35 CHAPTER 2: SAYING THE SAME THING ’What is your aim in philosophy?—To shew the fly the way out of the fly-bottle.’ ‘A picture held us captive. And we could not get outside it, for it lay in our language and language seemed to repeat it to us inexorably’. In ordinary English, we use the terms ‘sentence’, ‘statement’ and ‘proposition’ interchangeably but for some purposes we'll want to distinguish between them. In particular, when it comes to deciding when people are ‘saying the same thing’ we shall distinguish between the question of whether they are uttering the same sentence, making the same statement or expressing the same proposition. 1 DIFFERENT WAYS OF COUNTING Sentences, statements and propositions are not three different kinds of things: the question of whether we have the same sentence, same statement or same proposition signals different ways of counting the same things. We can count things in different ways by grouping them according to different features. Counting in the most fine-grained way—‘counting by token’—every individual object counts as one. There are 10 individual pieces of fruit here: But we could also count fruits by kind: counting in this way, by fruit type, there are three fruits here: apple, cherry and avocado:
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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.
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