Carnap. Hall and Bergmann on Semantics

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Hall and Bergmann on SemanticsAuthor(s): Rudolf CarnapReviewed work(s):Source: Mind, New Series, Vol. 54, No. 214 (Apr., 1945), pp. 148-155

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IJL-DISCUSSIONS.HALL AND BERGMANN ON SEMANTICS.

PROFESSORs EverettW. Hall1 andGustavBergmannoftheStateUJniversityf owa haverecentlyublished apersdiscussingeman-ticsas developedn a book ofmine.3 Thefollowingommentsreintended o clarifyomepointswhich eem to me to have beenmisconstruedn thesepapers. Thesepoints oncernthe nature fpuresemanticsnd, in particular,heproblem f extra-linguistic

reference. 1.

By semantics' understandfollowing lfred arski nd CharlesMorris) hetheoryftherelations etween xpressionsn a languageand theirdesignata,.e., the objects,properties,elations, tc.,towhichthe expressionsefer.Among he semantical ules foraconstructedymbolic anguage ystem dealtwith n what I call" pure emantics) theremay, .g.,be a rule1) stating hat certainsign, ay the letter a ', designates hicago, nd another ule 2)

statinghata certain ther ign, ay the etter P ', designateshepropertyfbeing arge. Other emantical uleswilltellus howtointerpretsentencefweknow he designata fthe signs ccurringin it. Thus, e.g.,we shall learn thatthe sentenceP(a)' of oursymbolicanguage ystem aysthatthe object designated y thesign a' hasthepropertyesignated y p '; hence,nviewoftherules 1) and (2), 'P(a) ' says thatChicago s large. It can theneasily eshownhat he onceptf ruth ith espectothe ymboliclanguagen question an be definedn (pure) emantics. n orderto avoidsome echnicalomplexities,willnotgivehere hedefini-

tion n itsgeneral orm. It seems lausible hat, fthedefinitionsconstructedn a suitableway, t will ead to the followingesultsa particularnstance; the sentence P(a) ' is true f and only fChicagos large, hat s to say, fthe physicalworldwe see aroundus is such that Chicago, hatwell-knownomplex hysical hingconsistingfhouses, treets, tc., s large. So much s stated n(pure) emantics.However,hetaskoffindingutwhetherrnotChicagos large, ndthereby hetherrnotthesentenceP(a) ' istrue,s nota task of semanticsutofempiricalcience. Semanticshas

theasknot f

act-findingut

finterpretinglanguage.lthoughlimitedothis ask, emanticsoesand must eferoextra-linguisticentities,.g.,physical bjects, heir ropertiesnd relations. Thisis clear romhe xamplesmentioned: ule 1) refersn theonehand

1E. W. Hall, " The Extra-Linguistic eferencefLanguage,Part II:Designation f the Object-Language, MND, vol. liii, 1944, No. 209,pp. 25-47.

2 G. Bergmann, Pure Semantics, entences,nd Propositions, ibid.,No. 211,pp. 238-257.

8 R. Carnap,ntroduction oSenantics, 1942.







RUDOLF CARNAP: HALL AND BERGMANN ON SEMANTICS. 149

toa certainign, uton theothero thething hicago, nd tstatesa certain elation etween he sign and the thing; analogously,

rule 2)refersotonly o a sign ut lsoto a certain hysicalroperty,viz., hatof being arge; and, he semanticaltatementiven bovewhich tates truth-conditionor he sentenceP(a) ' refers ntheone handto this entence, ence o something ithinhe anguage,buton theother and othe tateof ffairsor possible act rwhatelseyouwant o call t) ofChicago's eing arge, ence o somethingextra-linguistic.

In mybook haveexpoundedn detail he nature f emanticssbrieflyutlined bove. I haveespeciallymphasizedts distinctionfrom yntax Morris' syntactics) ; while the atterdiscipline

dealsonlywithrelationsmong xpressionsn a language ndthuswith an entirelyntra-linguisticubject-matter,t belongs o theessentialcharacteristicsf semantics hat it refers ot onlytolanguagebut also to extra-linguisticatter. The book does notonly tateand emphasizehischaracteristicn abstract erms, utalso illustratestbya greatnumberfexamples fsemanticalulesforvarious anguage ystems,uch as the two rulesgivenabove,and of semanticaltatementsoncerningruth, s in the exampleabove, nd other emanticaloncepts.

2.In viewofthese actst will eemunderstandablehat felt ome

surprise-orhould rather ay" amazement ?-when I sawthatProfessor all in the papermentionedomes o the conclusionhat(pure) emantics,s I constructt andapply t,doesnotandcannotrefer o anything xtra-linguistic,ut deals onlywithrelationsbetween xpressionsn a language, nd thatall appearance o thecontrarys merely ue to somecareless,misleadingormulationsfmine. Thisresult s not stated s an incidentalemark,ut rather

as thechief hesis na lengthyiscussionloc. cit., p. 25-36) fmybook,reiteratedgainandagain nvarious orms. I willgiveonlya few xamples fformulationsn wbichHall ascribes o meviewswhich re just theopposite f my conceptionfsemantics. Theitalicsand insertionsn parenthesesre Hall's; the insertionsnsquarebrackets re mine.) " Carnapmeansto ruleout all con-sideration f thedesignationf' ero-levelxpressionsi.e., expres-sions n theobject-language,ike a ' and' P '], i.e.,of ny xpressionssavethenames fexpressions (p. 25 f.). " Pure semanticsannotsay anything boutthe designationr truth fany expressiont

zero-levellike a', ' P ', ' P(a) '], forto do so would nvolve nassertionhowever eneral nd abstract) boutmatter ffactaswell as aboutlanguage, nd wouldthereforee descriptive.Thisconclusionthoughxplicitlymine) eems o be fairly rawn; thatis, Carnap eems o accept t" (p. 27). "Designation s whollyrelationwithinthe anguage ystem] , thereforeithin language(semantical)ystem,hereforeota relationf anguage r inguistic







150 RUDOLF CARNAP:

elements o extra-linguisticact (p. 27). "The key dea is thatdesignations to obtainbetween woexpressionsn a metalanguage.. .

.No extra-linguisticeferencef

anguagesconsidered (p. 27,footnote ). " Carnap . . means hatpure emantics,n studying

truth,s confinedopropositionsssertinghe truth-)equivalencefsentencest differentevels (p. 28). "lHe is sayingnotthatwecanpredicateruth nlywhenwe know herelation f a zero-levelsentencelike P(a) '] to fact,butquitetheopposite,hatwe canproperly redicateruth nthe basisof inguisticsemantical)ulesalone:" (p. 29); comparewiththisthe followingassagein mybook p. 33): " Thuswehave found truth-conditionor a certainsymbolicentence]n [the anguageystem]3 as determinedy the

[semantical]ules fS3. Butthese ules onot sufficeo determinethe truth-valuei.e., ruth rfalsity]f that entence]. In order ofind his,we mustknow ertain acts naddition otherules. Thiswould ead us outside f semanticsntoempiricalcience,n thiscase into geography."Hall says furtherp. 34): " I thinkhe[Carnap]wouldsimply dmitthat semantics annotescape thelinguacentricredicament. emanticsrearbitrarilyrbyconven-tionaldivision f labourconfined o language in its designativeaspects) s abstracted romll matter ffact,he might laim."

OnceHall is convincedhat intend o restrictemanticsointra-linguisticmatter nd,in particular,he relation fdesignationopairsofexpressions,e proceeds o give a newand strangenter-pretationothose fmyformulationshichmanifestlypeak boutextra-linguisticntities;hebelieves imselfompelledo reject henatural,iteralnterpretationecause hiswouldviolatemy llegedprinciplef restriction. e says p. 30) : " Thusthedesignata f4u ' and 'p ' mightbe thought o be extra-linguistic.. . This,however, ould learly resupposehatexpressions. . [can desig-natel thesame extra-linguisticntity,nd is thussubjectto the

criticismfthat ssumption enoted bove,namely hat tviolatesCarnap'srestrictionf designationo pairsof terms." However,there replaceswheremy eferenceso objects, roperties,nd otherextra-linguisticntities re so clear and explicitthat not evenartificialeinterpretationilldo. In these xtremeasesthere s nootherway eft han uggesting " correctionof myformulations.For instance, all quotes p. 29,footnote ) thefollowingentencefrommy book (p. 24) "The objectdesignated y . . . has thepropertyesignatedy- - -" (where echnical ames fsigns tandat theplaceofthe dots nddashes). Onemighthink tdifficulto

maintainnviewofthis entencehatmysemanticsever efersoobjects and properties.But not so forHall; he simply ssumesthat didn'tmean t. He saysthat he entenceuoted is a littlemisleading. n placeof object ' object-sign'wouldbe less mis-leading,and in place of 'property ' property-sign." Conse-quently, e translateshesentenceuoted nto" theobject-signasthepredicate-signttached o it"; and this,he thinks,s what







HALL AND BERGMANN ON SEMANTICS. 151

actuallymeant. The same methods againapplied ater p. 32).Hall quotesmyheading p. 128) "'Proceduresfthe secondkind:

theelementsfL-ranges re extra-linguistic. How is thiscom-patible with the thesisthat semantics everrefers o anythingextra-linguisticSimple gain; youbave merelyo assume hatI meantby the termextra-linguistic'omethingntra-linguistic.Hall says: " Carnap's heading . . is misleading. nstead of' are extra-linguisticit shouldread are symbolswhosedesignataare extra-linguistic'r are syinbols fthezero-level." Thushehas again provedhispoint hat mysemanticalheory eals exclus-ivelywith expressionsnd neverwithobjectsor properties ranythingutside f anguage. His argamentations quite rrefut-

able. I recommendo all philologistshisfar-reachingethod orascertaininghat n author ctuallymeans; ifwe were o apply tto his own tatementp. 39) " WithRussell's olution fhisproblemI disagreewholeheartedly, we could readilyestablish hat heactuallymeant o say that he agreed ompletely.

How is thisprofusionf thoroughmisunderstandingso be ex-plained I wish oemphasize irst fall that hey recertainly otdue to careless eading r rash and dogmatic onclusionsn Mr.Hall's side. Onthecontrary,he discussionnhispaper s markedby careful nd conscientiousrocedure.He saysrepeatedlyhatthe nterpretationt whichhe arrivess his mpression,isfeeling,hisconclusion. He admits hat he maybe mistakenn this nter-pretation. Severaltimes he considers lternativenterpretations(thechief neof hese soutlinednp. 26; I agreewith im hat hisisnotwhat meant); andonly fterengthyeliberationfreasonspro and condoeshe accepthis nterpretation.

As I see t,theexplanationis tobe foundn thefact hatMr.Hallmakesone initialmistake, light n appearance ut seriousn itsconsequences.After his, ll bis derivations,areful hough hey

are, ead himto more nd more rrors. Even the oneoriginal inicannotbe ascribed o carelessness; t consistsn continuinghetraditionf certainonfusionfwhich omeof he bestmen nthefield f ogichave beenguilty.

One ofthefundamentalistinctions hichmustbe madewheinspeaking boutlanguage s thatbetween sing n expressionndreferringo it. When say: " Chicagos a large ity , I amusingtheword Chicago'; I am referringot to this wordbut to thethingwhosename s thisword, iz.,the cityofChicago. On theother and, f wish orefer o thewordChicago', e.g., norder o

saythat tconsists f evenetters,must senot heword Chicago'buta namefor t. I may, .g., ntroducec ' as a namefor heword' Chicago'; then canexpress heaboveassertion y means fthesentence: "c consistsof seven letters . A simpler nd morecustomaryrocedureor onstructingnamefor linguisticxpres-sion consists n simplyncludinghe expressiontself n quotationmarks. Thus wemay ay: ' Chicago' consists fseven etters.







152 RUDOLF CARNAP:

It does not matterwhichmethod orconstructingname foraniexpression e use; theessential oint s that we use a name forthe

expressionndnot the

expressiontselfwhenever e intend o

speak abouttheexpression. f we do otherwisee.g., fwe say:" Chicago onsists f seven etters), then the expressions usedambiguously,nd manycoinfusionsre apt to arise. At the firstblush, he distinctioneems minormatter nd to urge t seemsratherpedantic. However, t is in fact a veryseriousmatter.Frege first mphasized he necessity f the distinction;andrecently arski,2 uine,3nd I 4 haverepeatedlyalledattentionothesamepoint. It hasb6en hown hatthe neglect f the distinc-tion n the Introductiono PrincipiaMathematicaas made many

pointsobscure nd ambiguous nd in somecases has even causedserious onfusionnd errors. Certain ater authors,who followedthe example fWhitehead nd Russellrather hanthatofFrege,have created tillmore onfusionsnd errors.

The onefundamental istakemadebyHall is justtheneglect fthis distinctionetweenusingan expressionnd referringo it.Consider he semantical ule: " 'a ' designatesChicago . Therule aysthat herelation fdesignationoldsbetween woentities,which re specifiedn the rule. What are these woentities? Wefindntherule tthefirstrgument-placei.e., t theplaceprecedingtherelation-worddesignates) thenameofa sign. (In the aboveformulationhisname s builtwith he helpofquotationmarks; inmybook, use instead ertainGermanetterswhich re ntroducedas technical amesofsigns; thisdifferences inessential,s men-tionedbefore). Therefore, hat s referredo in thefirst lace isthe sign whose name occurs,viz., thefirst etterof the Roman lowercase alphabet. At the secondargument lace (i.e., followingheword designates) wefind heword Chicago. Therefore,hat sreferredo inthe econd lace-and this s thedecisive oint-is the

entity hosenameoccurs t the econd lace; this ntitys notthewordChicago but the physicalhing hicago. Thus we see thatthe rule as formulatedbove can be interpretedn onlyoneway;it says that in the symbolicanguage ystemn question) hefirstletter f he lphabet esignatesthat s, s used sname f)the hingChicago. In additiono examples frules fdesignationike heoneabove, have givenn mybooka general escriptionftheformftheserules D12-B, p. 53); thisdescriptionays that, s we haveseen nthe example bove, henameof an expressiontands t thefirst rgument-placei.e., the place precedinghe relationword

1G. Frege,Grundgesetze,ol. , p. 4.2A. Tarski, ntroductionoLogic, 18; see also the useful xercises 4

and *5 on p. 65.9 W. V. Quine,Mathematicalogic, 4 ; seealso the footnote np. 283.

-Quine, " Whitehead nd the Rise ofModern ogie" (in ThePhilosophyofA. N. Whitehead,d. A. Schilpp, p. 127-163), ee pp. 142, 145, 151f.

4Carnap,LogicalSyntax, 42. IntroductionoSemantics, p. 236 f.







HALL AND BERGMANN ON SEMARTICS. 153

'designates), and another xpressionabovethewordChicago )stands t thesecond rgumentlace; and it saysfurthermorehat

thesecond xpressions thetranslationnto hemetalanguagehere,English)ofthat expression hosename stands t thefirst lace.(In our xample,heword Chicago is theEnglish ranslationf hesigna '.) To sum tup, theruleuses t the twoargument-places,name f sign ndanexpression;t referso sign nd a thing. Byconfusingseofan expression ith eferenceo an expression,allarrives t theerrolneouseliefhatdesignations a relation etweentwo expressions. Rules of designationf the form 'Chicago'designates hicago or "'a' designates " seemto Mr. Hall stillmorepuzzling. Rulesof thisform,t is true, o not conveymuch

information; utthedecisive oint s that they oo contain xtra-linguistic eference.The first ule says that theword Chicagodesignateshething hicago,ndthe second ays thatthe sign adesignateshething .) Hall's inferences justas fallaciouss thefollowing ould be: "The sentenceJack is olderthanPeter'containswonames fpersons;thereforehis entencepeaks boutnames nd not aboutpersons". It seems o me thatall ofHall'smisinterpretationstemfrom he onebasicmistake havetried oindicate. Thismistake learly nderlieshewholefirst artof hisdiscussionpp.25-28). It is most xplicitlyormulatedtthefollow-ing two places. 1. Discussingmy generaldescriptionf rulesofdesignationD12-B),Hall says p. 27,footnote): " Thekey deais thatdesignations to obtainbetweenwo expressionsn a meta-languagewhen hefirsts thename ofan expressionfwhich hesecond s a translation.... But what s named nd translateds a,linguisticxpression.No extra-linguisticeferences considered."2. In mybook have sometimessed, nstead ftheformulation" ' P ' designates he propertyf being arge (e.g., p. 24), theshorter ormulation ' P ' designatesarge (? 12); the latter

formulations moreconvenient,hough dmittedlyot in accord-ance withcustomarynglishgrammar.This shorter ormulation.does not nvolve ny ambiguityecause heuseornon-usefquota-tionmarksmakes lways learwhether e speakof heword largeor of thepropertyarge i.e., the propertyfbeing arge). Hallmakesherethesame mistake s before; he ignores hefactthat,althoughlarge' is certainly word, argecannotpossibly e a,word. He says p. 28): " Carnap's xamples: 'Gross inGermandesignateshesame entitys 'IP' in his[languageystem]3, ViZ.,large. But here argemust e a word inEnglish) ota propertyf

fact. For, designates' in " 'Gross' designatesarge and "P'P'designatesarge is defined y pairsofexpressions'Gross , large;' P ), large) hefirstmembers f which re namesofexpressionsfwhich he secondare translations, encethe designatumn each(large) s an expression. . . So againwe find hatonlynamesofexpressionsre allowed o designate,nd theycan onlydesignateexpressions."Thus we see in bothpassagesherequoted,howthe







154 RUDOLF CARNAP:

inistake which I have called the basic one leads to further rrors,first o the conclusion hat the designatum n the case in question isan expressionwhile in fact it is an extra-linguisticntity, nd thento the general onclusion hat semanticsdoes not make any referenceat all to extra-linguisticmatter. It could easily be sbown that allthe numerousothermisunderstandingsf myformulations nd theindependent rrorsn Hall's paper, of which a fewhave been quoted,earlier, rowout of the same root.

3.

In the articlementioned bove, ProfessorBergmana discussesthe

nature and functionof pure semantics as developed in my book.iSome pointsin his discussionare interesting, therparts I findhardto understand. Unfortunately,his discussion also involves someserious misunderstandings nd errors. Since they are similar tothose of Hall discussedabove, I can be briefhere. Bergmanngivesthe following haracterization fpure semantics,which seems to me,to say the least, very misleading: " Meta-languages of the kind. are called semanticalmetalanguages. Pure semantics is the

.study of such metalanguages formallyconsidered (p. 246). 1,should preferto say that pure semantics is the study of object

languages,not ofmetalanguages, nd further,hat it is not a formalstudy but a studyofinterpretation. I am not certainwhether hepassage quoted is merelyan inadequate formulation r whether tshows an actual misunderstanding f the nature ofpure semantics.The following ointsseemto make the latteralternativemore ikely.

Bergmann says: " The one domain of these predicates [therelational predicates of designation] consists of the names of the.expressions fthe object language,the otherdomain,ofthemetalin--guisticnames of the referents designata] of those expressions"-(p. 245). This seems to me a confusion between names and theentitiesnamed; in fact-as earlierexplained in a discussion of therule " 'a' designates Chicago "-the firstdomain contains expres-sionsofthe object language (e.g.,the sign a '), not theirnames, and-thesecond domain containsthe designata ofthose expressions e.g.,the thingChicago), not theirnames. On thebasis ofthis misunder-standing,Bergmann rrives,n a way similar o Hall's, at the absurdconclusion that puresemanticsdoes not deal with theextralinguisticreferents,he designata" (p. 248). A confusion fthe same kindasthatmentioned bove is to be found nthefollowing assage (p. 252):

"In the statement:(3) 'Fido is a dog' is trueifand onlyif (Fido is a dog). Carnaprefers o the quoted expressionas a sentence, while the bracketedexpression s called a proposition." In fact,presumably ike mostother logicians, I call the quoted expressiona name of a sentenceand the bracketed expression sentence; in the book under discus-sion, I do not apply the term proposition to sentencesor to any







HALL AND BERGMANN ON SEMANTICS. 155

otherexpressions.Bergmann elieves rroneouslyhatmy terms' proposition',individual',and designata, " ifthey reto occurin pure semantics, o not refer o any extralinguisticeferents"(p.252). Thefact hatmy hoice f hese ermsndtheformulationsin which use them how learlyhat intendo referoextralingu-istic ntitiess explainedwayby Bergmann,ustas byHall,bytheassumptionhatmyformulationsointaina misleadingerminologyand certainmbiguities(p. 238, imilarly.252). This ssumption,however,s merelyhe outcome fBergmann'smisunderstanding,as the example fthe termpropositiotn'hows.

4.

My remarksnHall's andBergmann'sapersmaybe summed pas follows.

(a) The two authorsfail at some crucial pointsto make thenecessaryistinctionetween se and mentionf an expression,notherwords, etweenn expressionnd-its ame.

(b) Consequently,heynterprethat sayaboutrules fdesigna-tion as iftheexpressionssed n theseruleswere xpressions en-tioned; thus hey ome othe rroneousonclusionhat hedesigna-tum salways n expression.

(c) Consequently,heybelieveerroineouslyhat pure semanticsdoesnotrefer o extra-linguisticatter.When saythatcertain fmyformulationsfsemanticaltate-

ments nd ruleswere ntended o refero extra-linguisticntities,expect hatHall andBergmann illconcede hispoint, ecause tisgenerallygreed hat n author s thefinaludge na question s towhathemeant osay. Ontheother and, n authors not hefinaljudge n a question s to whathe didactually ay, .e.,whetheresucceededn formulatinghathe intendedo say. (For instance,whenHallwritesp. 26, ine17): " thatA designateshatmatter ffact , I wonderwhether e did notactuallymeanto say: " that' A' designates . .".) Therefore, all and Bergmann ave todecidewhetherheywillagreewithmewhen saythat the nter-pretationfmyformulationss referringo extra-linguisticntitiesis theonly orrectne andthattheirnterpretationsre basedonaconfusionfuseandmentionf an expression. have often oundthatfor hosewhohave acquired hehabit of thisconfusiont isveryhard vento recognizet. But I tbink hatall thosewhoarefree fthis onfusion,n otherwords,hosewhodistinguishlearly

betweennexpressionnd tsname,will greewithmeonthispoint.'-Just afterhavingwrittenmy comments, findthat ErnestNagelcomesto a similar onclusion. In hisreview fHall's paper Journal fSymbolic ogic,vol. ix, 1944,p. 46), he says: " This is an unfortunatemisunderstandingf Carnap's language,and in consequence he entirediscussion f semanticsuffersrom fundamentalgnoratiolenchi."

RUDOLF CARNAP.

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