35

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:

36

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

37

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).

38

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’.

39

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:

40

(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

41

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.

42

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

43

‘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!

44

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.

45

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...

46

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.

47

Soin‘moving’fromtheactualworldtow*,shiftingfromEnglishtoEnglish*,wedon’tchangethemathematicalfactthat**+**=****istruebut**+**=*****isfalse.Wejustchangethensubjectsotospeak.We’renolongertalkingaboutthemathematicaltruththat**+**=****:we’reexpressingthemathematicalfalsehoodthat**+**=*****Thefirstistrueatallpossibleworlds;thesecondisfalseatallpossibleworlds.Mathematicalpropositionsareeithernecessarilytrueornecessarilyfalse,evenifitisacontingentmatterhowweexpressthem!

48

STUDYQUESTIONS

1 InordinaryEnglish‘identical’and‘same’areambiguous:sometimeswemeansametype,othertimeswemeansametoken.Giveexamplesofsituationsinwhichwemeansametypeandsituationsinwhichwemeansametoken,e.g.whatdowemeanwhenwetalkabout‘identicaltwins’?

2 Giveanexampleofasituationinwhichdifferentsentencescanbeusedtoexpressthesameproposition.[synonomy]

3 Giveanexampleofasituationinwhichthesamesentencemaybeusedtoexpressdifferentpropositions.[ambiguity]

4 Giveanexampleofasituationinwhichsentencesthatexpressthesamepropositionareusedtomakedifferentstatements.

5 Giveanexampleofasituationinwhichsentencesthatexpressdifferentpropositionsareusedtomakethesamestatement.