmoregenerallyMorris(2007:Ch.2).13Wittgenstein’susemaybeclosertoRussell’s:see(Russell1910:158).Russellassociates‘sense’withdirection;somethingwhichWittgensteinadoptsatTLP3.144.14Including,apparently(andsurprisingly)Potter(2000:164).15ThisisalsotheviewofJohnston(2007b).Theopposingviewisheld,e.g.,byPears(1987:88).16Johnston(2007b)doesseemtotakethistorequireaformofrealism;butper-hapstherealismhehasinmindisnothinglikeasstrongas(R).17Thewordstranslated‘wehavetoattendtotheuse’intheNotebooksarethesameasthosetranslated‘wemustconsiderthe…use’intheTractatus.‘Attendto’isbetter,Ithink(theGermanis‘achten’);theinterpretationIwillsuggestinamomentwouldslightlyfavour‘haveto’over‘must’(asabetterwayofexpressingapractical,ratherthanametaphysical,necessity).18ThenotionispresentinthePrototractatus(PTLP:3.2013—theancestorofTLP3.2and3.21).19WhereinFregedoestheviewWittgensteinopposesappear?Perhapshere:However,notonlyadenotation,butalsoasense,appertainstoallnamescorrectlyformedfromoursigns(Frege1893:§32)20Thesetwostrandsofthe‘austere’conceptionofnonsensearedistinguishedinMorrisandDodd(2008);IhavesincediscoveredthatsomethingratherlikethisdistinctionistobefoundinGlock(2004:222)—thoughhetakesquiteadif-ferentviewoftheissues.21Ileaveasideherethequestionwhetheritsufficesfortheclaimthatnumbersareobjects,madeinFrege(1884:§§55–63)—evenifthatwas,arguably,themostimportantreasonwhyFregehimselfembracedtheprinciple.\nNOTES37522Ogdentranslates‘Zusammenhang’with‘connexion’(PearsandMcGuinnesshave‘nexus’),and‘Verkettung’with‘concatenation’(theLatinword‘catena’,ofcourse,meanschain);Ihavevariedthetranslationslightly,tomaketheetymo-logicalpointclearer.23TheexamplesofthepredicatesIamusingherearesimple,butonlyforthesakeofexpositoryconvenience.Idonotmeantodenythat‘Ifxishuman,thenxismortal’isaone-placepredicate,and,indeed,fortheissueswhichconcernushere,itseemstomethatthiscomplexpredicatecanharmlesslyberegardedasaone-placepredicate.For(someof)theissueshere,seeDummett(1981:27–33).Thesepointsariseagaininsection4F,below.24CompareRussell(1984:98).25ThisisthekindofargumentwhichWittgensteinlaterthoughthewasrelyingon:seePII:§66.26McGuinnesshimselfsuggests‘Suchandsuchcombinations(sc.ofobjects)hold’(McGuinness2002a:78),despitesponsoringanalternativeinthecolla-borationwithPears.27InthiscontextitisironicthatFogelinshouldhavebeenatsomepainstoexplaintheworkingofthedemonstrativein‘Thisishowthingsstand’(Fogelin1987:48);thereisnodemonstrativeintheGerman.28NotethatWittgensteinseemsclearlytohavelinkedcomplexityandgenerality,inthediscussionintheNotebooksfromwhichtheseremarksintheTractatusderive(NB,pp.63–64).29Compare:‘Butthisissurelyclear:thepropositionswhicharetheonlyonesthathumanityuseswillhaveasensejustastheyareanddonotwaituponafutureanalysisinordertoacquireasense’(NB,p.62).ThisisonerespectinwhichRussellmisunderstoodtheTractatus:MrWittgensteinisconcernedwiththeconditionsforalogicallyperfectlanguage—notthatanylanguageislogicallyperfect,orthatwebelieveourselvescapable,hereandnow,ofconstructingalogicallyperfectlanguage,butthatthewholefunctionoflanguageistohavemeaning,anditonlyfulfilsthisfunctionasitapproachestotheideallanguagewhichwepostulate.(Russell1922:8)30ThedebategoesrightbacktothebeginningofdiscussionoftheTractatus.Roughlyspeaking(therearesubtledifferencesbetweenviews),Ramsey(1923),Stenius(1960),andMcGuinness(2002b)attributearealistview,whereasAnscombe(1971),Ishiguro(1969),andRicketts(1996)attributeanominalistview.31NotethatthisechoesTLP2.03.32ThisishowDummettdefines‘complex’predicates(Dummett1981:29).33ThispointismadebyAnscombe(1971:101–02).34WhatmightFregehavehadinmind?Theissuesherearequitetechnical,buthereisanindicationofthekindofthinghemighthavebeenconcernedwith—rememberingthathecannotconsistentlyhavethoughtthatsingulartermswereanymoreself-standingthananyotherkindofexpression.Itisclearthathe\n376NOTESthoughtthatthereisafundamentalasymmetrybetweensingulartermsandcertainotherkindsofexpression,atsomeleveldistinctfrombeingthecorrelateofaname,inthesenseof‘name’involvedintheTractatus.Onewayoffleshingoutsuchanasymmetrymightbeasfollows.Thereseemstobeadistinctiontobemadebetweendifferentkindsofoccurrenceinsentencesof‘isugly’(forexample):thereareoccurrencesinsimplesentences,like‘Socratesisugly’,ontheonehand,and,ontheotherhand,thereareoccurrencesincompoundsentenceslike‘IfSocratesisugly,it’snowonderthatheisinterestedinintel-lectualmatters’.Itisnaturaltothinkthatthemeaningoftheword‘ugly’isfixedbyitsoccurrenceinsimplesentences,andoncethatmeaningisestablished,itissimplyre-usedinmorecomplexsentences.Incontrastwiththis,thereseemstobenosimilardistinctionbetweentheoccurrenceofthename‘Socrates’insimpleandincompoundsentences.Thismightbethoughttobethebasisofadeepasymmetrybetweencompleteandincompleteexpressions,whichmightgroundacorrespondingdistinctionbetweenkindsofentityintheworld.Fortheseissues,seeRamsey(1925b)andDummett(1981:27–33).35Itmightseemthattherewasalsoathirdoption:mighttherenotbeasingleasymmetry,whichwasnotexactlyofthekindwhichFregeidentified?Whetherthisisaliveoptiondepends,inpart,onwhatFregewasreallyconcernedwithindistinguishing‘saturated’from‘unsaturated’entities.Forabeginningonthisissue,seeDummett(1981:Ch.8);seealson.34above.36ColinJohnston(forthcoming)hasrecentlyurgedthattheTractatusisneutralonthenatureofthefundamentalobjects,butitisnotclearthathehasinmindexactlytheneutralitywhichissuggestedinthemaintext.37InthelettertoRussellwhichisquotedfromintext(a),Wittgensteinseemstoassimilatequalitiesandrelationstoforms,whileconceivingofformsinverymuchthemannerRusselldidlaterinRussell(1984)—thatis,asentirelygeneralfacts(CLpp.24–25).38ItissignificantthatthischangeinWittgenstein’sviews(reportedtoRussellinJanuary1913)followedameetingwithFregeinDecember1912.39ThispassageisalsoquotedbyRicketts(1996:70–71),whotakesittoindicateaversionofthenominalistinterpretation.40ItisworthrecallingthatWittgensteinadoptedtheviewthattherearetwokindsof‘indefinable’followingconversationswithFrege,asnotedearlier.41Formoreonthiswholeissue,seeChapter6below,onSolipsism.42IamverygratefultoPeterSullivanforhiscommentsonanearlierdraftofthissection.5LOGICANDCOMPOUNDSENTENCES1AlthoughShefferisgenerallycreditedwiththediscovery,itappearsthatsome-thingverylikeitwasoriginallymademanyyearsearlierbyCharlesSandersPeirce:seePeirce(1976).2ForSheffer’suseofthestroke,‘|’,forjointdenialseeSheffer(1913:487).Hedidnotthereeitherusethedaggerordealwithalternativedenial.Thecommoncurrentuseoftheterm‘ShefferStroke’andthesymbol‘|’toexpressalternative\nNOTES377denial(NAND)seemstoderivefromJeanNicod.Inhis(1916),Nicodofferedboththejointdenial(NOR)andalternativedenial(NAND)interpretationsof‘|’assufficientforhispurposes,butoptedfortheNANDreadingbecauseitoffersasimplertranslationof‘’.TheuseofthestrokeforalternativedenialandthedaggerforjointdenialcanbefoundinQuine(1952:18),whichprobablyhadalargeinfluenceinitself,althoughthereisstillarobusttraditionofreservingtheterm‘ShefferStroke’andthesymbol‘|’forjointdenial.3SeealsoNL:95.4Landini’spointisthatdiagrammaticwaysofpresentingtruth-functionalitywereinexistencewellbeforeWittgenstein,andthisisindisputable.Heseesnosig-nificantmathematicaladvanceinWittgenstein’slayingoutoftruthtables,andthistooisareasonablepoint.Hisexamplesdonot,however,showanypre-cedentfortheparticulardiagrammaticlayoutwhichWittgensteinused:thischoiceoflayoutmaynotbeverysignificantmathematically,butitdoeshavethevirtueofmakingthemeaningofthelogicalconstantsveryobvious,eventoanon-mathematicalmind.Notthatitmattersagreatdeal.5NotethatIherelayoutthetruthtablefor‘pq’inthewayWittgensteindoes,notinthewaywhichisnowroutine.Inmodernlayouts,thetruth-valuesassignedtothevariablesintheboxontheleftalternatemovingdowntheright-handcolumnofthatbox,changehalfasofteninthenextcolumnleft,halfasoftenagaininthenextcolumnleftofthat,andsoon.Wittgenstein’slayoutissimplythereverseofthat:thetruth-valueassignmentsalternateintheleft-handcolumn,changehalfasofteninthecolumntotherightofthat,andsoon.6Theformulaat4.27,bywhichthenumberKnisdefined,canbeexplainedinformallyasfollows.Itdefinesthenumberofwaysinwhichtheworldmightbeiftherearenpossibleatomicfacts.Thatnumberis:thenumberofwaysinwhichnoneoftheatomicfactsmightobtain;plusthenumberofwaysinwhichjustoneoftheatomicfactsmightobtain;plusthenumberofwaysinwhichexactlytwooftheatomicfactsmightobtain;plus…—andsoon,untilwehaveaddedthenumberofwaysinwhichallnatomicfactsmightobtain.7ThisiswhatIcalledtheminimalsenseofthenotionofapredicate,inChapter4,section4F,above.8ItseemssometimesnottobenoticedthatWittgensteinactuallyoffersnosug-gestionforaconvenientnotationforeitherofmethods2or3:itissometimessimplyassumedthat,wherethefunctionis–‘fx’wecansimplyplace‘fx’insteadof‘n’withinthebracketsin‘N(…)’.ItakeitthatthisassumptionliesbehindFogelin’sobjectionsatFogelin(1987:78–80).9Thisruleis,ineffect,thatadoptedbyPeterGeach(1981).ItisimportanttorememberthatWittgensteinhimselfoffersusnoguidancehere,andsomesuchruleisneeded.Inparticular,theruleneedsanexplicitindicationofthevariablewhichisfreeinfunctionexpressions(asisdoneherebyplacingitattheheadoftheexpression),inorderbothtoaccommodatethedifferencebetweenexisten-tialanduniversalquantification,andtodealwithsentencesinvolvingmixedquantifiers(suchasthosewemightwriteas‘(x)(9y)fxy’or‘(9x)(x)fxy’).Fogelin(1987:78–80)arguesthattheTractatuscannotaccommodatemixed\n378NOTESquantification.Itseemstome,rather,thatWittgenstein’saccountoftheN-operatorissimplyincompleteifwhatweareafterisanexplicitrepresentationofordinaryquantification.Onmyview,allWittgensteinneedsforhismainphilo-sophicalpurposesisforappropriatechoicesofvaluesofthevariable‘n’toyieldtherightresults;hedoesnotneedtoprovideanotationwhichenablesustorepresentthosechoicesperspicuously.LeoCheung(2000)offersausefuldis-cussionoftheFogelin–Geachdispute.10Itmightbethoughtthat,since(aswehavenoted)theN-operatordoesnot‘characterizeaformbutonlythedifferencebetweenforms’(5.241),beingvaluesof‘N(fx)’cannotmarkoutacommonform—thatis,‘N(fx)’cannotitselfbeafunction.Butwecanseethatthereisnoproblemhere,ifwetakecareaboutwhattheclaimthattheN-operatordoesnot‘characterizeaformbutonlythedifferencebetweenforms’reallyamountsto.Thesentences‘fa’,‘fb’,‘fc’allhaveacommonform(theformwhichwewriteas‘fx’).Soeachofthemhasacertainform.Take‘fa’inparticular.IfweapplytheN-operatortothatwereachasen-tence(‘N(fa)’)whichhasadifferentform.ThatdifferenceisthedifferencetheN-operatormakes,anditisadifferencebetweenforms.Ofcourse,if‘N(fa)’hasacertainform—adifferentformfrom‘fa’—thatallows‘N(fa)’,‘N(fb)’,and‘N(fc)’alltohavethesameform,whichwecanwriteas‘N(fx)’.Noneofthisrequiresthat‘N(fx)’itselfbetheresultofadirectapplicationoftheN-operatorto‘fx’.11Ramseythoughtsotoo:seeRamsey(1925a:7–8),(1926:74).12ThisexplanationisinspiredbythehelpfullyinformalaccountprovidedbyMarkRichard(1998).Standardexplanationsareintermsofassignmentsofobjects(orsequencesofobjects)tovariablesunderinterpretations:see,forexample,Sainsbury(1991:197).13Forthispoint,seeField(1972).14Atleast,thesimpleinfinityoftheobjectsdoesnotcreateaproblem.15TheformalresultwasreachedindependentlyinthesameyearbyAlonzoChurch(1936)andAlanTuring(1936).SinceitwasreachedfirstbyChurch,itisnowcommonlyknownasChurch’sTheorem.ThepointofthisparagraphwasmadebyCheung(2000:255),thoughhetakesthistoshowthattheTractariansystemstrictlyonlydealswithfinitedomains.16Atleastwhentherearemany-placedpredicates.17Anscombe(1971:132)seemstotakethisasanobjectiontoWittgenstein’scon-struction,ratherthanasanobjectiontoaparticularinterpretationofWittgenstein.18ThisisthesourceofsomeofFogelin’sworriesabouttheadequacyoftheN-operator:seeFogelin(1987:78–82)19SoWittgensteinthinksitiscrucialtoruleoutexactlythethingwhichRussellproposedasthesolutiontothedifficultyofexpressingwhatcannotbesaid,inhisIntroductiontotheTractatus(Russell1922:23);itishardlysurprisingthatWittgensteindislikedRussell’sIntroduction.Russell’sideaofahierarchyoflan-guagesinitiallylooksmuchmoreseriouslyatoddswithWittgenstein’sviewsthanthesuggestionthatWittgensteinwaslookingfora‘logicallyperfectlan-guage’(Russell1922:8).Butinfactbothremarksfailtoappreciatethecentrality\nNOTES379ofthesame-formassumptionwhichshapesthewholeofWittgenstein’sapproachbothtolanguageandtophilosophyingeneral.20Kripke(1980).21ThisisoneofthethingsAnscombecomplainsofinwhatshetakestobe‘themostcommonview’oftheTractatus:seeAnscombe(1971:25–26).22MichaelPotterusesthispassagetoshowthatWittgensteinwantedtoinsistthatthesamenotionofnegationmustapplytoallsentences,thoughhedoesnotseethatinsistenceasinturnderivingfromanargumentliketheargument(CF1)–(CF3)ofmytext(Potter2000:172).23ThisistheimpressiononereceivesfromRamsey(1925:11).24ThisishowitstruckRamsey(1925a:4–5),(1926:75).25Thecarefuldifferentiationoftheterms‘sinnlos’(‘withoutsense’)and‘unsinnig’(‘nonsense’)isoneofthegreatphilosophicalimprovementsofthePearsandMcGuinnesstranslation,incomparisonwithOgden’s.Note,however,thatWittgensteindoessometimesuse‘sinnlos’,whenitseemsthathemightequallywellhaveused‘unsinnig’(5.132;5.1362),eventhoughhedoesnotappeartouse‘unsinnig’tocharacterizethenon-picturinglimit-casemeaningfulnessoftautol-ogiesandcontradictions.Ofcourse,itwouldnotbealtogethersurprisingtofindacertainfluiditybetweentheterms,givenWittgenstein’sratherparticularaccountofnonsenseat5.4733,recalledat6.53.26See,forexample,theformulationofChurch(1940).27WhiteheadandRussell(1927:168).28Landini(2007:159–66)arguesthattheworkthatmathematicsneedstobedonecaninfactbedonewithoutusingidentity,providedthatweuseexclusivequanti-fiers(quantifierswhichusevariablesinarestrictedwaypreciselyinordertodealwiththeabsenceofidentity,asintroducedbyWittgensteinin5.532and5.5321).29Frege(1879:§8).30Frege(1892a).31SeeRussell(1918).32Infact,Ramseythoughtthatthismeantthatitwaswrongtoregardmathema-ticaltruthsasbeingjust‘equations’,inthesenseinwhichWittgensteinunder-stoodthatterm:therearesomethingswhichRamseythoughtsimplycannotbeaccommodatedonsuchanaccount(Ramsey1925a:17–19).33Thosewhowanttogodeeperintotheproblemsshouldconsult,forexample,Potter(2000)andLandini(2007).34ThispointismadebyLandini(2007:175).35ThisseemstobetheviewtowhichLandinitends(Landini2007:183).36Landini(2007)tracesthisnotionofthe‘power’ofanoperationbacktoRussell’snotionofthe‘power’ofarelation,inRussell(1901).Healsopointsoutthatthenotionisusedtodefinesuccession,addition,andmultiplication,inWhiteheadandRussell(1927:*301):see(Landini2007:180).37Potter(2000:179–81)takesWittgensteintobearguingforanadjectivalaccountofnumerals(asopposedtoasubstantivalone,likeFrege’s,whichtakesnumeralstofunctionassingularterms).ItseemstomethatthecontrastbetweenadjectiveandsubstantiveisnotlargeenoughforWittgenstein’s\n380NOTESpurposes,sinceitseemstomethatbothadjectivesandsubstantivesmaycountasnamesinWittgenstein’ssense,andhencerefertoobjects(seeChapter4,section4F,above).Thisdoesnot,however,underminethesubstantivepointwhichPotterismaking,whichhedescribesasapresentationofanargumentforanadjectivalaccountofnumerals.38SeePI:I,§1:‘Butwhatisthemeaningoftheword“five”?—Nosuchthingwasinquestionhere,onlyhowtheword“five”isused.’39Wittgensteinintroducedtherathercumbersomebracenotationof6.1203forpreciselythispurpose.Notethatheexplicitlyrestrictsitsuseto‘casesinwhichnosignofgeneralityoccursinthetautology’.40Church(1936);Turing(1936).41ThusWhite(2006:107);asimilarviewhasbeenexpressedinconversationbyWarrenGoldfarb.42ThusFogelin(1987:82)andLandini,whoseemstoholdthatthechiefpointofintroducingtheN-operatoristoshowlogictobedecidable(Landini2007:125–46).43Itishardtobeconfidentinthisinterpretation,butitisatleastnaturaltoreadtheopeningparagraphofRamsey(1928)asanexpressionoftheattitudeofsomeonewhoexpectedtheretobe‘aregularproceduretodeterminethetruthorfalsityofanygivenlogicalformula’,theproblembeingmerelythatoffindingit.Anditisalso(perhapsunsurprisingly)naturaltoreadthesameattitudeintothefamousformulationoftheprobleminHilbertandAckermann(1928:72–81).44Hume(1739–40:I,iv,6).45ThesetworemarkswereconsideredinconnectionwiththesubstanceargumentinChapter1,section1D,above.46Indeed,despitetheobjectionmadeinhisown(1923),RamseystillfeltabletodescribeWittgenstein’sextensionalismas‘extremelyplausible’(Ramsey1925a:9).47Ramseymadethispointinhisoriginalreview(Ramsey1923:31).48ForanaccountoftheunravellingoftheTractatusfromthispoint,seeHacker(1986:Ch.5).KeytextsareRLFandPR(Ch.8).6SOLIPSISM,IDEALISM,ANDREALISM1This,IsuspectistheviewofPeterSullivan:seehis(1996).2InthisdisputeStrawson(1966)istakentobea‘two-worlds’theorist,whereasAllison(1983)representsa‘one-world’traditionofinterpretation.3See,e.g.,Russell(1912:Ch.1),(1914).4Thereare,however,hintsofthetraditionalpreoccupationsofempiricisminthethingssuggestedasexamplesofobjectsintheNotebooks:e.g.,NL:3,45.5Schopenhauer’smainworkbeginswithastatementofsolipsismwhichhasstrongechoesintheTractatusandthepreliminarynotesontheissueintheNotebooks:seehis(1818/1844:I,3–5).Infact,SchopenhauerprovidesthekeybackgroundbothtoWittgenstein’sapproachtosolipsism,andtohisapproachtolifeingeneral(seeChapter7below).Forpreliminaryreadingonthis,seeZöller(1999),and,moregenerallyJanaway(1994).6Sullivan(1996:203)emphasizestheimportanceofthisconnection.\nNOTES3817ThisisbroadlytheconclusionreachedbyPears(1987:Ch.7);ifthisisright,despitetheoccasionalechoesofRussell(e.g.,Russell(1914)),itisnotRussell’skindofposi-tionwhichheisbothendorsing(as‘quitecorrect’)anddismissing(asunsayable).8Thenotionofa‘blind-spot’isusedatNL:100.9Note,however,thatitdoesnotinvolveanygeneralcommitmenttothePrincipleofBipolarityasaprinciplewhichappliestoallpropositions:(SC)isonlyaprincipleaboutwhatcanbestated(i.e.,asserted,described,orpictured).Tautologieswouldnotcountasstatements.10ItisnaturaltoseethisassumptionasrequiringnomorethanisrequiredinthisremarkfromtheNotesonLogicwhichwehavealreadylookedat(inChapter1,section1D,andChapter5,section5F):WhenwesayAjudgesthatetc.,thenwehavetomentionawholepropo-sitionwhichAjudges.Itwillnotdoeithertomentiononlyitsconstituents,oritsconstituentsandform,butnotintheproperorder.Thisshowsthatapropositionitselfmustoccurinthestatementthatitisjudged.(NL:94)11Diamond(2000)andMcGinn(2007:Ch.11)seemtotakethisasthesourceofthedifficultyofstatingsolipsismintheTractatus:if,however,itis(A4),(A5),and(A6)whichrepresentpositionsframedbythegeneralaccountoflanguageintheTractatus—thatsentencesaremodels—Ithinkthismustbewrong.12Note,though,thatadifferentword,‘meint’,isusedin5.62:thisisclosertotheordinaryEnglish‘mean’or‘intend’(itcanmeanbelieve).13ItissignificantthatinPT,thispassageoccurslaterthanthepassagewhichbecameTLP:5.621–5.641.ItakeitthatthisshowsthatWittgensteincametothinkthatitwas5.61,ratherthantheremarkswhichfollow5.62,whichgivethedeepexplanationofthe‘correctness’ofsolipsism.14Intheoriginal1922impression,Ogden’stranslationrendersthisparagraphasfollows:Thattheworldismyworld,showsitselfinthefactthatthelimitsofthelanguage(thelanguagewhichonlyIunderstand)meanthelimitsofmyworld.ThisversioncommitsWittgensteintosomeformof‘privatelanguage’,inasensenotunlikethatconsideredinWittgenstein(1953:§243),whichmakesitreadilyintelligiblethattheparagraphmightprovideanargumentforafamiliar(roughlyBerkeleyan)formofsolipsism.ButthisisclearlynotwhatWittgensteinhadinmind.AsLewy’snoteshows,the1922translationisclearlyjustmistaken,and,inanycase,thereisnothingintheTractatustosuggestthatheistherecon-cernedwithalanguagewhichisrestrictedtothethoughtsofasinglesubject.15Forthissuggestion,seeSullivan(1996).16Kant(1787:B131–32).17ThisisnotveryfarfromthesuggestionofPotter(2000:164–66).Potter,how-ever,takestheinterventionoftheselfinthetransformationof‘thedeadsign\n382NOTESintothelivesymbol’tobeaone-stepinterventionwhichtakesusrighttotheworld,whereasItakethetransformationof‘thedeadsignintothelivesymbol’tobejustthefirststep,withasecondstepneededtomovefromthesymboltotheworld;and,crucially,itisthesecondstepwhichisinplayhere.Thereis,perhaps,adisagreementbetweenusoverthedistinctionbetweensignandsymbolintheTractatus.Pottertakesasigntobe‘anelementofsyntax’(Potter2000:164),whereasItakesyntaxonlytoappearwithsymbols.Fortheseissues,seeChapter4,section4C,above,andJohnston(2007b).Aviewofthesamemoregeneralkindasthatsuggestedhere,andbyPotter,isalsosuggestedbySullivan(1996:210–11),andMcGuinness(2002c).18ItisalsosignificantthattheresponsetotheobjectionwhichisheresketchedonWittgenstein’sbehalfechoesDavidson’sargumentagainstthepossibilityofconceptualrelativity(Davidson1984b):aswesawinChapter4,section4B,n.8,Wittgenstein’ssame-formassumptionistantamounttotheassumptionofthecentralityofradicalinterpretation(RI),whichliesbehindDavidson’sargument.19Thiskindofcommunitarianneo-KantianismissometimesattributedtothelaterWittgenstein:see,e.g.,Williams(1981);Lear(1984).MyownfeelingisthatthiskindofviewisexactlywhatWittgensteinrejectsinthelaterwork.20SeeMcDowell(1994:lectureV).21IncludingSchopenhauer’s:seee.g.,his(1818/44:I,3–5)22Forthecontrast,seeChapter4,section4C,above.InthatsectionIarguedthat,ontheofficialviewoftheTractatus,syntaxcouldinprinciplebeestablished(andtherefore,thenatureofthesymbolscouldinprinciplebefixed)independentlyofthecorrelationswiththeworldwhichgivesymbolsmeaning.Someonewhodisagreedwithmeonthatpointwouldthinkthat,althoughitisonlysyntacticwell-formednesswhichisimportantfortheargumentwhichfollows,mysen-tencesonlypresentthemselvestomeassyntacticallywellformedinpresentingthemselvestomeasmeaningful—thatistosay,inmymakingsenseofthem.ItmaybesignificantthatthosewhoareinclinedtodoubtthepossibilityoftheestablishmentofsyntaxindependentlyoftheassignmentofmeaningaresometimesalsoinclinedtopresentsomethingliketheKantianapproachtoWittgenstein’ssolipsismwhichwasconsideredinthelastsection(see,e.g.,Potter(2000:164–66)).Imightaddthatitisatrivialmattertotransformtheargumentofthissectionintoonewhichconcernsmeaningfulness,ratherthansyntacticwell-formedness,eveniftheconversetransformationoftheargumentofsection6Disnothinglikesoeasy.23Itisworthpointingoutthatthiskindofthinkingmight,infact,bringsomethingatleastclosetofullmeaningfulness(ratherthanmeresyntacticwell-formed-ness)backintothepictureafterall.Forifmylanguageissyntacticallywell-formed,everycombinatorialpossibilityinmylanguagemustbeco-ordinatewithsomecombinatorialpossibilityintherealworld.Butthecombinatorialpossibi-litiesintherealworldarejustthepossibilitiesofcombinationoftherealobjectswhicharetheultimateconstituentsoftheworld.Soifmylanguageisevensyntacticallywellformed,theremustbeapossiblemappingbetweenitandtheobjectsintheworld.Andthatmightbethoughttobeatleastclosetothe\nNOTES383thoughtthatmylanguagemustbefullymeaningful,givenonlythatitissyn-tacticallywellformed.ThisisconnectedwithwhatIsuggestisWittgenstein’sresponsetogeneralscepticism,in6.51(seeChapter7,section7D,below).24Hume(1739–40:I,iv,6).25SeeDescartes(1641:IIandVI).26E.g.,Pears,who,infact,takes5.64tobeanendorsementofrealism(1987:188).27OnthesideofthosewhothinkthatWittgensteiniscommittedto(i)IplaceAdrianMoore:seeMoore(1985),(1992),(2003).OntheothersideIplaceMcGuinness(2002d)andSullivan(1996),(2003).7METAPHYSICS,ETHICS,ANDTHELIMITSOFPHILOSOPHY1PearsandMcGuinnesshave‘everythingthatissubjecttolaw’(TLP*).2ThepointcanbetracedbacktothefamousdiscussioninHume(1739–40:I,iii,6).3Hume(1739–40:I,iii,14).4Hencecauseisoneofthe‘categories’justifiedbytheTranscendentalDeductioninKant(1781/87).5SeeRussell’snoteto6.32intheOgdentranslation:‘I.e.nottheformofoneparticularlaw,butofanylawofacertainsort’(TLP,p.173).6Schopenhauer(1818/44:I,327–28).7ItisworthcomparingtheethicalviewoftheTractatuswiththatofthelaterLE.Here,Ithink,itisclearthatWittgensteinhaslostsomeoftheintensityoffeelingwhichanimatestheTractatus.8RecallthedefinitionofmetaphysicsinChapter1,section1F.9Carnap(1956:67).10See,e.g.,Hacker(2000).11ThisseemsalsotohavebeentheviewofRamsey(1923:472).12IthinkthisisconsonantwiththeaccountofmysticismtobefoundinMcGuinness(2000e).13Itisimportanttorecognize,however,thatthedivisionbetweenthosewhocallthemselves‘resolute’interpreters,andthosewhoarecounted‘tradition-alists’,includesmuchmorethanjusttheissueofhowtorespondtotheparadox:inonedimension,itisadisagreementoverwhattomakeofWittgenstein’snotionofnonsense;inanother,itisadisagreementofhowmuchoftheattitudesofthelaterWittgensteincanbereadintotheTractatus.Thecontemporarydebateisoftenunhelpfulinblurringthesedis-tinctionsbetweendistinctions.14TheclearestexponentofthisviewisHacker(2000).15ThispictureoftheIneffable-TruthsViewisencouragedbyConant(2000).16SeeGeach(1977).17IamverygratefultoDouglasWalkerforpointingoutthesignificanceofthistextasthedecisiveevidenceforthepointthatWittgensteincannotaccepttheexistenceofineffabletruths.\n384NOTES18See,e.g.,Diamond(1991);Conant(2000);Kremer(2001).ThiskindofviewisquestionedbySullivan(2002),androbustlyattackedbyProops(2001).19ThisviewwasdevelopedinitiallyinMorrisandDodd(2008).20OnceagainMcGuinnessgetsthetoneofthisjustright,describingitas‘aformofnegativetheology’(1988:300).NotethatheevenpreferstheOgdentransla-tiontohisown,togivethepropereffect.21IamthinkinghereinparticularofRLFandtheearlierpartsofWLC.SimilarpointsapplytosomepartsofWVC.TheworryherewasraisedbyRogerWhite.22Carnap(1963:25).23ThegeneralconceptionofthedialecticofthevarioustreatmentsoftheparadoxoftheTractatuswhichispresentedinthissection,aswellasthesolutionwhichisfinallyproposed,werepresentedinitiallyinMorrisandDodd(2008).IamextremelygratefultoJulianDoddforhispartinthewritingofthatpaper,andforbeinghappyformetopresentthatapproachagainhere,aswellasforhishelpinthegeneralclarificationoftheissuesinvolved.APPENDIX:THESUBSTANCEARGUMENT1Though,ofcourse,FregeusesthenotionofsenseinawaydifferentfromWittgenstein’s,sohewouldnothaveacceptedthisformulationofthepoint.ForFrege,senseisadimensionofmeaningdistinctfromreference:allexpressionshavebothsenseandreference.ForWittgenstein,ontheotherhand,onlynameshavereference,andonlysentenceshavesense.2Whatis,ineffect,thisobjectiontoProopsismadebyZalabardo(Unpublished:§5).Iendorsehisdiagnosis,butonlywithsomehesitation,becauseProops(2004:114–15)distinguishespreciselythetwothingsthatseemtoneedtobeconfusedifeverypremiseoftheargumentistolookplausible.3ThoughasnotedwhereIconsiderthisremarkinthemaintextofChapter1,thisviewseemstohavebeenexpressedearlierbyWittgensteinhimself(CL:24–25).\nBibliographyTherecentliteratureontheTractatusisvast.Whereshouldastudentgonext?IfyouwantadetailedaccountofWittgenstein’slife,uptothetimeofthepublicationoftheTractatus,gotoMcGuinness(1988):theﬁnalchapterofthisisalsoexcellentasanapproachtotheliteraryaspectsofthework.Monk(1990)providesafullbiography,coveringthewholeofWittgenstein’slife.Itissometimesusefultoreadmorethanoneintroductorytext.Stenius(1960)andAnscombe(1971)remainclassics;White(2006)isarecentadditiontothegenre.ForasurveyofthewholeofWittgenstein’soeuvre,Kenny(2006)isagoodplacetobegin.Stern(1995)goesmoredeeplyintooneaspectofWittgenstein’sphilosophy,coveringbothearlyandlatework.ItisalsoagoodideatoplaceWittgenstein’sphilosophyinthecontextoftheworkofRussellandothersinthesametradition.Monk(1997)isahelpfulbiographyofRussell.Hylton(1990)providesusefulbackgroundintheearlyhistoryofanalyticphilosophy.Potter(2000)placesWittgenstein’sworkinthecontextofawholetraditionofphilosophyofmathematics.Landini(2007)focusesmorestronglyontheinﬂuenceofRussell,andpursuesthetechnicalissuesingreatdetail.Fortherecentcontroversyoverthetreatmentofthework’sapparentparadox,theplacetobeginisCraryandRead(2000).FromthereitisworthmovingtoKremer(2001);Proops(2001);andSullivan(2002).WORKSBYWITTGENSTEINCLLudwigWittgenstein:CambridgeLetters;CorrespondencewithRussell,Keynes,Moore,RamseyandSraffa,ed.B.McGuinnessandG.H.vonWright(Oxford:Blackwell,1995)\n386BIBLIOGRAPHYLE‘ALectureonEthics’,PhilosophicalReview74(1965):3–12LOLetterstoC.K.OgdenwithCommentsontheEnglishTranslationoftheTractatusLogico-Philosophicus,ed.G.H.vonWright(Oxford:Blackwell,1973)NBNotebooks1914–1916,ed.G.H.vonWrightandG.E.M.Anscombe,trans.G.E.M.Anscombe,2ndedn,(Oxford:Blackwell,1979)NLNotesonLogic,printedasAppendixIofNBNMNotesDictatedtoG.E.MooreinNorway,printedasAppendixIIofNBPGPhilosophicalGrammar,ed.R.Rhees,trans.A.Kenny(Oxford:Blackwell,1974)PIPhilosophicalInvestigations,trans.G.E.M.Anscombe,3rdedn(Oxford:Blackwell,2001)PRPhilosophicalRemarks,ed.R.Rhees,trans.R.HargreavesandR.White(Oxford:Blackwell,1975)PTPrototractatus:anEarlyVersionofTractatusLogico-Philosophicus,ed.B.McGuinness,T.Nyberg,andG.H.vonWright,trans.D.PearsandB.McGuinness(London:RoutledgeandKeganPaul,1971)RFMRemarksontheFoundationsofMathematics,ed.G.H.vonWright,R.Rhees,andG.E.M.Anscombe,2ndedn(Oxford:Blackwell,1978)RLF‘SomeRemarksonLogicalForm’,AristotelianSocietySupplementaryVolume9(1929):162–71TLPTractatusLogico-Philosophicus,trans.C.K.Ogden(London:RoutledgeandKeganPaul,1922)TLP*TractatusLogico-Philosophicus,trans.D.PearsandB.McGuinness(London:RoutledgeandKeganPaul,1961)WLCWittgenstein’sLectures:Cambridge1930–1932,ed.D.Lee(Oxford:Blackwell,1980)WSPWittgenstein:SourcesandPerspectives,ed.C.G.Luckhardt(Ithaca,NY:CornellUniversityPress,1979)WVCLudwigWittgensteinandtheViennaCircle:ConversationsRecordedbyFriedrichWaismann,ed.B.McGuinness(Oxford:Blackwell,1979)\nBIBLIOGRAPHY387WORKSBYOTHERAUTHORSAllison,H.(1983)Kant’sTranscendentalIdealism:AnInterpretationandDefense(NewHaven,CT:YaleUniversityPress)Anscombe,G.E.M(1971)AnIntroductiontoWittgenstein’sTractatus,3rdedn(London:Hutchinson)Armstrong,D.(1997)AWorldofStatesofAffairs(Cambridge:CambridgeUniversityPress)Beebee,H.,andDodd,J.,eds(2005)Truthmakers:TheContemporaryDebate(Oxford:OxfordUniversityPress)Berkeley,G.(1734)ATreatiseConcerningthePrinciplesofHumanKnowledge,2ndedn(London:Tonson)Black,M.(1964)ACompaniontoWittgenstein’sTractatus(Cambridge:CambridgeUniversityPress)Block,I.,ed.(1981)PerspectivesonthePhilosophyofWittgenstein(Oxford:Blackwell)Carnap,R.(1956)‘TheEliminationofMetaphysicsthroughLogicalAnalysisofLanguage’,inA.J.Ayer,ed.,LogicalPositivism(NewYork:FreePress)——(1963)‘IntellectualAutobiography’,inP.Schilpp,ed.,ThePhilosophyofRudolfCarnap(LaSalle,IL:OpenCourt),pp.3–84Cheung,L.(2000)‘TheTractarianOperationNandExpressiveCompleteness’,Synthese:AnInternationalJournalforEpistemology,MethodologyandPhilosophyofScience123:247–61Church,A.(1936)‘ANoteontheEntscheidungsproblem’,JournalofSymbolicLogic1:40–41——(1940)‘AFormulationoftheSimpleTheoryofTypes’,JournalofSymbolicLogic5:56–68Conant,J.(2000)‘ElucidationandNonsenseinFregeandEarlyWittgenstein’,inCraryandRead(2000)Crary,A.,andRead,R.,eds(2000)TheNewWittgenstein(London:Routledge)Davidson,D.(1984)InquiriesintoTruthandInterpretation(Oxford:OxfordUniversityPress)——(1984a)‘RadicalInterpretation’,inhis(1984),pp.125–40——(1984b)‘OntheVeryIdeaofaConceptualScheme’,inhis(1984),pp.183–98Descartes,R.(1641)Meditationesdeprimaphilosophia,trans.J.Cottingham,asMeditationsonFirstPhilosophy,inJ.Cottingham,R.Stoothoff,andD.Murdoch,eds,ThePhilosophicalWritingsofDescartes,Vol.II(Cambridge:CambridgeUniversityPress,1984)Diamond,C.(1991)‘ThrowingAwaytheLadder:HowtoReadtheTractatus’,inherTheRealisticSpirit(Cambridge,MA:MITPress),pp.179–204——(2000)‘DoesBismarkHaveaBeetleinHisBox?ThePrivateLanguageArgumentintheTractatus’,inCraryandRead(2000),pp.262–92Dummett,M.(1981)Frege:PhilosophyofLanguage,2ndedn(London:Duckworth)——(1991)Frege:PhilosophyofMathematics(London:Duckworth)Field,H.(1972)‘Tarski’sTheoryofTruth’,JournalofPhilosophy69:347–75\n388BIBLIOGRAPHYFloyd,J.,andShieh,S.,eds(2001)FuturePasts:TheAnalyticTraditioninTwentiethCenturyPhilosophy(NewYork:OxfordUniversityPress)Fogelin,R.(1987)Wittgenstein,2ndedn(London:Routledge)Frege,G.(1879)Begriffsschrift:einederarithmetischennachgebildeteFormelsprachedesreinenDenkens(Halle:Nebert),trans.asBegriffsschrift:aformulalanguage,modeleduponthatofarithmetic,forpurethought,inJ.vanHeijenoort,ed.,FromFregetoGödel:ASourceBookinMathematicalLogic,1879–1931(Cambridge,MA:HarvardUniversityPress)——(1884)DieGrundlagenderArithmetik:einelogisch-mathematischeUnterschungüberdenBegriffderZahl(Breslau:Köbner),trans.J.L.Austin,asTheFoundationsofArithmetic:Alogico-mathematicalenquiryintotheconceptofnumber,2ndedn(rev.)(Oxford:Blackwell,1980)——(1892a)‘ÜberSinnundBedeutung’,ZeitschriftfürPhilosophieundphiloso-phischeKritik100:25–50;trans.M.Black,as‘OnSenseandMeaning’,inFrege(1984)——(1892b)‘ÜberBegriffundGegenstand’,VierteljahresschriftfürwissenschaftlichePhilosophie16:192–205;trans.P.Geach,as‘OnConceptandObject’,inFrege(1984)——(1893)GrundgesetzederArithmetik,BandI(Jena:Pohle);partiallytrans.M.Furth,asTheBasicLawsofArithmetic(Berkeley,CA:UniversityofCaliforniaPress,1964)——(1903)GrundgesetzederArithmetik,BandII(Jena:Pohle)——(1980)PhilosophicalandMathematicalCorrespondence,ed.G.Gabriel,H.Hermes,F.Kambartel,C.Thiel,andA.Veraart;trans.H.Kaal(Oxford:Blackwell)——(1984)CollectedPapersonMathematics,Logic,andPhilosophy,ed.B.McGuinness(Oxford:Blackwell)Geach,P.(1977),‘SayingandShowinginFregeandWittgenstein’,inJ.Hintikka,ed.,EssaysinHonourofG.H.vonWright,ActaPhilsophicaFennica28:54–70——(1981)‘Wittgenstein’sOperatorN’,Analysis42:124–27Glock,H.-J.(2004)‘AllKindsofNonsense’,inE.AmmerellerandE.Fischer,eds,WittgensteinatWork:MethodinthePhilosophicalInvestigations(London:Routledge),pp.221–45Goldfarb,W.(1989)‘Russell’sReasonsforRamification’,inC.W.SavageandC.A.Anderson,eds,RereadingRussell:EssaysonBertrandRuss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.11:153,160–614.032:1463.12:145,1604.04:123,146,207,3723.13:153,160,162,164,1664.041:1503.14:146,1654.0621:2073.1431:119,1474.1:3353.1432:147,185,187–88,1924.112:335–36,344,3.144:147,3744.113:336,3443.2:145,178,3744.114:336,3443.201:178,3744.115:336,3443.21:178,3744.116:336,3443.23:178,182,3564.12:123,150,3333.24:178,181–82,218,356,3734.121:151,2933.3:171,1744.1212:1513.31:1594.122:3333.311:172,1764.126:3333.312:1724.1272:3343.313:173–744.1274:3343.314:1744.22:174,187,190–91,2003.315:175,1794.24:188,2143.316:1764.241:2423.318:188,2144.242:2423.32:1614.27:211,3773.321:1614.442:210–113.322:1614.46:236,3723.323:161–62,166,3734.461:2373.324:1664.4611:2373.325:1664.462:2373.326:164–664.4661:236,3723.33:162–63,2394.5:19,176,231,375\nINDEXOFPASSAGESINTHETRACTATUS3954.53:1765.632:297,3025:13,229,254,3725.633:296,299,301–25.1311:2075.6331:3055.132:3795.634:268,2725.1362:3795.64:297,302–3,307,3835.21:2155.641:301,303,323,3815.23:2156:13,226–295.241:212,3786.001:226–29,232,235,2545.25:2156.02:247–515.251:215,231,2486.021:247–515.2522:226–276.1:236,312–135.4:2056.11:3125.434:2406.113:2385.44:2056.12:2375.441:2066.1203:3805.451:2356.122:252–535.47:2346.2:242–43,2465.473:13,1066.211:246–475.4733:158–59,162,165–70,334–35,6.22:243341,3796.23:243–445.5:216,2256.232:2445.501:216–19,2276.2322:244–465.502:217,2256.3:312–13,3195.51:2176.31:3145.52:217–20,2226.32:315–17,3835.526:1816.34:3195.5261:2236.342:3195.53:2416.35:3175.531:2426.36:315–16,319–205.532:3796.363:3145.5321:242,3796.3631:3145.5302:2416.37:137,236–37,312–13,3215.5303:2406.371:3185.535:2216.373:3235.541:2546.374:3235.542:2566.3751:261–625.5421:256,263,3016.4:320–21,3285.5422:47,86,258–59,3686.41:3215.5563:1836.421:3255.6:275–77,281,3056.422:322–23,3245.61:276–77,285,304–5,307,330,332,6.423:3233816.43:3245.62:263–308,329,340–41,380–83,6.44:324,326,3385.621:3836.45:326,338,3495.631:296–98,302–36.5:328,337–38\n396INDEXOFPASSAGESINTHETRACTATUS6.51:296,329–31,338,342,3836.53:331,339,341,343,345,3796.52:328,3386.54:7,19,144,311–12,331,331,334,6.521:329,337338–546.522:337–38,338,3427:13,264,351,384\nGeneralIndexapriori,16–17,37,47–48,100–101,Cartesian,seeepistemology,Cartesian106–7,113,136,192,204,231–32,causality,315–25236,238,253,268–69,310,314–15,Cheung,Leo,vi,378317,319–20,331,337,354Church,Alonzo,232,378–80Ackermann,Wilhelm,380class,67,109–13,229–30,240,247,acquaintance,16–17,74,101,103,108,112–249,251,37013,204,212–13,236,238,253,362,368colour,36,39,137,185,261–62aesthetics,325–27,338complete,seeunsaturatedaffairs,stateof,seefact,atomiccomplex,40,69,71–72,75,81,83,87–Allison,Henry,38090,92,99,102–5,127,146–48,178–analysis,177–83,192,261,356–58,372–73,82,184–85,250,355–58,368–69,375373,375–76;seealsosimpleanalytic,16–17,107–8,310–13compositionality,171AngelusSilesius,327Conant,James,169,383–84Anscombe,G.E.M.,375,378–79,385concept,66–67,70–71,76,91–94,99–apperception,278,288,294–95100,115–16,189–90,197,333,341–Aristotle,28,35,115,259,36542,350,369–71;conceptofhorse,Armstrong,David,36493–94,116,197,341,350,369–71attitudes,propositional,83–88,254–59,constants,logical,99–106,113,117,368139,204–26,228–29,370,377contextprinciple,98–99,169–76,195,Beebee,Helen,365198,369–70Berkeley,George,265–67,381contradiction,237,262,320,379;seeBipolarity,Principleof,133–35,272,372,alsotautology375copula,33,78,116,184,192,194,200Black,Max,372correlation,44–45,56,60–64,68–83,blind-spot,270–74,282,303,306–7,86,90–97,99–100,114–18,122,126,387;seealsolimit128–31,145,149,151–52,160–61,163,Bradley,F.H.,66177,180,186,189,191,193,196–98,201,204,207–9,233,251,257,283,Carnap,Rudolf,4,309–11,334,339,354,366–67,369–71,376,382347–48,383–84Crary,Alice,385\n398GENERALINDEXDavidson,Donald,366,369–70,373–243,251,293,333;offacts,41–42,74,382125–26;ofobjects,35,39,50,125,decidability,224–25,232,245–46,252–162,243;;ofpictures,126–27,131–53,296,38036,371–72;ofpropositions,48,150–Dedekind,Richard,10852;oftheproposition,general,19,depict(abbilden),122–23,129,132,159,169–77,226–35,361;oftheworld,371–73;seealsorepresent12,42–50,139,238,267,290,362–Descartes,René,300,38363;undepictabilityof,131–36,149–Diamond,Cora,352,381,38451,177,272–74,304–5,332–34directionproblem,narrow,84–85,367–68formal,218,226–27,237–38,252,333directionproblem,wide,86–89,367Frege,Gottlob,2–3,62–66,68–76,78–Dodd,Julian,vi,365,374,38479,81–82,93–94,98–101,105,–113,Dummett,Michael,370,375–76114–17,125,129,140,151,158–60,166,169–71,174,180–81,189–92,epistemology,48,74,100,103–5,212,194–98,200,203–6,213–14,229,245,253,266–67,287–300,329–31,239–42,244–45,247,250–52,254,341,383;Cartesian,74,245,287–259,341–42,350,356,366–67,369–300,38376,379,384equation,241–47,379function,70,76,93,100,188–89,205,ethics,310,320–28,337,348–49,383211,213–15,217–23,228–31,248,370,extensionality,254–62,380377–78;propositional,214,219,223external(quality),35,39;seealsointernalGaskin,Richard,viGeach,Peter,377–78,381fact(Tatsache),22,24–42,50–55,104,Georgallides,Andreas,vi124–30,138,146–49,159–60,174,generality,179–82,217–24177,193–95,198–200,204–5,208,Gödel,Kurt,232211,233–35,241,256–61,283–84,Goldfarb,Warren,vi,366,370,380324,328,333,364–66,376–77;atomicfact(Sachverhalt),31–42,50–55,125–Hacker,P.M.S.,380,38326,140,174,177,199–200,211,234–Hegel,GeorgWilhelmFriedrich,2,66,35,260,333,365–66,377;negative265(andpositive),38,51,365–66Hertz,Heinrich,146,371–73Fogelin,Robert,356,375,377–78,380Hilbert,David,380form,12,17,19,35–36,39,41–43,46–Hume,David,29,107,257,298,309–50,90,101–5,125–27,130–40,150–15,318–21,339,380,383;Hume’s58,162,169,172,175–77,184,192–Fork,310,312,319–2095,198–99,208–9,212–13,215–16,Hylton,Peter,385226–35,237–38,243–44,246,250–54,256,259,267,270–74,278,282–incomplete,seeunsaturated85,287,289–91,293–45,300,302–3,idealism,56–58,67,97–98,155–57,184,306,315–16,319,330,332–35,340,196,263–75,281–97,302–3,306–8,344,351,360–63,364–65,368,370–315,337,369,371;seealsorealism72,374,376,378–79.381–82;logical,andsolipsism39,48–50,136–40,150–51,175,238,identity,15,110,240–46,250,379\nGENERALINDEX399independence,logical,28,53–55,199–McGuinness,Brian,18–19,31,123–24,200,211,260–61132,136,144,176,205,364,375,induction,313–18379,382–84,385ineffable,16,272–75,304–7,316,320,mathematics,14–15,63,65,91,106–13,328–42,383;seealsosaying-showing204,241–54,310,379–80,385distinctionmeaning,thinnessof,68–77,196–97,infinity,221,357,370,372,378243–46,367internal(quality),35–36,154metaphysics,10,23,28–29,55,57–58,Ishiguro,Hidé,375107,113,143,163,198–202,260–61,264,268–69,284,302–3,309–13,Janaway,Christopher,380328–38,343,353–54,365,383Johnston,Colin,vi,369,374,376,382model,44,118–32,141–42,143–51,163,201,371–73;seealsopicture;ParisKant,Immanuel,13–18,35,37–38,47,courtroommodel,118–2363,78,97–98,107,111,113,163,Monk,Ray,327,385204,232,236,238,245,252–53,Moore,Adrian,vi,383264–74,277–87,292,295,298,306,Moore,G.E.,2–3,66–67,71,255308,310,312–13,315,319–20,331,Morrell,Ottoline,368337,365,367,369,381–82multiplicity,146,150,156,207,371,373Kenny,Anthony,385mysticism,326–27,337–38,349,351,Kierkegaard,Søren,333353–54,383Kremer,Michael,384,385Kripke,Saul,47–48,232,367,379N-operator,the,215–29,232–35,248,254,377–78,380Landini,Gregory,210,377,379–80,name,26,29,44–45,56,69,71–74,76–38577,87,91,93,102,115,147,160,174–language,colloquial,177–78,182–83,75,183–95,201,205–7,214,221,250–51200,203–4,372–73,375nature,lawsof,312–20Lear,Jonathan,382necessity,15–17,34–35,42–50,101,107,Leibniz,GottfriedWilhelm,28,365112–13,135–37,141–42,163,232,Lewy,Casimir,277,381236–39,252–54,267–68,272–74,life,meaningof,3,296,321,327–30,312–22,332–34,354,358–61,369337,354,398Nicod,Jean,377limit,30,268–77,282,293,297–301,303–nominalism,184,194,375–767,323–24,326,330–36,348–49,352nonsense(unsinnig),10,19,158–71,Locke,John,62,64,66,78,83,85,90,237,309–12,329–36,338–54,374,117–18379,383;‘austere’conceptionof,logic,3,13,16,65,99–106,139–40,169,171,374204–46,252–54,295–96,312,340,number,14,65,108–13,241,247–52,376–80;seealsospace,logical;form,369–70logical;constants,logicallogicism,106–13object(Gegenstand),24–27,30–50,55,61,67–68,76,93–94,103–6,109–11,McDowell,John,367,382113,122,125–27,132,177–96,199–McGinn,Marie,vi,366,385202,204–9,213,223,245,247–52,\n400GENERALINDEX256–58,300–302,330,341–42,350,quality,29–30,35,183–96355–63,369,371,376,379–80,382;quantifiers,117,215,217–26,377–79;object,logical,105–6,108,113,117,seealsogenerality205,212Quine,W.V.,365,373–74,377objectivity,61–83,114–18Ogden,C.K.,4,18–20,31–32,52,123–Ramsey,Frank,4–5,18,192,258,353,24,127,140,165,176,277,365,371–375–76,378–80,38373,375,379,381,383–84Read,Rupert,385ontology,108,186,189,364–66realism,56–58,96–98,139,155–57,operation,212–16,231,247–48163–64,184,191–92,194,202,264–65,269–72,284,287,291–93,296–paradox(oftheTractatus),7–8,10,12,97,302–3,307–8,369,371,374–75,272–75,304–8,311–12,334–36,338–383;seealsoidealism,solipsism54,383–84,385reducibility,axiomof,370Peano,Giuseppe,108,111,247,370relation,seequalityPears,David,18–19,31,123–24,132,represent(darstellen),17,122–23,159,136,144,176,205,366,369,374–75,205,276,371–73;seealsodepict379,381,383representation,generaltheoryof,123–36Peirce,CharlesSanders,376resolute(interpretationofTractatus),philosophy,8,10,12–18,23,63,100–10,343–44,383101,107,136,246–47,309–12,328–Ricketts,Thomas,vi,375–7638,354;seealsometaphysicsRussell,Bertrand,2–3,5,9,16,18,32,picture(Bild),43–44,119,122–23,371–47–48,62–64,66–68,71–77,79–94,73;seealsomodel99,101–6,111–13,114–18,125,129,picturetheoryoflanguage,143–202,149,151,156–57,180–81,195–98,371–73200,203–5,212,214,229–31,239,Plato,35241–42,245,247,251,254–55,257–possibility,seenecessity59,267,327,340,356,361–63,365–Potter,Michael,vi,370,374,379–82,38567-,374–76,378–81,383,385;predicate,69–70,76–77,91,93–94,multiple-relationtheoryofjudgement,99–100,109,116,183–97,214,229,47,83–90,117–18,258,368–69;231,369–71,375,377;seealsoRussell’sparadox,5,111–12,229–30,function239,367,370;theoryofdescriptions,Priest,Graham,37072–74,77,82,87,115,179–81,197,254;Proops,Ian,358,370,384,385theoryoftypes,91,112,239,376proposition(SatzinTLP),75,79–80,87,144,159–68,369–70,382;seesaturated,seeunsaturatedalsosentence;proposition,elementarysaying-showingdistinction,131,136,150–(Elementarsatz),32,174,177–78,186–51,206,237–38,243–44,246,252–54,89,214;proposition,generalform263–64,277,285–87,293–96,307,of,seeunderform;proposition,320,333,337–38,340–41,373,381unityof,25–26,77–99,117–18,198scepticism,97,266–67,288,295–96,prototype(Urbild),175,179–80,182329–31,337–38,383psychology,256,263,303,323Schopenhauer,Arthur,265,267,327,psychologism,65–67,115,170367,380,382–83\nGENERALINDEX401sense,70–72,76,78–79,89,115,140,symbol,152,158–68,172,208,237–40,150,159–60,171,179,181,193,195,242,290,373,381–82(seealsosign)206–10,213,233–35,242,244–45,syntax,161–68,230,239,289–94,382254,259,283,367,374,384;synthetic,16–17,107–8,112–13,204,determinatenessof,179–80;likeor236,238,245–46,253,264,268–69,oppositesense,193–95,208–10,310,313,316,319–20,331,337,354213,233–35,259,283;withoutsense(sinnlos),19,237,379tautology,224,236–38,243,246,312,sentence,25–26,37,64–65,75–99,319–20,372,381116–18,128,144,146–50,152,160,term,75–76,85–86,91–92,116,226–27164–77,185–98,200,206,213–15,thing,seeobject229,231–35,248,257–59,335,367,thought,71,75,78–79,140–42,144–45,369,371,384;seealsoproposition156–57series,109–10,218,22608,248,251traditional(interpretationofTractatus),set,seeclass10,339–42,383Sheffer,Henry,207,376translation,152–57,373–74ShefferDagger(NOR)andStroketruth-function,100,196,211–13,215,(NAND),207,216,228–29,376–77226,228–29,234,254;seealsoshow,seesaying-showingdistinctionconstant,logicalandN-operatorsign,59–60,95,130–31,146,159–66,truth-table,210–12,377239,381–82;seealsosymboltruth-value,70,75,79,100,129,197,simple,39–50,71–73,104–5,178–83,210,260,358–60218,240,245,251,300,355–63,375–truthmakers,364–6576;seealsocomplexTuring,Alan,232,378,380singularterm,seenamesolipsism,58,257,263–308,323,329–universals,183–9630,332,336–37,369,376,380–83;unsaturated,93,100,190,194,213,376seealsoidealismandrealismunsayable,seeineffablesoul,seesubjectspace,logical,26,137–38,325–26,349variable,103–4,172–76,179–80,216–Soames,Scott,36719,226,377–78;propositional,174–Spinoza,Baruch,28,36576,217,225Staehler,Tanja,viStenius,Erik,371,375,385Walker,Douglas,383Stern,David,385White,Roger,vi,364,380,384,385Stevens,Graham,367,369,371Whitehead,AlfredNorth,2,5,83–84,Strawson,P.F.,38091,230,367,379structure,41–42,125–26,333will,323–24,327subject,86–87,156–57,256–58,263,Williams,Bernard,265–66,382279,283,286,296–307,323–25,381;world,14–18,21–30,39–58,67–68,96–logicalsubject,76,91–93,18798,136–39,155–57,198–202,260–substance,39–50,76,182,201,232,61,275–302,321–26,337–38,355–63,300,330,355–63,365–66,380,384364–66,369Sullivan,Peter,vi,366,369–70,372,Wright,Crispin,370376,380–85Zalabardo,José,vi,361–63,366,384

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