Hacker - Frege and Witt Gen Stein on Elucidations

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Mind Association

Frege and Wittgenstein on ElucidationsAuthor(s): P. M. S. HackerSource: Mind, New Series, Vol. 84, No. 336 (Oct., 1975), pp. 601-609Published by: Oxford University Press on behalf of the Mind Association

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Frege and Wittgensteinn Elucidations,P. M. S. HACKER

IntroductionIn thepreface o ThePrinciples f Mathematics ussellwrote:The discussion f ndefinables-which orms hechiefpartofphilo-sophical ogic-is the endeavour o see clearly, nd to make otherssee clearly, he entities oncerned,n orderthat themind may havethatkindof acquaintancewith hemwhich t has withredness r thetasteof a pineapple.Where,as in thepresent ase, theindefinablesare obtained primarily s the necessaryresidue in a process ofanalysis, t is often asier to knowthattheremustbe such entitiesthanactually o perceive hem.2In the TractatusWittgenstein bjected to Russell's conception of in-definables.His criticismnvolved a three-prongedmovement.He ob-jected to Russell's treating logical connectives as indefinables.HecriticizedRussell's view thatcertain ategorial oncepts re indefinables.He thought hatthe idea ofobtaining n intellectual cquaintancewithindefinables hus conceived was absurd. Of course, it was not only

Russell whom he had in mind in his discussionofindefinables, ut alsothe ratherdifferentlaimsof Frege. Having criticizedhis predecessors,Wittgensteinntimatedhow the meaningsof genuine indefinables reconveyed-by elucidations r explicationsErlduterungen).In the following iscussion should liketo throw ome lighton theobscure Tractarian notionof an elucidation. t is of some importancefrom n historical ointof viewfor wo reasons.Firstly,t seems thattheidea and terminologyfexplaining ndefinablesy meansofelucidationshas its roots n Frege. This is not generally nown. So I shall startbyexamining rege's remarks n Erlduterungen.shallsubsequently dd afewpointsabout Russell's views on indefinables,nd then showWitt-genstein'sresponseto his masters. n the second place, clarification fWittgenstein'sotionofan elucidation s ofvalue for heproperunder-standing fWittgenstein'sater discussionsofostensivedefinition. hislatter opic, however,will not be examined n thispaper.Frege nd RussellFrege had little nterestn epistemology,nd his interest n the 'inde-finables f logic' were circumscribed y his concerns n the philosophyofmathematics. iven the quasi-chemical'pictureofanalysiswhich hehad,3 t was inevitable hat he shouldconceiveofanalysis s yielding, nI I am much indebtedto Dr. G. P. Baker and Dr. A. J. P. Kenny for theircomments n an earlierdraft f thispaper.2 B. Russell, The Principles fMathematicsCambridge, I903), p. V.3 Cf. G. Frege, On the Foundationsof Geometry nd Formal Theories ofArithmetic,d. and trs. E. H. W. Kluge, p. 6I.

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602 P. M. S. HACKER:the astresort,bsolute ndefinables. hese could be thought f as locatedatoneoftwopoles: the ndefinablesf ogic n thestrict ense, .e. summagenera and primitiveoperators,and the indefinables f language ingeneral, .e. conceptswhose extension onsistsof logically nanalysable'items given n experience.Frege was largely oncernedwiththeformer.In 'On Conceptand Object" Fregewrote:One cannotrequirethat everythinghallbe defined, nymore thanone can requirethat a chemist hall decompose everysubstance.What is simplecannotbe decomposed, nd what s logically implecannot have a properdefinition. ow somethingogically imple sno more givenus at the outsetthan mostof the chemical lementsare; it is reachedonlybymeansof scientific ork. f something as

been discovered hat s simple,or at leastmustcount as simple forthetimebeingwe shallhaveto coin a term or t,since anguagewillnot originally-ontainan expression hat exactlyanswers.On theintroductionf a namefor omethingogically imple, definitionsnot possible; there s nothing or t butto lead the readerorhearer,bymeansof hints, o understand he words as intended.It is interestingo note thatthe exampleof an indefinable ere s thatofthe super-categorial'otionof a concept. n otherwritings regeadvertsfrequentlyo the ndefinabilityf primitives,nd hisexamples re usuallyof a verygeneralcategorialnature, .g. 'judgment' 'Negation', op. cit.p. I26 n.), 'object' ('Function and Concept',op. cit.p. 32), 'truth' 'TheThought'2).To be sure, t s natural or philosopherwhose concerns reexclusively irected tthe foundations f mathematicso takeas indefin-ables such categorialnotions s arenecessary or he logicistprogrammeof reduction. ikewise, n his development f thepropositional alculushe tooknegation nd theconditional s primitive,nd in his elaborationof the predicatecalculus he took the universalquantifier s primitive.But if such categorialnotions as 'object', 'concept' and 'function', ndsuch fundamental pieces of logical equipment as 'if . .. then . . . ' arestrictlyndefinable, owcan we cometo understand hesewords?Allwehave so farbeen told is thatthe reader'mustbe givenhints.Fregeturnedhis attention o thematter n his I906 article On theFoundationsof Geometry':We must admit logically primitive lementsthat are indefinable.Even here there eemsto be a need to makesure thatwe designatethesamethingbythe samesign word).Once theinvestigatorsavecome to an understandingbout the primitive lements nd theirdesignations,greement boutwhat is logically omposite s easilyreached by means of definition. ince definitionsre not possibleforprimitive lements, omething lse mustenter n. I call it ex-plicationErlduterung).t is thisthereforehat erves hepurposeof

mutualunderstandingmong nvestigatorsO.F.G., p. 59).I G. Frege, 'On Concept and Object', in TranslationsromthePhilosophicalWritings f GottlobFrege,p. 43, ed. and trs. by M. Black and P. Geach(Blackwell,Oxford, 960).2 G. Frege, 'The Thought', in P. Strawson ed.), Philosophical ogic,p. I9(O.U.P., I967).


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FREGE AND WITTGENSTEIN ON ELUCIDATIONS 603The terms hatrequire xplication re whatFregecalls logically rimitiveelements'.Whereas in his non-geometricaliscussionshis examplesareusually categorial onceptsof logic, here, n thegeometrical ontext,hesuggests hat point' and 'straightine' would requireexplication.Whatis the pointof an explication?t is,as Frege puts t, pragmatic'. t servesthe purposeofbringing thers o understand term, ndefinablen thesystem n question, n theway in whichone understands t oneself. tshouldensurethatotherswillsubsequently ssociatewiththeexplicatedterm he samesense as thatwhichonehas assigned toneself. xplicationsbelong to the preamble, r propaedeutic' f a science.They precedethestructure f the science itself nd the propositionswhichperform heexplicativefunction re not themselvespart of the science,neitherbyway of axioms nor by way of theorems.Frege gives no examples ofexplicative propositions.He says that explications will generallybepropositions sentences)that containthe expression n question', andstresses hat n orderto achieve one's explicative urposeone 'mustbeable to count on a littlegoodwilland co-operative nderstanding; orfrequently e cannotdo without figurative ode ofexpression'.So far what is said is unobjectionable, lthough perhaps also un-illuminating. ut the remaining oints are highlyobjectionable. Fregestresses hat xplicationsreonlynecessaryor o-operative nderstanding.Whatthenoftheassignment f senseto a primitiveermbytheexplicatorhimself?He conveysto othersthe sense he assignsto primitives yexplications, ut how does he convey t to himself? ywhatprocessdoeshe assignsense to a primitive erm?Frege appears to see no problemhere. He saysthat the solitary nvestigator ill have no need ofexplica-tions, incetheseareonlynecessary or ommunicative urposes.All thatscience demands s that heoriginatorfan explication nowsfor ertainwhat he meansbytheprimitive ign,and that he remain n agreementwithhimself'.AnyonefamiliarwithWittgenstein's rgument gainstaprivate anguagewill recognize mmediatelyheproblemsraisedby thisapparently rivialdemand. It is even more markedwhen Frege pointsoutthat

Sincemutualco-operationna science s impossiblewithoutmutualunderstanding f the investigation, e musthave confidence hatsuch an understanding an be reached, althoughtheoretically hecontrarys not excluded.Frege's disregardfor the assignment f sense to the 'primitives' r'indefinables' flanguage n general s perhapsexplained n a passagein'Logic in Mathematics'.Fregewrites s follows:One mustdistinguish eal definitions rom xplications Erlduter-ungen).Whenwe begina sciencewe cannot voidusingwords of ourlanguage; But these words are on the whole unsuitable for ourpurpose, fortheyare insufficientlyrecise,and fluctuate n use.Scienceuses terms fartwhichhave a completely recise nd fixedreference; n orderto come to an understandingbout theirrefer-ences, and to exclude possible misunderstandings,ne providesexplications.To be sure, n orderto do so, one mustagainemploywords of [ordinary] anguage which,as they are, mayhave similar


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604 P. M. S. HACKER:defects o thoseregardingwhichtheexplicationwas meant to help.So itmay eem thatyetfurtherxplications renecessary. heoretic-allyspeaking ne nevercomes to an end; but from practicalpointof view one does manage to come to an understanding n thereference fwords.'It is significanthatsomepages laterFrege returns o thesubject n thecontext f indefinables flogic':It is impossible o conveybymeans of a definition hat a functionis because herewe are concernedwithsomething imple and un-analysable. t is only possibleto lead someonetowhat t is that onemeans, nd to clarifytby means ofconnectionswithwhat sknown.An explicationmustreplacea definition ere,and has to relyuponan understanding illing omeetone halfway.2It is clear thatFrege had no interest n the primitives f language ingeneral.How sense is assignedto a primitive erm of languagewas nota question which arose forhimin his investigations. e was concernedonlywith heprimitivendefinables f a 'system'ofscience, nparticulargeometrynd logic.Hence thekinds of itemsrequiring xplication reeithercategorialnotions ike function', r primitivesn geometry uchas 'point'.Explication ftheseterms s notpartof,buta propaedeutic othescience nquestion, nd willconsist ffalling ackupon theresourcesof ordinary anguage,thefunctioningfwhich s taken orgranted.Themeaningoftheprimitive cientificerm s explainedby employingt inordinary actual entences, ivena co-operative istener.So much forFrege. Turningnow to Russell, two pointsare worthnoting.The first oncerns ThePrinciples fMathematics. have alreadyreferred o the section in which Russell seems to hanker afteranintellectualntuition findefinableogicalobjects. The mootquestion s-what were the objects? In chapter I of the book Russell identifiessymbolic ogic as the studyof generalrules of inference. he notionswhich appear in the propositionsof symbolic logic are the 'logicalconstants'.Amongthese is a small class of 8 or 9 indefinable ogicalconstants nterms fwhichothers re tobe defined.Russell ists mplica-

tion,classmembership,henotion uch hat, henotionofrelation, ruthand propositional unction. n overlapwithFrege is obvious. One oftheaimsof thebookis to lead thereader o an intellectualcquaintancewiththese ndefinablesimilar o his acquaintancewith simple deas' oftasteor colour.The secondnoteworthy oint concerns passage in PrincipiaMathe-matica.3 n the openingchapterof thebook *i Russell pointsout thatevery ystem fdefinitions ust start rom minimal angeofundefinedterms.These he calls 'primitivedeas'. Like Frege he skirts oundtheissue of theexplicability fprimitives.The primitivedeas are explained ymeans ofdescriptionsntendedtopointout to thereaderwhat smeant,but theexplanations o not

I G. Frege, Nachgelassene chriften, . 224, ed. H. Hermes, F. Kanbartel,F. Kaulbach (Felix Meiner,Hamburg, I969).2 Op. cit., p. 254.3 I owe thisreference o Dr. G. P. Baker.


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FREGE AND WITTGENSTEIN ON ELUCIDATIONS 605constitutedefinitions, ecause they really involve the ideas theyexplain.

Arguably uch a claim is wholly unobjectionablewithin he frameworkofthe development f a formal ystem.The bearingthis trivialremarkhas for he concernof this paper is upon one of the puzzling passages nthe Tractatus Logico-Philosophicus,amely 3.263. Here WittgensteinwroteThe meanings fprimitive ignscanbe explainedby means of eluci-dations [Erlduterungen].lucidationsare propositions hat containtheprimitive igns.So they an onlybe understood f the meaningsof thosesignsare alreadyknown.Not surprisinglyhispassage has occasionedpuzzlement.,The Fregeanand Russellian backgroundbeing filled n, it is clear that the passagereachesback to these antecedents. s we shall see,^ t also reachesforwardto the laterdiscussionofostensivedefinition.Indefinablesn the TractatusUnlike Frege and Russell, Wittgenstein'snterestswere not circum-scribedby the searchforthe foundations fmathematics.His concernwas withfoundationsf anguage n general.Moreover,his aspiration oproducea Begriffsschriftas not conceived fas theproduction fa sharpand subtle nstrument hich would constituten improvementverthelogical disorder f ordinary anguage. It was rather he production f aperspicuous representation f what is already present in ordinarylanguage,which, s he stressed, s in perfect rderas it is. Hence whenhe comesto the problem f ndefinables, e is concernedwith ndefinablesoflanguage n general.How did he tacklethisproblem, ndwhat s theproper interpretationf T.L.P 3.263? I shall turn first o his criticalremarks n Fregeand Russell.Frege and Russell had includedamongthe indefinables f logic suchnotions as object, relation, oncept,function.They thought hattheseexpressionshad a designating ole, thoughsincetheywere indefinable,what t was thatthey designated ould onlybe grasped through nder-standing lucidationswhich did not definebut employedthe terms nquestion. Wittgenstein houghtthat this involved a misapprehension.One ofhis earliest nd most cherishednsightsn I9I2 was thatno 'realvariables' but onlybound variablesoccur withinpropositions.Alreadythenhe conjectured hatfrom his insight t followedthattherewere'no logicalconstants' in Russell's senseof thetermpresumably). y thetime he wrote he Tractatushe had cometo believethatwhatFregeandRussell had thoughtof as indefinable logical constants'were eitherformal onceptsor operators.A formal oncept uchas 'object', function'and hence concept' too),and he mentionsalso 'number', 'complex', 'fact', cannot occur in aproposition. They are not names (nor function-names) nd are notrepresentedn a conceptualnotationby functions. hey are variables.2I E.g., M. Black,A Companion o Wittgenstein'sractatus, p. I I f. C.U.P.,i964). It is noteworthy hat the sense of 'Erlduterung'n this passage isquite differentrom ts sense in 4.II2 and 6.54.2 Cf. 'Notes on Logic', in Notebooks914-I6, p. I05, ed. G. H. von Wrightand G. E. M. Anscombe (Blackwell, I96I).


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6o6 P. M. S. HACKER:They aregivenas soon as any objectbelonging o the valuerangeofthevariable s given.Complexconcepts are definedby theircharacteristics(Merkmale).But formal oncepts pseudo-concepts) renot. Rather heir'characteristics' re formalpropertieswhich are not representedbyfunctions.They are representedby logico-syntacticaleaturesof thesymbols epresentinghevalues ofthevariable hatconstitutesheformalconcept. This criticismhad far-reachingmplications,not only con-structively or the Tractariandoctrineof showingand the consequentinexpressibilityfessences,but also critically or ogicism,n particularRussell'stheory ftypes nd axiomof nfinity.The secondpoint ofcriticism f his predecessors' ccount ofindefin-ables concerned ogical connectives nd quantifiers. n the Tractatus4.03I2 he refers o his insight hat the logical constants' re not repre-sentatives as his 'Grundgedanke'. e offers varietyof compressedarguments o supporthis contention. f theconnectiveswere,as Russelland Fregesupposed,primitiveigns, ndefinables,twouldbe inconceiv-able that hey re nterdefinable.utthey re nterdefinable,nd itmattersnot at all whether ne starts, ike Frege, with mplication nd negation,or withdisjunctionnd negation.Secondly,unlikenames forobjects orrelations) he logical connectivesused brackets o indicatetheirscope.Thirdly,withregard o negation, f not' were an indefinable rimitivename then not-notp' would differn sense fromp'. But it does not-the apparent 'logical constant' vanishes in the reiteratednegation.Fourthly, he vanishing f logicalconstants ccurs withthe quantifierstoo: '- ( 3 x) fx'saysthe sameas (x) fx, nd '( 3 x) fx & x = a' saysthe same as 'fa'. In shortthe logicalconstants thusconstrued) re notindefinable ames at all. The only indefinables f logic', accordingtoWittgenstein,rethegeneralpropositional orm nd theoperatorN (a),and these are notnames,and hencenotindefinables.If logiccontainsno indefinables, hat ofthe indefinables f languagein general?They are the simple names of the Tractatus.These haveBedeutung ut no Sinn. The meaningof a simplename is thesubsistentobject forwhich the name stands. The logico-syntacticalorm of thename, i.e. the combinatorial ulesdeterminingts employment,ndicatethe logico-metaphysicalormofthe object ofwhich t is thename (i.e.its ontological ategory).Which particular bject out of the totality fobjectsbelongingto a givenontological ategory s signified y 'A' isnotdetermined ylogicalsyntax utbyconventionalorrelationf namewithobject. How is thecorrelationone,and how smeaningBedeutung)conveyed?The shortanswer s-the correlations mental intentional)and meaning s conveyedbyErlduterungen. t is to this thatwe can nowturn.That names pin' the formal tructure f languageon to theworld sevident. o too is thecontentionhat hecorrelationsmentalorpsycho-logical. I have argued for this interpretationlsewhere,'and will notrepeatmyself.The questionwhich I should like to raise concernsthe

P. M. S. Hacker, Insight nd Illusion. Wittgensteinn Philosophy nd theMetaphysics fExperience, p. 45 ff.Oxford, 972). Cf. Notebooks9I4-i6,pP. 33, 53, 68, 70, 99, I29-30.


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FREGE AND WITTGENSTEIN ON ELUCIDATIONS 607natureof a TractarianErlduterung.he FregeanErlduterungelongstothe propaedeutic f a science, and can relyupon prescientificanguage.Although he primitive erms f a system annotbe explainedwithin hesystem, hey can be rendered ntelligible n ordinary anguage,eventhoughno rigorous omplete definitionan be provided.But this easymove was not availableto Wittgenstein. nlikeFrege hisconcern s withlanguage n general. o was a Tractarian rlduterungf a name a' simplyany sentence, rueor false, n which a' occurs,e.g. 'fa', which sentenceisused in thehope,and with he ntention,hat he hearerwillunderstandboth that a' means a, and that fa? Was Wittgenstein,ikeFrege, implyrelyingupon an understandingwilling to meet one half-way? his iscertainly ossible. The history f the termmight uggest t (although hedifference etween Frege and Wittgenstein ust alluded to suggestsotherwise).But thereare considerationswhich suggestthat in the un-explained and unthought ut notion of an ErlduterungWittgensteinnsome sense wished to combine the true-falsefeatures f an ordinaryproposition with the apparent (and later repudiated) featureof anostensivedefinition, amely inking anguagewith reality.The absence of the term hinweisendenrkldrungs irrelevant o thediscussion ince thistermhad not yet been invented.Firstly,n one ofthe few passages in the Tractatus n whichhe says anythingbout pro-jection he writes Das Bild ist so mitder Wirklichkeiterknupft;s reichtbis zu ihr' Tractatus . I5 II). Italicizing o s a naturalwayof ndicatingeitherphysical rmental intentional) stension.Moreover, t is thewaywhich Wittgensteinlmost always employed,both before he Tractatus(Notebooks9I4-I6, p. 53, italicization f dieses'and 'jene') and in hissubsequent writings cf. especially he Grammatik). n the otherhand,'so' is not talicized n the Proto Tractatus.Moreover, he facsimile fthecorrespondence etweenOgden and Wittgenstein'n May 1922 runsasfollows: Ogden gives his rendering Thus the picture s linked withreality; t reachesup to it' and commentsYou had putSuch thepicturein a correction or o linked uch is impossible, nd I thinkyoumayhavemeant to change other words too and forgotten? hus makes goodEnglish, or do you mean a forwardreference?'Wittgenstein eplied' "Thus" is all right'. t is difficulto knowexactlywhattomake ofthisexchange.Certainly he Ogden translationarrieswith t a forceful ack-reference hich s absent n the German ext.Yet Wittgensteincquiescedin thetranslation. o maybe so' is nota hint tostension,ndthepicture'sattachingo reality y means of reaching ut to it concerns nlypictorialformthe thesisof somorphism) nd notthe pictorial elationship.A second kind of evidence supporting he claim that the Tractatuscontains tacitand confuseddoctrine f ostension s to be found n theNotebooks. ere he appearsto havehad inmindsomethingkin to osten-siveexplanation fmeaning, .e. the use of a sentencen whicha nameispinnedto an object, s it were,while simultaneouslyn assertionsmade.Most strikingly e have theenigmatic emark What seems to be givena priori s the concept: This-identical with the conceptof the object'I L. Wittgenstein, etters o C. K. Ogden,ed. G. H. von Wright,followingp. 54 of the text Blackwell, Oxford, 973).


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6o8 P. M. S. HACKER:(Notebooks, . 6i). A little arlierhe had claimed Names are necessaryfor an assertion hat this hingpossesses that property' op. cit. p. 53).And finallywe have the completely xplicitremark I mean [by "lyingon"] just THIS' (op. cit. p. 70).Thirdly, n a conversationwithWaismann n July 93Z Wittgensteinremarked: Logical analysis nd ostensivedefinition ere unclearto mein theTractatus. thought t the time hat here s a "connection etweenlanguage and reality".1 Certainly f a TractarianErlduterungs akintoostensive efinition,nd if names have onlyBedeutungnd no Sinn, andif the Bedeutung f a name is a sempiternal bject, thenErlduterungenwould, inter lia, establish 'connection etween anguageand reality'.It was againstthis thesis that Wittgensteinwas laterto argue so ve-hementlyn his doctrines f theautonomy f anguageand grammar.2WhatunclaritymightWittgensteinavehad in mind n theremark oWaismann?Briefly ut,thesalient ointsmaybe thefollowing: ccordingto the Tractariangenerative onceptionof language The meaningsofsimple igns words)mustbe explained erkldrt)o us ifwe are to under-standthem.Withpropositions, owever,we makeourselvesunderstood'(Tractatus 4.026). This is done by means of elucidations which arepropositions ontaining he primitiveigns, nd hence canonlybe under-stood ifthemeaningsof those signsare alreadyknown.The meaningsarethe objectswhichconstitute he substance fthe world. t is plausibleto think hatthis schematic onceptions a dimapprehension f theroleof ostensivedefinitionn assigning ense to, e.g., colourpredicates, ndthe role of paradigmatic amples in the grammar f such expressions.Wittgenstein as later to stressthat what Tractarianobjectswere (i.e.the only cogent wayofmaking ense of themetaphysicalmuddle) wasnothingmore thansampleswhich are elements four methodofrepre-sentation, otelements f the world which we represent y ourmethodofrepresentationWittgensteinndderWiener reis,p. 43; Investigations,section50). SimilarlyWittgenstein arpedon the dangersof confusingthe genuine proposition This is A' (where this' designatesan objectwhich has the propertyA, for example) with the ostensivedefinition'This is A' (where this' s A) which s not a genuineproposition. gain,it s plausible o see this s a criticismfsomethingacit n theTractarian'Erlduterung'.his suspicion s, I think, onfirmedn a striking assagein the Bemerkungen,ection6:When I explain to someonethe meaningof a word A by saying'This is A' and pointing t something,hisexpression anbe meantin two ways. Either t is itself proposition nd thencan only beunderstood f the meaningof 'A' is already known, .e. I have toleave it to fate whether he hearer will graspthe proposition s Imeant t or not. Or thepropositions a definition.The second sentence s virtually opiedfromTractatus .263. Of courseone mightclaim thathe did not make this erroneous onflationn theTractatus-the 'Erlduterung' id indeed leave it to fate whether thex Ludwig Wittgensteinnd der WienerKreis, p. 209, shorthandnotesrecordedby F. Waismann,ed. B. F. McGuinness (Blackwell, Oxford, 967).2 Cf. Insight nd Illusion, pp. I56 ff.


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Hacker - Frege and Witt Gen Stein on Elucidations