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CHAPTER2:SAYINGTHESAMETHING
’Whatisyouraiminphilosophy?—Toshewtheflythewayoutofthefly-bottle.’
‘Apicturehelduscaptive.Andwecouldnotgetoutsideit,foritlayinourlanguageandlanguage
seemedtorepeatittousinexorably’.
InordinaryEnglish,weusetheterms‘sentence’,‘statement’and‘proposition’interchangeablybutforsomepurposeswe'llwanttodistinguishbetweenthem.Inparticular,whenitcomestodecidingwhenpeopleare‘sayingthesamething’weshalldistinguishbetweenthequestionofwhethertheyareutteringthesamesentence,makingthesamestatementorexpressingthesameproposition.
1 DIFFERENTWAYSOFCOUNTINGSentences,statementsandpropositionsarenotthreedifferentkindsofthings:the
questionofwhetherwehavethesamesentence,samestatementorsamepropositionsignalsdifferentwaysofcountingthesamethings.Wecancountthingsindifferentwaysbygroupingthemaccordingtodifferentfeatures.Countinginthemostfine-grainedway—‘countingbytoken’—everyindividualobjectcountsasone.Thereare10individualpiecesoffruithere:
Butwecouldalsocountfruitsbykind:countinginthisway,byfruittype,therearethreefruitshere:apple,cherryandavocado:
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Alternatively,wecouldcountbycolor.Therearetwocolors:redandgreen.
Thepointisthatkindsandcolorsaren’tadditionalobjectsoverandaboveindividualpiecesoffruit.Rathercountingbykindandcountingbycoloraredifferentwaysofcountingthesamethings,inthiscaseindividualpiecesoffruit.Thesamegoesforcountingsentences.Wecangroupthemdifferentlyand,onthebasisofthesedifferentgroupings,countthemindifferentways.
Thereisnomysteryaboutwhatsentencesare.Asentenceisaphysicalobject,madeofsounds,quantitiesofinkorpixels,whichisusedtodoalinguisticjob.Asentenceconsistsofwordsofalanguagearrangedaccordingtothegrammaticalconventionsofthatlanguage.Peopleusesentencestodoavarietyofjobs,e.g.toaskquestions,makepromises,giveordersandmakestatements.Sentencesthatmakestatements,typicallydeclarativesentences,havetruthvalue,thatis,truth-or-falsity,invirtueofthetruthvalueofthestatementstheymake.Notallmeaningfulsentenceshavetruthvaluehowever.Questions,forexample,mayhave‘yes’or‘no’answers,buttheyaren't,strictlyspeaking,trueoffalse;ordersmaybeobeyedordisobeyed
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buttheyaren't,literally,trueorfalse.Weareinterestedinsentencesthatmakestatements,thosethatmaybetrueorfalse,andindifferentwaysofcountingthosesentences.
2 COUNTINGBYSENTENCETOKENANDSENTENCETYPEWhenweusewordslike‘identical’,‘same’andtheircognatesthereisoftenatype-token
ambiguitythatcomesaboutbecausewedon’tknowwhatkindofcountingisintended.
Theyworethesamedress Theyworethesamedress
Thewomenontheleftarewearingdifferenttokensofthesametypedress.Thoseontherightarewearingthesametokendress.
Incountingsentences,too,wecancountbytokenorbytype.SupposeIwrite:
(1)JohnisPaul'sbrother
(2)JohnisPaul'sbrother
InonesenseIsaidthesamethingwhenIwrote(1)and(2):(1)and(2)arethesametypesentence,thatis,theyconsistofthesamewordsinthesameorder.Buttheyarenotthesametokensentence,thatis,theyaren'ttheverysameindividualphysicalobject,butaredifferentobjects,occupyingdifferentplaces,consistingofdifferentbitsofink(orpixelsifyou'rereadingthisonline).
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Atthispointyoumaybetemptedtoask:‘What’satype?’‘What’satoken’.Inanimportantsensethatisthewrongquestiontoaskbecauseitassumesthattherearesuchthingsastypesandtokensoverandabovethebusinessofcounting-by-typeandcounting-by-token.Thoughbackinelementaryschoolweweretoldthatnounswere‘namesofpersons,placesorthings’thisisn’tquiteright.InEnglish,andothernaturallanguages,notallnounsdothejobofnamingorreferring.Somenounsfigureinidioms,anddon’trefertoanything:
(3)AisthesameheightasB
Butthereisn’tathirdthing,aheight,inadditiontoAandB:therearejusttwobears.
(4)JohndidthewashforMary’ssake
ButthereisjustJohn,MaryandtheWash—thisisn’t,inadditiontothepeopleandlaundry,suchathingasa‘sake’.
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Therearen’tanysuchthingsassakesandheightsintheworld,eventhoughlanguagemaymisleadusintothinkingthattheyare.Theheightsandsakesin(3)and(4)canbeparaphrasedawayassomethinglike:
(3ʹ)AandBareequallytall.
(4ʹ)JohndidthewashinordertobenefitMary.
Inthesamewaywecouldparaphraseawaytypesandtokens:Sentence(1)istype-identicaltoSentence(2),but(1)isnottoken-identicalto(2).Therearen’ttwodifferentkindsofthings,token-sentencesandtype-sentences.Therearejusttwodifferentwaysofcountingsentences:wecancount-by-sentence-tokenorcount-by-sentence-type.Counting-by-tokenmeanscountingeachutteranceorinscriptionasone.Counting-by-typeiscountinggroupsofsentences,inparticularthosethatareofmoreorlessthesameshape.Sentencesareofthesametypewhentheyconsistofthesame(type)wordsinthesameorder,asisthecasewith(1)and(2).
Buttherearedifferentwaysofgroupingsentencesandsodifferentwaysofcountingthem.Wecould,forexample,groupthembymeaning.Wecan,thatis,countsentencesbythepropositionstheyexpress.Onceagain,however,propositionsaren’tanadditionalkindofthing.Rathercounting-by-propositionisanotherwayofcountingthesamekindsofthings,viz.sentences.
3 COUNTINGBYPROPOSITION
Propositionsarewhatsentencesexpress;theymaybeunderstoodasthemeaningsofsentences.Thusthesentences(1)and(2)above,sincetheymeanthesamething,expressoneandthesameproposition.However,differentsentencetypesmayalsoexpressthesameproposition.(1),(2)and(3)expressthesameproposition.
(1)JohnisPaul'sbrother
(2)JohnisPaul'sbrother
(5)JohnisthemalesiblingofPaul.
Although(3)isnotthesametype(ortoken!)sentenceas(1)and(2)itissynonymouswiththem:allthreesentenceshavethesamesenseordictionarymeaningsotheyexpressthesameproposition.
Conversely,sometimesthesamesentencecanhavemorethanonemeaning:sentences,like(6),whichcanexpressdifferentpropositions,areambiguous:
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(6)LastnightIshotanelephantinmypajamas.
Grouchodisambiguated(6)byadding,‘AndwhathewasdoinginmypajamasI’llneverknow’.
4 CONTEXTDEPENDENCE:COUNTINGBYSTATEMENT
Somesentencesarecontextdependent,thatis,whattheysaydependsuponthecontextinwhichtheyaresaid,thatis:bywhomtheyaresaid,thetimeorplaceatwhichtheyaresaidorotherfeaturesofthespeaker'ssituation.
Considerthefollowingsentences,asstatedonthedaysindicatedinbrackets(note,thebracketedexpressionsaren’tpartsofthesentencesbutjustindicatewhentheyareuttered):
(7)[statedSeptember11,2014]TodayisThursday.
(8)[statedSeptember12,2014]TodayisThursday.
(9)[statedSeptember12,2014]YesterdaywasThursday.
‘TodayisThursday’iscontext-dependent:whatitsays,inoneway,dependsonwhenitissaid.(7)saysthatSeptember11,2014isaThursday;(8)saysthatSeptember12,2014isaThursday.Butinanotherway,insofaras(7)and(8)expressthesameproposition,theystillsaythesamething:theyhavethesamesenseordictionarymeaning.So‘sayingthesamething’isambiguous.Whenwesaythattwosentences—ortwopeople—aresayingthesamethingwemightmeanthatwhattheysayhasthesamedictionarymeaningor,alternatively,wemightmeanthatthey’reascribingthesamepropertiestothesamebitoftheworld—thatthey’resayingthesamethingaboutthesamething.(7)and(8),utteredonSeptember11and
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September12respectively,havethesamedictionarymeaningbuttheyaren’ttalkingaboutthesamething:they’retalkingaboutdifferentdays,viz.September11,2014andSeptember12,2014respectively.(9),however,issayingthesamethingaboutthesamedayas(7)eventhoughitdoesn’thavethesamedictionarymeaningas(7):todayisyesterdaytomorrow!Themoral:thequestionofwhethertwosentences,ortwospeakers,are‘sayingthesamething’isambiguous—andconfusing.
Toeliminateconfusionbetweenthesetwodifferentwaysofsayingthesamethingweintroduceafussydistinctionbetweenexpressingthesamepropositionandmakingthesamestatement—andunderstandthelatterassayingthesamethingaboutthesamething.(7)and(8)arenotaboutthesamething:(7)sayssomethingaboutthedaySeptember11,2014;(8)saysthesamethingaboutSeptember12,2014.Sowewillsaythattheymakedifferentstatements,eventhoughtheyexpressthesameproposition,thatis,havethesamedictionary-meaning.But(9)makesthesamestatementas(7)so,althoughitexpressesadifferentpropositionfrom(7),wewillsaythatitmakesthesamestatement,namelythatSeptember11,2014isaThursday.
Again,therearenosuchthingsasstatementsorpropositionsasdistinctfromsentencesintheworldontheaccountsuggestedhere.Thereare,onceagain,justdifferentwaysofcountingsentences.Forconveniencewe’vedecidedtousetheterminologyof‘samestatement’and‘sameproposition’torepresentdifferentwaysofgroupingsentences.
5 THEMEANINGOFMEANING
‘Meaning’isambiguous:whenwethinkofthe‘meaning’ofawordorexpressionwhatweusuallyhaveinmindisitssenseordictionarymeaning.Sometimes,though(aswhenIsay‘Imeanyou!’)theword‘mean’meansaboutness,orreference.ThemathematicianGottlobFregemadethedistinctionbetweensenseandreferenceinhisarticle‘AufSinnundBedeuting’(‘OnSenseandReference’)Wecanunderstandsenseasdictionarymeaning,aswhenwesay,“’bachelor’means‘unmarriedmalewhoneverhasbeenmarried.’Referenceisaboutness,orpicking-out—meaningasin‘Imeanyou!’Crudely,wecanthinkofthesenseofawordastheidea(thoughFregearguedthatsenseswerenotideasintheheadbutabstractpublicobjects!)Thesenseofawordiswhatpeoplewhounderstandthatwordgrasp,butwhichpeoplewhodon’tunderstanditdon’tgrasp—whatweordinarilythinkofasthemeaningofaword.Thereferenceofawordisthethingitpicksout.
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Englishandothernaturallanguagesincludeavarietyofindexicals,wordswhosereferencechangessystematicallydependingwhere,when,bywhomorinwhatcircumstancestheyaresaid.Theseincludepronounslike‘I’,‘you’,‘she’and‘he’,demonstrativesincluding‘this’and‘that’,andawholerangeofotherwordsincluding‘here’,‘there’,‘today’,‘yesterday’andsoon.Thesewordsdon’tchangetheirsensewhenutteredbydifferentpeopleatdifferenttimesorplacesorindifferentcircumstances.‘I’alwayshasthesense,‘thefirstpersonsingular’,butwhenutteredbydifferentpeopleitreferstodifferentpeople.Thesenseof‘here’is‘thevicinityofthespeaker’buttheword‘here’picksoutdifferentplaceswhenutteredbyspeakerswhoareatdifferentplaces.
Dog
Sense
Reference
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‘Here’inanindexical:theplaceitpicksoutdependsonwherethespeakeris.Sotheseguysaren’tdisagreeing:they’retalkingaboutdifferentplaces!
Indexicalsmakesentencesinwhichtheyoccurcontext-dependent.Andwhensentencesarecontext-dependentyoucanhavesameproposition/differentstatementordifferentproposition/samestatement.(1),(2),and(5)arenotcontext-dependent:theyallexpressthesamepropositionandmakethesamestatementwherever,whenever,inwhatcircumstancesandbywhomevertheyarespoken.
(1)JohnisPaul'sbrother
(2)JohnisPaul'sbrother
(5)JohnisthemalesiblingofPaul
(7)-(9)arecontext-dependent:thestatementstheymakedependonthecontextinwhichtheyarespoken,inparticular,thedateonwhichtheyaresaid.
(7)[statedSeptember11,2014]TodayisThursday.
(8)[statedSeptember12,2014]TodayisThursday.
(9)[statedSeptember12,2014]YesterdaywasThursday.
Onceagain,don'taskwhattypesandtokens,statementsandpropositions‘really’are—becausetheyaren’t!Talkingaboutthemasiftheywereobjectsalongsideindividualsentencesisconvenientbutmisleading.Insteadweshouldthinkofcountingbysentencetoken,sentencetype,propositionandstatementasdifferentwaysofcountingthesameitems—likecountingagroupofstudentsbyindividualstudent,bymajor,byclassyear.
Sentencesmaybothexpressthesamepropositionandmakethesamestatement.Andsometimestheydo.Butsometimestheydon’t.
It’scoldhere!
It’snotcoldhere!
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THEMORALOFTHESTORY
Whenweaskwhethertwospeakersare‘sayingthesamething’weneedtobeclearaboutwhatwe’reasking.Areweaskingwhetherthey’reexpressingthesameproposition?Whetherthey’remakingthesamestatement?Orwhetherthey’reutteringthesamenoises(ormakingthesamemarks).
5.1 SOWHATKINDOFQUESTIONSCOULDTHEREBEONATESTABOUTTHIS?
Anexampleofaquestiononcountingbysentencetoken,sentencetype,statementandproposition(fromapasttest):
TrueofFalse?(seetheCinderellastoryabove)
___1 CinderellaandUglyareutteringthesametypesentence.
___2 CinderellaandUglyareutteringthesametypesentence.
___3 CinderellaandUglyareexpressingthesameproposition.
___3 CinderellaandPrincearemakingthesamestatement.
___4 CinderellaandPrinceareexpressingthesameproposition.
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6 THEPUZZLEABOUTNECESSARYTRUTHS
Nowthatwe’vedistinguishedbetweendifferentwaysof“sayingthesamething”we’reinapositiontoreturntothepuzzleaboutnecessarytruths,whichrecall,wentlikethis:
Howcananythingbelogicallyimpossible...orlogicallynecessary?!!?Wecanalwaysdescribea"world"inwhichagivenstateofaffairsobtains,ifwe'reclever.Take"allbachelorsareunmarried":Icandescribeaworldwere"bachelor"means"maleunder30"andsuchaworldisoneinwhichtherearemarriedbachelors,right?Similarly"2+2=4"and"2+2=5":it'sjustamatterofhowyoudefinethesymbols,right?
Thisargumentcanbegeneralized:itiscontingentthatanygivenwordhasthesenseitdoes:wecanchangelanguagesoitseemstherecanbenonecessarytruths!Butthisiscrazy:changinglanguagedoesn’tchangetheworld!Sowehavetorespondtothisthreat!
Canwereallyconceiveof,orcoherentlydescribe,aworldatwhichtherearemarriedbachelorsorwhere2+2≠4?Recallthatwhenwearguedthat‘SanDiegoisinCalifornia’wascontingentweweren’tinitiallysuccessfulintellingastoryaboutapossibleworldatwhichourfaircitywassomewhereelse.Ourfirstattemptwas,rather,astoryaccordingtowhichtherewasacitynamed‘SanDiego’inTexaswhich,itturnedout,wasadifferentSanDiegofromtheoneweknowandlove.Thismeansthatwe’vegottabecareful:sometimeswethinkwe’reimaginingapossibleworldofacertainkindwhenwe’rereallyimaginingadifferentkindofpossibleworld.
This,Iclaim,iswhat’sgoingonwhenwethinkwe’reimaginingapossibleworldatwhichtherearemarriedbachelorsoroneatwhich2+2=5.Youmaythinkthatw*isapossibleworldatwhich2+2=5...
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Butthinkagain.Arguablyw*isaworldatwhichspeakersmakethenoises(andwritethemarks)‘2+2=5’tomeanwhatwemeanwhenwesay‘2+2=4’!ThenumberEnglish*speakerscall‘5’isadifferentnumberfromthenumberwecall‘5’thathappens,intheirlanguage,tohavethesamenameasthenumberwecall‘4’.Toshowthat‘SanDiegoisinCalifornia’wascontingentweneededtodescribeapossibleworldinwhichthiscitywassomewhereelse—notaworldinwhichtherewasacitysomewhereelsethathappenedtohavetosamename.Toshowthat‘2+2=4’wascontingentwewouldhavetodescribeapossibleworldinwhichthenumberswetalkaboutwhenwesay‘2’and‘4’don’taddup—notapossibleworld,likew*,wheredifferentnumbershavethesamenames!
WhenEnglishspeakersandEnglish*speakerssay‘2+2=5’theydon’tmeanthesamething.Theyaren’tsayingthesamethingintherequisitesense,thatis,theyaren’texpressingthesameproposition.
English-SpeakerandEnglish*-Speakerareexpressingthesameproposition(andmakingthesamestatement)eventhoughtheyareutteringdifferenttypesentences!Thesesentencesinthosetwodifferentlanguageshavethesamesense.
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Soin‘moving’fromtheactualworldtow*,shiftingfromEnglishtoEnglish*,wedon’tchangethemathematicalfactthat**+**=****istruebut**+**=*****isfalse.Wejustchangethensubjectsotospeak.We’renolongertalkingaboutthemathematicaltruththat**+**=****:we’reexpressingthemathematicalfalsehoodthat**+**=*****Thefirstistrueatallpossibleworlds;thesecondisfalseatallpossibleworlds.Mathematicalpropositionsareeithernecessarilytrueornecessarilyfalse,evenifitisacontingentmatterhowweexpressthem!
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STUDYQUESTIONS
1 InordinaryEnglish‘identical’and‘same’areambiguous:sometimeswemeansametype,othertimeswemeansametoken.Giveexamplesofsituationsinwhichwemeansametypeandsituationsinwhichwemeansametoken,e.g.whatdowemeanwhenwetalkabout‘identicaltwins’?
2 Giveanexampleofasituationinwhichdifferentsentencescanbeusedtoexpressthesameproposition.[synonomy]
3 Giveanexampleofasituationinwhichthesamesentencemaybeusedtoexpressdifferentpropositions.[ambiguity]
4 Giveanexampleofasituationinwhichsentencesthatexpressthesamepropositionareusedtomakedifferentstatements.
5 Giveanexampleofasituationinwhichsentencesthatexpressdifferentpropositionsareusedtomakethesamestatement.
