frege, f.l.g. on concept and object

8/13/2019 Frege, F.L.G. on Concept and Object.

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Mind Association

On Concept and ObjectAuthor(s): Gottlob Frege, P. T. Geach, Max BlackSource: Mind, New Series, Vol. 60, No. 238 (Apr., 1951), pp. 168-180Published by: Oxford University Presson behalf of the Mind Association

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II.-ON CONCEPT AND OBJECTBY GOTTLOBFREGE(First published n the Vierteljahrsschrifti4rwissenschaftlichePhilosophie,6 (1892): 192-205.)

Translation yP. T. GEACH. (RevisedbyMAXBLACK.)192] In a series farticlesn this Quarterlynintuitionnd itspsychical laboration, ennoKerryhas several imesreferredomyGrundlagenerArithmetiknd otherworksofmine,some-times greeingnd sometimes isagreein,githme. I cannotbutbe pleased at this,and I thinkthe best way I can showmyappreciations to takeup thediscussionf hepointshecontests.This seemsto meall themorenecessary, ecause his oppositionis at leastpartlybased on a misunderstanding,hichmight esharedbyothers, fwhat sayaboutthe concept; andbecause,even,partfrom his pecialoccasion, hemattersimportantnddifficultnoughfor more horoughreatmenthanseemedtome suitable n myGrundlagen.Theword concept is used n variousways; itssense s some-timespsychological,ometime,ogical, nd sometimes erhapsconfusedmixture f both. Sincethis icence xists, t is naturalto restrictt byrequiringhatwhenoncea usage is adopted tshallbe maintained. What I decidedwas to keep strictlyo apurelyogicaluse; thequestionwhetberhisorthatuse ismoreappropriates one that I should iketo leave on one side,as ofminormportance.Agreementbout themodeofexpression illeasilybe reachedwhen onceit is recognizedhatthere s some-thing hat deserves specialterm.It seems omethatKerry'smisunderstandingesults rom isunintentionallyonfusing is ownusage of theword concept'withmine. This readilygivesriseto contradictions,orwhichmyusage s notto blame.193] Kerrycontestswhathe callsmydefinitionf concept'.I would remark,n the first lace, thatmyexplanation s notmeant as a properdefinition.One cannot require hat every-thingshall be defined,ny more than one can requirethat achemistha,ll ecomposevery ubstance. What ssimple annotbedecomposed,ndwhat s logically imple annothave a properdefinition.Now somethingogically imple s no moregivenus168


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GOTTLOB FREGE: ON CONCEPT AND OBJECT 169at theoutset hanmost f hechemical lements re; it sreachedonly by meansof scientific ork. If something as been dis-covered hat s simple, r at least must count as simplefor hetimebeing,we shallhave to coina term or t, since anguagewillnot originallyontain n expressionhat exactlyanswers. On'the ntroductionf namefor omethingogically imple, defini-tion snotpossible; there s nothing or t but to lead thereaderor hearer,by means ofhints,to understand he words as isintended.Kerrywould ike to say thatthe distinction etween onceptand object s notabsolute. "In a previous assage.",hesays,"Ihavemyselfxpressed heopinion hat the relation etween hecontent f the conceptand the concept-objects, in a certainrespect, peculiar nd irreduciblene; butthis was in no wayboundupwith heview hatthepropertiesfbeing concept ndofbeingan object are mutually xclusive. The latterviewnomoie follows rom he fQrmerhan t wouldfollow, f,e.g.,therelationoffather nd son wereone that couldnot be furtherreduced, hat a man couldnot be at once a father nd a son(though f coursenote.g.father fthe man whose orn e was)."Let us fasten n this imile Iftherewere, rhadbeen,beingsthatwerefathers ut couldnot be sons,suchbeingswouldob-viously equitedifferentn kind romll men,who re sons. Nowit is somethingikethisthat happenshere. The concept as Iunderstandheword) s predicative.' On theother and, nameof an object,a propername, is quite incapableof being usedas a grammatical redicate. Thisadmittedly eeds elucidation,otherwiset might ppear false. Surely one can just as wellassertofa thing hat t is Alexander he Great, r s the numberfour, r s the planetVenus, as that t is green r is a maimmal194] Ifanybody hinks his,he is not distinguishinghe usagesofthe word is '. In the ast two examples t serves s a copula,as a mereverbal ign fpredication. (In this ense the Germanword st]can sometimese replacedby the merepersonal uffix:cf.diesBlatt stgrin and diesBlatt rimnt.)n sucha case wesaythatsomething allsunder concept,nd the grammatical redi-catestandsfor his concept. In thefirst hree xamples, ntheotherhand, is ' is used ike the equals sign n arithmetic,oexpress n equation.2 In the sentence The morning ter is

1 It is, nfact, hereferencef a grammaticalredicate.2 Juse theword equal' and thesymbol = ' in the sense the sameas', ' no other han', 'identicalwith'. Cf.E. Schroeder,Vorlesungenueber ie Algebra erLogilc Leipzig,1890),vol. 1, ?1. Schroedermusthowever e criticizedornotdistinguishingwofundamentallyifferent12


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170 GOTTLOB FREGE:Venus , we have twoproper ames,morning tar and 'Venus',for the same object. In the sentence the morning tar is aplanetwe have a proper ame,' themorningtar , and a concept-word, planet'. So far s languagegoes,no morehas happenedthanthat Venus has been replacedby a planet ; butreallytherelation as becomewhollydifferent.An equation s rever-sible; anobject'sfalling nder concept sanirreversiblerelation.In the entencethe morningtar s Venus , is 'is obviously otthemere opula; its content s an essential art ofthepredicate,so thatthe word Venus' does.not constitute he wholeofthepredicate.' One might ay instead: 'the morning tar is noother han Venus'; what was previouslymplicit n the singleword is' is hereset forth n foar separatewords, nd in 'is noother han' the word is' now really s themerecopula. Whatis predicatedhere s thus not Venus but no other hanVenus.These wordsstand fora concept; admittedly nlyone objectfalls underthis,but sucha conceptmuststill always be distin-guishedfrom he object.2 We have herea word Venus' thatcan neverbe a proper redicate, lthough t can195] form artofa predicate. IThereference of this word sthussomethinghatcannever ccur s a concept, utonly s anobject. Kerry oowouldprobably otwish odispute hatthereis something f this kind. But this wouldmean admittingdistinction, hich t svery mportantorecognize,etweeia hatcaD occuronlyas an object,and everythinglse. And this dis-tinctionwouldnot be effacedven f twere rue, s Kerry hinksit is,that there re concepts hat can also be objects.There re, ndeed, ases that eem osupport is view. I myselfhave indicated inGrundlagen,53, ad fin.) thata conceptmayfallunder higher oncept-which,however,must notbe con-fusedwithone concept'sbeingsubordinate o another. Kerrydoesnotappealtothis; instead,hegives hefollowingxample:" the concept horse is a concept asily ttained , and thinksthatthe concepthorse is an object, n factone of theobjectsthatfallunder heconcept concept asily ttained . Quiteso;the threewords" theconcepthorse' " do designate n object,,buton thatvery ccounttheydo not designate concept, s Irelations; the relation f an objectto a concept t fallsunder, nd thesubordinationf one concept o another. His remarks nthe Vollwurzelare likewise pento objection. Schroeder's ymbol does not simplytake theplace ofthecopula.1Cf.myGrundlagen,66,footnote. 2Ibid., ?51.3Cf.mypaper On Sense and Reference' Ueber innundBedeutung),shortlyoappear n the ZeitschrifturPhil.undphil. Kritik.


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ON CONCEPT AND OBJECT 171am usingthe word. This s in full ccordwith hecriteriongave-that the ingular efiniterticle lways ndicates n object,whereas he ndefiniterticle ccompanies concept-word.1Kerryholds that no logical rulescan be based on linguisticdistinctions;but my ownway of doingthis is somethinghatnobody an avoid who ays down uchrules t all; forwecannotcome oanunderstanding ith ne another partfromanguage,and so in the endwe mustalwaysrelyon otherpeople'sunder-standingwords, nflexions,nd sentence-constructionn essen-tiallythe same way as ourselves. As I said before, was nottrying o give a definition, ut only hints; and to this end I'appealed to the generalfeeling or he German anguage. It ishereverymuch o my advantagethatthere s suchgood accordbetween helinguistic istinctionnd thereal one. As regardsthe ndefiniterticle here re probablyno exceptionso our ruleat all forus to remark,part from bsoleteformulasike EinedlerRath' [' Councillor']. The matters not so simple or hedefinite rticle, speciallyn the plural; but196] thenmy criterion oes not relateto this case. In thesingular, o far as I can see,thematters doubtful nlywhensingular akestheplaceofa plural, s in thesentencethe TurkbesiegedVienna , 'the horse s a four-leggednimal'. Thesecases are so easily recognizables specialonesthatthevalue ofourrule s hardly mpaired y their ccurrence. It is clearthatin the firstentence the Turk is thepropernameof a people.The secondsentence s probablybest regarded s expressinguniversaludgment, ay 'all horses re four-leggednimals' or'all properlyonstituted orses refour-leggednimals'; thesewill be discussed ater.2 Kerry calls my criterion nsuitable;

I Grundlagen,51; ?66,footnote; ?68,footnoten p. 80.2 Nowadayspeople eem nclined o exaggeratehe scopeof the state-ment hat differentinguisticxpressionsre never ompletelyquivalent,that a word an neverbe exactly ranslatedntoanother anguage. Onemight erhaps o evenfurther,ndsay thatthe ameword s never akenin quite the same wayeven by men who share a language. I will notenquire s to themeasure f truth n these statements; would onlyemphasize hat neverthelessifferentxpressions uiteoftenhave some-thingncommon, hich callthe ense, r, n the pecial ase of entences,the hought. In otherwords; wemustnotfail o recognizehat he amesense, he amethought,may be variously xpressed;thus hedifferencedoesnothereconcern he sense,but onlytheapprehension,hading, rcolouringfthethought,nd s irrelevantorogic. It is possible or nesentence o givenomoieandno less nformationhananother; and,forall themultiplicityf anguages,mankind as a commontock f houghts.Ifall transformationftheexpression ere orbiddenntheplea that hiswould alter hecontents well, ogicwould imply e crippled; for he


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172 GOTTLOB FREGE:for urely, e says, n theseintencetheconcept hat I am nowtalking bout s an individual oncept'thenamecomposed f hefirst ightwords tandsfor concept; buthe is not taking heword' conceptin my ense, nd t s not n what haiveaid downthat the contradictionies. But nobodycan require hat mymodeofexpressionhallagreewithKerry's.It must ndeedbe recognizedhathereweare confrontedyanawkwardnessf anguage,which admit annotbeavoided, fwesay thattheconcepthorses nota concept,'whereas, .g.,the197] city fBerlinsa city ndthevolcanoVesuviussa volcano.Languageis here n a predicamenthat justifies he departurefrom ustom. The peculiarityfour case is indicatedby Kerryhimself,ymeansof he quotation-marksround horse'; I useitalicsto the same end. Therewas no reasonto mark out thewords Berlin' and 'Vesuvius' in a similarway. In logicaldiscussions ne quite oftenneeds to assertsomethingbout aconcept, nd to express his n theform sualfor uch ssertion',viz., to make what is asserted fthe concept ntothe contentofthe grammatical redicate. Consequently,ne wouldexpectthatthereferencef thegrammaticalubjectwouldbe thecon-cept; buttheconcept s suchcannotplaythispart, nviewof tspredicative ature; it mustfirst e convertednto an object,2or,speakingmoreprecisely,epresentedyan object. Wedesig-natethis objectby prefixinghe words the concept ; e.g.

'The conceptman s notempty'.Herethefirsthreewords re to be regarded s a proper ame,3which can no more be used predicativelyhan ' Berlin' or'Vesuvius . Whenwesay Jesusfallsunder heconceptman',then, etting sidethecopula,thepredicates:

' someone alling nder heconceptman'andthis meansthesameas: a mantask of logiccan hardlybe performed ithout rying o recognize hethoughtnitsmanifold uises. Moreover,ll definitionsould henhaveto be rejected s false.1A similarhing appenswhenwesayas regardshe entencethisroseis red': thegrammaticalredicateis red' belongs o thesubject thisrose Here thewords Thegrammaticalredicate is red " arenotagrammaticalredicate uta subject. Bythe very ctof xplicitlyallingit a predicate, edeprivet of hisproperty.2 Cf.myGrundlatgen,. X.3I callanything proper ame f tis a signfor n object.


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ON CONCEPT AND OBJECT 173But thephrase

'the conceptman'is onlypart ofthispredicate.Somebodymight rge, s against hepredicative ature ftheconcept, hat nevertheless e speak ofa subject-concept.Buteven nsuchcases,e.g., nthe sentence' all mammalshave redblood'we cannot fail to recognize he predicativenature of theconcept; forwecouldsayinstead:198] 'whatever s a mammalhas redblood'

or: ' ifanythings a mammal, hen thas redblood'.When I wrotemyGrundlagenerArithimetik,had not yetmade the distinction etween ense and reference; and so,underthe expression conitentf a possible udgment',I wascombiningwhat I now designate by the distinctivewords'thought' and 'truth-value'. Consequently, no longeren-

tirely pproveof theexplanation thengave (op. cit.,p. 77), asregards ts wording; myviewis, however, tillessentially hesame. We may say nbrief,akingsubject' and 'predicate' inthe inguisticense: A concepts thereferencef predicate;Anobjectis something hat can neverbe thewholereference fapredicate, utcanbethe referencef subject. It musthereberemarkedhat he words all ', any , no , ' some , areprefixedto concept-words. n universal nd particular ffirmativendnegativeentences, eareexpressingelations etween oncepts;weusethesewords o indicate hespecialkindofrelation. Theyarethus, ogicallypeaking, ottobemore losely ssociatedwiththe concept-wordshat follow hem, utareto be related o thesentence s a whole. It iseasytosee this nthecaseofnegation.If in thesentence

' all mammals re land-dwellers'the phrase all mammals expressed he logical subjectof thepredicate re land-dwellers,hen in orderto negate the wholeI WhatI callhere hepredicative ature ftheconcepts justa specialcaseof heneedof upplementation,he unsaturatedness, that gave astheessential eature f a functionnmywork unktion ndBegriffJena,1891). It wasthere carcely ossible o avoidthe xpressionthefunctionF(x) ', although here oo the difficultyrose that thereferencefthisexpressionsnot a function.2 Cf.my essay Sense and Reference'n the ZeitschriftarPhil. undphil.Kritik.


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174 GOTTLOB FREGE,sentenceweshouldhaveto negate hepredicate: 'are not and-dwellers'. Instead,we mustput the 'not' in front f 'all ';fromwhich t follows hat 'all' logicallybelongswith hepre-dicate. On the otherhand,we do negatethe sentence' Theconceptmammal s subordinate o the concept land-dweller'by negating hepredicate: 'is not subordinateo theconceptland-dweller'.If we keep t in mind hat n my wayof speaking xpressionslike the concept ' designate otconcepts ut objects,mostofKerry's bjections199] already collapse. If he thinks cf. p. 281) that I haveidentifiedoncept nd extension fconcept,he is mistaken; Imerely xpressedmy viewthat in the expressionthe numberthat applies to the conceptF is the extension f the conceptequunumer,usg theconcept ' the words ' extensionof theconcept couldbe replacedby concept. Noticecarefullyhathere the word concept' is combinedwith the definiterticle.Besidesthis was only casual remark; I did notbase anythingupon t.

ThusKerrydoesnotsucceed nfillinghegapbetween onceptand object. Someonemight ttempt,however, o make use ofmyownstatementsn this sense. I have said that to assignanumber nvolvesan assertion bout a concept;1 I speak of-propertiessserted f a concept, nd I allow thata conceptmayfall under higher ne.2 I havecalled existence propertyfaconcept. How I meanthisto be taken s bestmadeclearby ai,example. In thesentence theresat least onesquarerootof4 ',we have an assertion, otabout (say) thedefiniteumber , norabout- 2, butabouta concept, quare oot f4; viz., hat t snotempty. But if express he samethought hus: 'The conceptsquarerootof4 is realized, then the first ix wordsform hepropername of an object,and it is about this objectthat some-things asserted. But notice arefullyhatwhat s asserted ereis not the samething s was asserted bout the concept. Thiswillbe surprisingnly o somebodywhofails o see that thoughtcanbesplitupinmanyways, othatnowonething, ow nother,appearsas subjectorpredicate. Thethought tself oes not yetdetermine hat s to be regarded s thesubject. Ifwesay thesubjectofthis udgment',wedo notdesignatenything efiniteunlessat thesametimewe indicate definite indofanalysis;as a rule,wedo this n connexionwith definite ording. Butwe mustneverforget hat differententencesmay express he1Grundlatgen,46. 2 Ibid.,?53,


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ON CONCEPT AND OBJECT 175same thought. For example,the thoughtwe are consideringcould also be taken as an assertion bout the number :'the number has the property hat there s something fwhicht is thesquare'.Languagehas meansofpresentingowone,nowanother, art200]of hethoughts thesubject; one ofthe mostfamiliarsthedistinctionf ctive and passiveforms. It is thusnot mpossiblethatonewayofanalysing given houghthouldmake t appearas a singularudgment; another,s a particularudgment; anda third, s a universaludgment. lt need not'then urprise sthatthe same sentencemaybe conceived s an assertion boutaconcept nd also as an assertion bout an object; onlywemustobserve hatwhat s asserted s different. n the sentencethereis at least one squarerootof4 ' it is impossible o replacethewords squarerootof4 ' by theconcept quare oot f4 '; thatis, the assertion hat suitstheconceptdoes not suit the object.Although ur sentence oesnotpresentheconcept s a subject,it asserts omethingbout it; it can be regarded s expressingthefactthata concept allsunder higher ne.' But this doesnot nany wayefface hedistinctionetween bjectandconcept.We see to beginwith hat in thesentencethere is at least onesquare rootof 4 ' the predicativenatureof the concept s notbelied; wecould ay there s somethinghathas thepropertyfgiving he resiult when multiplied y itself. Hence what ishere asserted bout a conceptcan neverbe asserted bout anobject; for proper amecan neverbe a predicative xpression,thought can be partof one. I do notwantto say it is falsetoassert boutan object what s assertedhereabouta concept; Iwantto say it is impossible, enseless, o do so. The sentence'there is JuliusCaesar is neither rue nor false but senseless;thesentence there s a man whosename s JuliusCaasar has asense,buthere gain we have a concept, s theindefiniterticleshows. Weget the same thing nthesentencethere s onlyoneVienna'. We mustnot et ourselvesbe deceived because lan-guageoftenuses the same wordnow as a proper ame,now as aconcept-word; n our example,the numeral ndicates hat wehavethelatter; ' Vienna is here a concept-word,ike metro-polis'. Using it in this sense, we may say: 'Trieste is noVienna'. If, on the otherhand,we substitute JuliusCoesar'201] for hepropername formed y the first ix wordsofthe

1 In my Grundlagen called such a concept a second-order oncept; inmy work Funktionund Begriff called it a second levelconcept,as I shalldo here.


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176 GOTTLOB FREGE:sentence the concept quareroot f4 is realized', we get a sen-tencethat as a sensebut s false; for heassertion hat omethingis realized as the word s beingtaken here)can be trulymadeonly about a quite special kind of objects,viz., such as can bedesignated ypropernamesofthe formthe concept '. Thusthe words theconcept quare oot f4 'have an essentially iffer-ent behaviour, s regards ossible ubstitutions,rom he words' square rootof 4 ' in our original entence; that s, the referenceofthe twophrases s essentially ifferent.'What hasbeen hown ere n one exampleholdsgoodgenerally;the behaviour ftheconcept s essentiallyredicative,venwheresomethings being sserted bout it; consequentlyt can be re-placed there nlyby another oncept, everbyan object. Thustheassertion hat s made about a concept oesnot uit n object.Second-level oncepts,which oncepts allunder, re essentiallydifferentrom irst-leveloncepts,which bjectsfallunder. Therelation f an object to a first-leveloncept hat t fallsunder sdifferentrom he (admittedly imilar) elation f a first-leveloa second-leveloncept. (To do justice t onceto thedistinctionand to the similarity, e mightperhaps say: An object fallsunder first-leveloncept; a concept allswithin second-levelconcept.) The distinctionfconcept nd objectthusstillholds,with ll itssharpness.2With this therehangstogetherwhat have said (Grundlagen,?53) about my usage of the words property and ' mark';Kerry'sdiscussion ivesme occasion o revert nce more o this.The wordsserve to signify elations,n sentences ike ' 0 is aproperty fr and O is a mark fQ'. In my wayofspeaking,a thing anbeat once a propertynda mark, ut not of hesamething. I call the concept nderwhich n objectfalls tsprop-erties; thus 'to be 1 is a propertyf r'

1Cf.my essay 'Sense and Reference (cited above).2 [When Russell says thatexpressions ike 'the King ofFrance' are notnames but incomplete symbols,he is saying what would be put thus inFrege's terminology: " In 'the King of France is bald', 'the King ofFrance' is not a name of an object; what it stands for s something n-complete,ungesdttigt-asecond-leveloncept,withinwhich the conceptbaldis falsely asserted to fall. The second-level concept in question is theconcept: conceptnderwhichomebodyalls who s a KingofFrance ndapart romwhom obodys a Kingof France; no first-level oncept fallswithinhis,becausenobodys a King ofFrance."It should, however,be emphasized that Frege himselfgives an entirelydifferentccount f definiteescriptions.Cf. Ueber inn undBedeutung,pp. 39-42.-P.T.G.]


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ON CONCEPT AND OBJECT 1771S justanotherwayofsaying:

' r fallsunder heconcept f a 'If the object r has theproperties, X, and IF, I maycombinethem ntoQ; so that t is the samethingf saLyhatr has theproperty , or,thatr202] has theproperties , X, and YF. I then call 0, X, and fmarks f theconceptQ, and,at the sametime,propertiesf F.It isclear hattherelations f Ztor and toQ are quitedifferent,and that consequently ifferenterms are required. r fallsunder he concept ; butQ, whichs itself concqept,annot allunder he first-leveloncept P; onlyto a second-levelonceptcould it standin a similarrelation. Q is, on the otherhand,subordinateo i.Let us considern example, Insteadofsaying:

'2 is a positivenumber'and'2 is a wholenumber'and'2 is less than 10'wemayalso say'2 is a positivewholenumber ess than 10'.Here tobe a positive umber,to be a whole umber,to be essthan10,appear as propertiesfthe object2, and also as marksoftheconcept positivewhole umberessthan10.This s neither ositive, or wholenumber, or ess than10. Itis indeed subordinateo theconceptwhole umber,utdoesnotfallunder t.Let us now comparewiththiswhatKerry ays in his secondarticle p. 224). "By the number we understandhe result fadditivelyombining and 1. The concept bjecthere ccurringis the numerical ndividual4; a quite definite umber n thenatural number-series.This object obviouslybears just themarks hat are named in its concept, nd no othersbesides-providedwerefrain,s we surelymust, rom ounting s prapritof the object its infinitely umerousrelations to all otherindividualnumbers; ('the ' number is likewise he result ofadditively ombining and 1.)"


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178 GOTTLOB FREGE:We see at oncethatmydistinctionetween ropertynd markis herequite slurred ver. Kerrydistinguisheserebetween henumber and 'the ' number . I mustconfesshat thisdistinc-tion sincomprehensibleo me. The number isto be a concept;'the' number is to be a concept-object,nd noneother hanthenumericalndividual . It needsno203] proof hatwhatwe havehere s notmydistinctionetweenconcept nd object. It almost ooks s thoughwhatwasfloating(though ery bscurely) efore erry'smindweremydistinctionbetween he sense ndthereferencef hewords the number '.

But it s only he referencefthewords hat canbe said tobe theresult f additively ombining and 1.Again,howarewe to take theword is in thesentences thenumber is the result of additively ombining and 1 and" ' the number istheresult f dditivelyombining and 1 " ?Is it a mere opula,ordoes thelp to express logicalequation?In the first ase, the wouldhave to be left utbefore result',and thesentenceswouldgo like this:'The number is a result f additively ombining and 1';" ' The' number is a result fadditively ombining and 1."In thatcase,the objectsthatKerrydesignates y' thenumber ' and " ' the number "

wouldbothfall under he conceptresult f dditivelyombining and 1.

Andthentheonly questionwould be whatdifferenceherewasbetween heseobjects. (I am hereusing he wordsobject ' and' concept' inmyaccustomedway.) I shouldexpress s followswhatKerry s apparentlyryingo say:'The number has those properties,nd thosealone,which remarks f heconcept: result f dditivelyombiningand1.'I shouldthen express s follows hesenseofthefirst fourtwosentences:

'To be a number is the same as being resultof additivecombinationf 3 and 1 ';In thatcase,what conjecturedust now to have beenKerry'sintentionouldalso be putthus:'The number4 has thoseproperties,ndthosealone,whichare marks fthe concept nurmber'.(We need notheredecide whether his s true.)


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ON CONCEPT AND OBJECT 179204] The inverted ommasaroundthe definite rticle n thewords 'the' number " could n thatcase be omitted.But in theseattemptednterpretationse have assumed hatinat least oneofthetwo sentenceshe definiterticlesnfrontf' result and number ' were nserted nlybyan oversight. Ifwe take thewordsas theystand,we can onlyregard hemashaving he senseofa logicalequation, ike:'The number4 is none other than the resultofadditivelycombining and 1'.The definite rticle nfront f result' is here ogicallyustifiedonly f t is known i) thatthere s sucha result ii) thatthere snotmore hanone. In thatcase,thephrasedesignatesn object,and is tobe regardeds a proper ame. Ifbothofoursentenceswereto be regarded s logicalequations, hen, incetheirrightsidesare identical,t would follow romhem hatthenumberis the number ,or, fyouprefer,hatthe number is no otherthan ' the number ; and so Kerry'sdistinctionwouldhavebeenproveduntenable. However, t is notmy present ask topointoutcontradictionsn hisexposition; hisway oftaking hewords object and 'concept' is notproperlymyconcern ere.I am onlytrying o set myownusageofthesewords n a clearerlight, nd incidentally howthatin any case it differsromhis,whetherhat s consistentrnot.I do not t all disputeKerry's ight ouse thewords concept'and ' object' inhisown way, fonlyhewouldrespectmy equalright, ndadmitthat withmyuse ofterms have got holdofadistinction f the highest mportance. I admitthat there s aquitepeculiar bstacle n theway of an understanding ithmyreader. By a kind of necessity f language, my expressions,taken iterally,ometimesmissmy hought; I mention n object,whenwhat I intend s a concept. I fullyrealizethat in suchcases I wasrelyingpona readerwhowouldbe ready o meetmehalf-way-whodoesnotbegrudge pinchof salt.I Somebodymaythink hatthis is an artificiallyreateddiffi-culty; that there s no need at all to take accountof suchanunmanageable hing s whatI call a concept; that onemight,likeKerry, egard n object'sfalling nder concept s a relation,inwhichhe amething ouldoccurnow s object,now s concept.205] Thewords object' and 'concept wouldthen serveonlyto indicate hedifferentositionsn the relation. This may bedone; butanybodywhothinks hedifficultys avoided thiswayisverymuchmistaken; t is only hifted.For not ll theparts fa thought an be complete; at least onemustbe 'unsaturated',


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180 GOTTLOB FREGE: ON CONCEPT AND OBJECTor predicative; otherwiseheywouldnothold together. Forexample,the sense of the phrase the number2 ' does nothold togetherwiththat of the expressionthe conceptprimenumber'without link. We apply such a link n the sentence'the number 2 falls underthe conceptprimenumber'; it iscontainednthewordsfalls under , whichneed tobe completedin two ways-by a subject nd an accusative; and onlybecausetheir ense s thus unsaturated arethey apableof serving s alink. Onlywhentheyhave been supplementedn thistwofoldrespectdo we geta complete ense, thought. I say thatsuchwords or phrasesstand fora relation. We now get thesamedifficultyorthe relation hat we were trying o avoid for theconcept. For thewordsthe relation fan objectto the conceptit falls under designatenot a relationbut an object; and thethree roper ames thenumber ','the concept rime umber','the relation fan objectto a concept t fallsunder , holdalooffrom ne anotherust as much s the first wodo bythemselves;howeverwe put themtogether, e getno sentence. It is thuseasyfor stosee thatthedifficultyrising romhe unsaturated-ness ofone partofthethought an indeed be shifted, utnotavoided. 'Complete' and 'unsaturated' are of course onlyfiguresfspeech; butall that wishor am able to do here s togivehints.It maymake t easier o come o anunderstandingf hereadercomparesmyworkFunktion ndBegriff.Forover hequestionwhat t sthat s calleda functionnAnalysis,we comeup againstthesameobstacle; and onthoroughnvestigationtwillbefoundthat the obstacle s essential, nd founded n the natureofourlanguage; thatwe cannotavoid a certain nappropriatenessflinguistic xpression; and that there s nothing or.t but torealize hisand alwaystakeit into account.

frege, f.l.g. on concept and object

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