jorgensen _ some reflections on reflexivity

8/3/2019 Jorgensen _ Some Reflections on Reflexivity

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Mind Association

Some Reflections on ReflexivityAuthor(s): Jorgen JorgensenSource: Mind, New Series, Vol. 62, No. 247 (Jul., 1953), pp. 289-300Published by: Oxford University Press on behalf of the Mind Association

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VOL. LXII. No. 247.] July,1953'

A QUARTERLY REVIEWOF

PSYCHOLOGY AND PHILOSOPHYI.-SOME REFLECTIONS ONREFLEXIVITY

BY J0RGEN J0RGENSENIN thispaper wish o adva,nceheviewtha.t o-called eflexivephenomenadoes not exist. Especially, wish to defendthefollowingheses:(i) There are no reflexive elations r any other o-calledre-flexive henomena.(ii) In particular, o languageor linguistic xpression s self-referring.(iii) The paradoxesof the Epimenides-typean be solvedand

explained n a quite elementary aywithout nyneed fora moreor esscomplicatedheoryf ogical ypes.(iv) A simpleform fsucha theory eemsnecessary, owever,in order o explainthesyntactical se of theword" all ".By means of thistheoryvariousparadoxes, e.g. Russell'sparadox,are elimin.atednd explained.Myconsciousmotives or ryingo defend hesetheses re asfollows:First, I have always felt a certaindisproportionxistingbetweenthe complicatedmeansused to avoid the paradoxesand the.relative implicity fthe paradoxesthemselves. It isgenerally hought oolish o dynamite utterflies,nd as com-pared withthesimpler aradoxes at least,the varioustheoriesof ogical ypes eemto meto be of a too subtlechaaractero beaccepted ightly.19 289


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290 J0RGEN J0RGENSEN:Secondly, heso-called olutions ftheparadoxeshave alwaysleftme in a certain tate ofuneasiness. True,the theories ftypeshave, ftenable, hownhowtheparadoxescanbe avoided,but theyhave not shownhow theycould arise. A quite satis-factoryolution fthem hould, n my opinion,not onlyconsistin directions s to how to avoid them,but shouldalso exposetheerrorswhich ause them, .e. it shouldnot onlyprevent, utalso explainthem.I think can givean explanationwhichwill serve s a meansofpreventinghem, ndwhich s at thesame timemuch impler

thanthe theories ommonlysedfor hispurpose.Let me startby a veryelementarynd well-knownxampleofa logical para.dox. The expression This sentence s falseis generally onsidered aradoxicalbecause it leads to contra-dictory onclusions: If it is true,then t is false and if it isfalse, then it is true. Since these consequences re contra-dictory, he expressionmentioned s consideredmeaningless.But it is likewisethoughtthat the expression an obtain ameaning, f the so-called" systemic mbiguity of the words" true and " false" is takeninto account. This I think s amistake. The expression" This sentence is false is notmeaningless ecause it leads to contradictoryonsequences, utfor muchdeeperand simpler eason; and it cannotobtainameaningby meansofany logical theories r deviceswhatever.Mypoint s, that the expression This sentence s false isnot a sentence t all in any logical sense. If the expressionmentioned s considered sentenceand the word "false " isconsideredhelogicalpredicate f thissentence,henthelogicalsubjectcannotbe thewholeexpression, ut at mosteither hewords" This sentence or the designation fthese words. Inthe firstcase the whole expression s meaninglessbecause" false is notthekindofpredicatewhich an be meaningfullyascribed o descriptionss " Thissentence Andin the attercase thewholeexpressions meaningless ecausethedescription" Thissentence hasnoobject, herebeingno sentence owhichthesewordscan refer. In neither ase caii any conclusions edrawnfromheexpressionmentioned,ndnoparadoxes merge.If the whole expression This sentence s false is assumedtruly o be a sentence ffirmingts ownfalseness,hen t has nopredicate,but the expression s a wholeis functionings thelogical subjectof a new sentence hat mustread: " The sen-tence 'This sentence s false is false . Then the includedsentences true,and the includingentence alse. And that istheendof t. No paradoxemerges.


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SOME REFLECTIONS ON REFLEXIVITY 291The included xpressions meaningless, owever,f it is con-sideredto affirmts own falseness. This is seen whenwe re-

member hat " false is a predicateof sentences or proposi-tions). When it is predicated t, therefore, resupposes hatthere s a sentenceof which t can be predicated wrongly rtruly). But if we are merelyconfronted iththe expression"This sentence s false , then there s no sentenceof which"false " can be predicated.The sameapplies,ofcourse, o theexpression This sentenceis true" which s also meaningless,lthoughnobodyhas,to myknowledge, rawnanyparadoxicalconsequences romt. Andthe same is, ofcourse, he case withthe expression This sen-tenceconsists f sixwords , which s neither ruenorfalke, utsimplymeaningless,ecause there s no sentence o which t canrefer. When the expression" This sentenceconsists of sixwords is often onsidered truesentence he reason s, in myopinion,that we are accustomedto conceivethe description" Thissentence as a descriptionf a sentence,nd theexpres-sionmentioned,einga sentencen a grammatical,lthoughnotin a logical, ense, we conceivethisexpression s thevery en-tence spoken about. But then our conception s reallynotexpressed n thegrammatical entencementioned, ut mustbeformulated n the more complicated entence: " The (gram-matical) sentence This sentence onsists f six words consistsof six words , where heincluded xpressions thelogicalsub-ject and the last occurring hrase " consistsof six words isthe logicalpredicate.It seems to me that this analysis also explainsthe paradoxfromwhichwe started. In the expression This sentence sfalse the description This sentence is rightly ssumedtorefer o a sentence, nd no other grammatical) entence hantheexpressionmentioned eingpresented,t is wronglyssumedthat the descriptionefers o this veryexpression,whichthenlosesits logicalpredicate nd therefores no logicalsentence tall. Not observing hischangebecause we seemto continue osee a sentencebefore s, we think hatwe can drawcontradic-toryconsequencesfrom t and therefore elieve that we geta paradox.The most important eneralization hat can be made fromtheseconsiderationss, to mymind, hatno sentence an referto itself, r thatno sentences re self-referring.nd thiscan,as faras I can see, be extendedto any linguistic xpressionswhatever,nay, to all so-called reflexivephenomena. Myreasonsforbelieving hisareas follows:


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292 J0RGEN J0RGENSEN:A phenomenonfwhateverkind t maybe is not a symbol,i.e. is notfunctionings a symbol,unless t is contained n aprocessof symbolizations a part ofthisprocesstakingplacein an organism. The linguistic ounds or figuresre in them-selvesor isolatedfrom processofsymbolization ot symbols,but solely sensationalphenomenaproduced by symbolizinghumanbeingsforwhomtheymayrepreseintr refer o some-thingdiffereintrom hemselves. Outsidethe symbolizingro-cessthey rebutremnantsfa linguistic rocess-just as a deadorganism s buttheremnants f a living rganism. The sounds

or figures re becoming ymbols gain, only f they are againused as such by becomingpart of a. new symbolizing rocess.A sentential xpression s such, i.e. as an auditive or a visualphenomenons notby itself eferringo anything, ut a humanbeingcainuse it forreferringo something ifferentrom hesententialexpression. He cannot,however,by means of asentential xpression efer o thisverysentential xpression-thisfact being a consequence fthe verynature ofsymboliza-tion. And nthesamewaya wordcan onlyfunction s a word,if t is partofa symbolizingrocess. If a wordor a sententialexpressions tofunction s a linguisticxpressionheremustbesomething ifferentrom hemto whichtheymayrefer ia anorganism, ut theycan neverrefer o themselves-thatwouldbe tantamount o theirreferringo nothing. Therefore,in-guisticphenomena re never elf-referringrreflexive.And this applies, I think, o all otherphenomena s well.Thereare no reflexivehenomena t all. This seemsto me tobe a simple onsequence fthe.notion frelation. Anyrelationpresupposest leasttwotermswhichmaybe moreorless alikein variousrespects, ut whichcan nevercoalesceinto a single-term,ftherelation hall notdisappear. If onlya single ermis giventherecannot be any questionof a relation. The soleone 1 couldthinkof is identity hich s often onsidered rela-tionwhich n objecthas to itself. But iden.tityn thissense sin my opinionno relation t all. It is but anothername forobject-the same object. To be sure,we can speak of twooccurrences r two appearancesof one and the same object,as well as we can speakoftwoobjectsbeing dentical n certainrespects, .g. whentheyhave the sane property r are havingthe samerelation o something. That,however, oesnotmeanthat there retwoproperties rrelationshatare identical, utsolelythat the sameproperty elongsto both objects,or thatseveral objects are having the same mutualrelation as someotherobjectshave-a property r a relationbeingsomething


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SOME REFLECTIONS ON REFLEXIVITY 293that cannotbe localized n space or time. Two differentpotsof colourmay have the sameshade of colour,we say. This,however, oes notmean that thereare two dentical hades ofcolour, utthatthe same (oneand thesame) shadeofcolour sto be found n the twospotsofcolour. There s no rela,tionfidentity etweentwo shades of colour,but the two differentspotsof colourhave a property viz. the shade of colour) incommon.Thepropertys thesame-and this s the senseofthephrase"the twospots of colourare identicalwithrespecttocolour . Two differentbjectsmayhave a propertyn com-mon; but thisfactdoes not constitute relationof identitybetween heobjects. As theyare two heycannotbe identical.Orly thecolours identicaln thetwo objects, .e. theyhavethesamecolour,but thereare not two colourswitha relationofidentity etween hem.Further,t maybe said that twodifferentameshave iden-tical meanings, f they denote the same object. But it haspresumably o senseto say, as it is oftendone,thatan objectis identicalwith tself,f " identical shouldheremean (indi-cate) a relation. Theexpression every bject s identicalwithitself can inmyopinion olelymean, hatno object s difterentfrom tself ua object,evenif t mayhave various ppearancesin differentituations. Eitheran object is the sameobject atvariouspointsof timeor space, and if so it cannot have anyrelation o itself, r the object s not thesameat variouspointsof timeor space,and if so there re severalobjectswhichmaystand n variousrelations o each other, ut noneofwhichcanhavea relation f dentityo anyof theothers. 4If I am rightn maintaininghat no objectorterm an haveanyrelation o itself, henall talkofso-called eflexiveelationsis senseless-a thesisthat I would illustrate littlefurtherymeans ofa fewexamples.In the sentence Theblackboards black" theword" black-board" designates blackboard. But in the sentence"Thewords ttheblackboard consists f 13 letters thewords"theblackboard designatenothing, ut are the veryobject aboutwhichsomethings predicated. The last sentencereally de-generatesntoa predicationywhich predicate, iz. " consistsof 13 letters , is predicated bout thepresent bject,viz. theword-image the blackboard -exactly as when somebodypoints t a blackboard nd says " is black" or solely" black".In the sentence The words the blackboard' consistsof 13letters the words" the blackboard is neither he subject-termnor the designation f the logical subject,but the very


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294 J0RGEN J0RGENSEN:subject tself,.e. theobjectaboutwhich omethings predicated.In thiscase the object, which s thegrammaticalubjectofthestatement,s exceptionally word-image,ut it is not a word,if " word is to be understood s something hat designatessomething.Take thenthe sentence The word long is itself hort .Here the word "long " designatesnothing-although t isgenerally sed to designate property, hichdoes not belongto the word-image long . But in the sentence" The word'short is short the second "short" designates propertythat belongs o theword-image short" itself. This,however,does notmean, hat the word" short herereferso itself. No,it designates property hat exceptionally elongsto the ex-pression short itself, .e. a property hatbelongs,notto theword short , butto theword-imageshort . And thisword-image s not a word, .e. it is notfunctionings a symbol n asymbolizing rocess,but is simplyan object that happens tohave the property alled short.We are now able to dispose of and explain Grelling's orWeil's) paradox according o which t is apparently ossibletoprove hata heterological ord s notheterological. A propertyword (e.g. an adjective) is called heterological,f designatinga propertywhich does not belongto the word, .e. the word-image, tself. The adjective" long" e.g. s a heterological ord.If thenweaskwhether heword heterological itself s hetero-logical,we seemto be led to contradictorynswers: if it isheterological,t is not heterological;and if it is not hetero-logical,then t is heterological. This paradox s in my opinionsolved and explainedwhenwe realizethat it is absurdto ask,whetherheword" heterological itself s heterologicalrnot.The word" heterological designates property elonging ornotbelonging) o a word, iz.a word hatdesignates propertywhichbelolngs o the corresponding ord-image. n ordertodecidewhether word s heterologicalr not, t is necessary olook at its word-image. But it has no sense to predicate heproperty heterological" to the word-imageheterological",because theword" heterological does notdesignate propertyof a word-image, ut a property f a word,namelya worddesignating property. The paradox arisesby a falseidenti-fication fa wordwith ts correspondingord-image-only heword can be meaningfullyaid to be heterological,whereasadjectives s " long" or " short can onlybe ascribed o word-images. Wordscan neither e longor short, nd word-imagescan neither e heterologicalorhomological.


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SOME REFLECTIONS ON REFLEXIVITY 295A paradox of a similar haracter s Berry's paradox whichruns as follows: In English, he lowest ntegernot nameableinfewerhan19syllabless found obe nameable n 18 syllables.This seems to be a contradiction.The number s 111777, .e."one hundred nd eleventhousand evenhundxed nd seventyseven . This numberdesignation ontains19 syllables. Butthe numbermentioned a,nalso be unambiguouslyermed:" The least integer ot nameable n fewer hannineteen ylla-bles" wherewe haveonly18 syllables.The paradox seemsto depend on the simplefact, that the

relation etween n objectand its designations assumedto bea one-onerelation,whereas t is reallya one-many elation.Au objectcanbe designated nambiguouslyy variousdifferentdesignations,nd theseneedinot containthe same numberofsyllables. There is no contradictionn saying: " The leastintegerwhosenumber-nameonrtainst least 19 syllablescanalsobenamedbyanothername thatcontains ut18 syllables .Confer .g. the description the largestEnglishtown whosename containsat most two syllables on the one hand, and" London" on theother. Herethetownvondon s designatedby the disyllable" London" as well as by the much longerdescription the largestEnglish towinwhosename contains tmost two syllables , but there s no contradictionn namingthis town n bothways. If, however,we assume thattherela-tionofdesignations one-one, henwe have to facethe paradox:" The largestEnglish town whosename contains t most twosyllables as a name thatcontainsmanymorethan twosylla-bles ". Reallythisstatementoncerns wodifferentames, ndthere s no paradoxat all. Theappearance f paradox dependsuponthewrong ssumption hatthetownhas but one name.In a similarway it is, in my opinion, ossibleto disposeofand explain the paradox of " the relationwhichholds betweenR and S whenever does not have therelationR to S "-mypointbeingthat it is meaninglesso assumethat a relationRcan be its ownrelatum. But there re otherparadoxeswhichdependona wrong seofthe wordorconcept f" all ", and thesolution f which eemsto me to claima kind ofdistinctionftypes-although very impleone. The mostfamous ftheseparadoxes s, of course,Russell's paradoxto which will nowturn.It iswell-knownhat thisparadoxconcernsheclass ofclasseswhich renot members fthemselves. Apparentlyhisclass is,a member f tself,f t is nota member f tself; aind t is nota member f tself,f t is a member f tself. The solution hat


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.296 J0RGEN J0RGENSEN:Ruhssellffers ependson the assumption hat " a propositionabout a class is alwaysto be reduced to a statement bout afunctionwhichdefines he class, i.e. about a functionwhich ssatisfiedythemembersf the classandbyno other rguments(Prin. Math.,Vol. I, p. 62-63. 2nd edn.). Hence a class can-not,by the vicious-circlerinciple,ignificantlye an argumentto its definingunction,nd therefore either atisfies ordoesnot satisfyts definingunction,nd so is neither member fitselfnornot a member fitself.While agreeingwithhis conclusion am not at one withRussell n respectof the argument hat leads to it. To me itseems simpler o resort o the followingolutionwhichat thesametimegivesan explanation f the appearanceof thepara-dox.A class is a collection fobjectsthatare said to be membersof theclass. A class,therefore, ustcontain t least twomem-bers n order o be a class. Incidentally mayremark hatforthe same reason I considerexpressions s "null-class and" unit-class to be merelywaysofspeaking fa,onsde parler)and not existing ntities. If we put theparticle all " beforea class name in a propositionbout a class,we are not predi-cating omethingboutthe class as suchbut aboutitsmember-ship distributively,.e. we are ascribing he predicate o eachmember fthe class. The proposition All S are P " says thateach S severallyhas theproperty -not that the class S hasthis property. "All horsesare four-legged means e.g. thateach horsehas four egs-not that the class ofhorseshas fourlegs. This s thesimple easonwhy classis typically iflerentfromtsmembers,ndwhy classcannotbe a member f tself.Whatever therproperties classmayhave,it mustcontain tleast two membersn orderto be a class at3 ll. And a classcannot,no morethan any otberobject, have any relationtoitself, .g.be a member fitself. Thatwouldmeanthattherecouldbe a classwithoutmembers, ut that is absurd. There-fore, heexpression theclass of classeswhich renotmembersof themselves is a meaninglessxpressions wellas the expres-sion " the class of classes which are members f themselves.Andthereforeheparadoxdoesnotarise at all.To be more xplicit: A class, S, presupposes hat thereareobjectswhich re members fit. If these objectshave a com-monproperty,, thenthe class S can be dlefineds thecollectionofall theobjectsthathave thisproperty. But thispropertycannotbe a propertyf the class S becausethat would mean,that S shouldbe one of the objectsbelonging o the class S,


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SOME REFLECTIONS ON REFLEXIVITY 297since this class was defined s the collection f all the objectshavingtheproperty . If we tryto escapethis conclusion ydefining: "The class S consistsof all objects having theproperty except he class S ofthese objects-plus this class ",thenwe do not knowwhat S meansand thereforeo notknowwhatwe should xceptfromhisclassand thenadd to theotherobjectsin the class in order to get S. This way of escape isthereforempossible. To be sure, we may tryto define heclass S "intensionally withoutknowingwhether here aremembersn it or not according o the scheme: "The class Sconsistsof all objectsthat have the property ". But suchdefinitions to my mindanalyticor verbal. It solelymeansthat f here reobjectshaving heproperty we will call thlemmembers f the class S. By this we have defined he use oftheword" S " but not a class, becausewe do not knowwhethersuch class exists or not, i.e. whether here are objects havingtheproperty ornot,and ifthere re no suchobjectsthere sno class to be defined. The intensional efinition,herefore,snot a definition f a class but solelyof a word, hypotheticalclassname. To sumup: We mustdistinguishetween lassesand class names. Classesmustat leasthave twomembers,ndcan never be membersof themselves. So-called intensionaldefiritionsfclassesarereallybutdefinitionsfclassnamesandconcerns olelyourlanguage,but notreal collections fobjects.At thispoint twill,however, erhapsbe expedient o remarkthattheword all " and " class" have what Russell calls " sys-temic mbiguity. As alreadymentionedheproposition AllS are P " meansthat every singleS has P (or belongs o theclass P). The collection r class of P's maybe said to be anenatityf another ogical type than the members f it. Thistype may be called type I. If severalclasses of type I aredefined,we may collectthem n a super-classnd say that allclassesof type are members fthesuper-classwhich s,how-ever,ofanother ogical typethatmaybe calledtype I. Andso on, in accordancewithRussell'ssimple heory ftypes.The objects fromwhichwe start the construction f thishierarchyf classesmaybe of variouskinds. They may,e.g.beindividual hings, r single properties f individualthings, rrelationsbetween ndlividualhings. But if we speak of "aproperty fa property or " a relationbetween elations weare movingup in a hierarchy f properties r a hierarchy frelations-each new type being characterized y its membershavingmembers f the next owertype. The word" all" alsochanges ts designativemeaningor function s we ascend the


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298 J0RGEN J0RGENSEN:hierarchy, he word " all" placed beforea class-name n apropositioneferringlwaysto themembersfthe class namedand never o thatclassitself.I think here s no need of any morecomplicated heory flogical types. But what about the so-calledreflexibilityflanguagesAs is well-knownwe can, in a certainsense, speak of alanguage n the la,nguagetself, nd Carnaphas even, in his" LogicalSyntaxofLanguage ", takenthetrouble o constructan artificialanguage containing ts own syntax. May suchlanguages hennotbe reflexivehenomenaI don'tthink o, a,nd hallnowtry o showwhy. To do so itwill, believe,be sufficiento consider ur everydayanguage.This is, as Tarskisomewhereemarks,n " open" language nthe sense that its vocabularyas well as its syntaxmay bechangedorextended s thelanguagedevelops. But it is inmyopinrionopen" in an even morefundamentalense: If I pro-nounce sentence 2 aboutanother entence ,, thenS2 s a newlinguistic henomenon-even f it is perhapssimilarto S, insucha way thatthere s but a numerical ifferenceetween ,and S2* If S2 consists fthe " same" words ssS,, and ifthesewordsare arranged n the " same" orderas thesewordsarearranged n S,, thenS2 may be said to have spokenabout S,without hanging itherthe vocabularyor the syntaxof thelanguage in which the two sentencesare spoken. But thevocabulary nd thesyntaxofa lan,guages but an abstraction,a structure, hilethelanguage tself s a concrete henomenonintimeorspace-or more trictly an unlimited ourseorla;pseof concretephenomena. As long as a language s used, it is" open", even fitsnewsentences re built ofelements f oneand the same vocabulary, nd according o one and the samesyntax. Therefore sentencecan neversay anything boutitself. It is, indeed,not a sentence eforet is finished,nd ifsomethings to be said about it, thenthissomethingmust besaid after hesentences finished. Thecase is similar oRoyce'smap ofEnglandwhichhe thoughthould. on,tain map ofthemap, a.nd map ofthemap ofthemap,and so on,in order obe complete. That is not the case. There shouldnot be anymap ofa map before hefirstmap is designed. Andwhenthefirstmap is designed here houldonlybe a map ofthismap.In order to be complete map ofEnglandshallnever containa (complete)mapof tself. An infiniteumber fmapsofmapsofEnglandnever xists, nd thereforehouldneverbe mapped,butanynumber freallydesignedmapsofmapscanbemapped,


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SOME REFLECTIONS ON REFLEXIVITY 299and the latestofthem s alwaysthe correct nd completemapcorresponding o the prevailing tate of affairs-until t isfinishedtself. Thena newmap shouldbe madecontaininghepreceding ne. And when ithatne is finished newone, andso on. As longas Englandand the mapping f England s notfinished ew maps ought o be made,but theinfinitys alwaysa progressivene and never contains finishednfinity. n asimilarwaythe anguage s always progressing.Any repetitionof a sentence s a newoccurrencefthesentence,nd a sentencecannotsay anything f a sentencehat is not yet finished,utat mostoftheabstract ormwhich heunfinishedentencemaybe assumedto have-when it is finished.In the same way alanguagecannot say anythingbout thislanguageas a whole,because the pronouncementbou4 the "whole" languagewilladd somethingo it. But onepartof a languagemay verywellsay somethingbout another concrete r abstract)partofthelanguage, rovided hat this other artalready xists. Andtheparts may verywell be similar,but can neverbe identical.This is but anotherway to say thatalsentence an neverreferto itself, everbe itsownsubject.Similarly,elf-consciousnesss never reflexivehenomenon.The act ofconsciousnessn whichwe are conscious fourselvesbeingconscious f somethings alwaysa newact of conscious-ness,and thisnew act ofconsciousness an onlybe consciousnyet another new act of consciousness.Therefore n act ofconsciousness an never be consciousof itself. But we, aspersonsexisting n time can successively e consciousof ourprecedingacts of consciousness, lthoughwe can never beconscious f ourpresent ct of consciousness efore t is corn-pleted. That wouldmean to jump over our own shadow,orrather: thatwouldmean to be conscious fsomething ithouttherebeing anything o be consciousof. " Introspectionsalways retrospection, as Professor ylehas said,I think.Themainpoint s, inmy opinion, hatknowings a temporalprocess, nd thatanyact of knowingmustexistbeforewe canknow it-otherwisewe could knowor speak about an act ofknowinghat does niob et exist n the sense that it wo-uld enothingt all.In thesamewaywe can,I believe,disposeofother eeminglyreflexivehenomenas, e.g. " a theory ftheories , " a conceptof concepts , "linowledge of knowledge, and so on. Butwhat about the so-calledreflexive lasses of numbers Aretheynotgenuinely eflexive I don't think o, and I believethe so-calledparadoxesofthe infiniteeriesofnumbers an be


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300 J0RGEN J0RGENSEN: SOME REFLECTIONS ON REFLEXIVITYshowntodependon a failure o distinguishetween wosimpleforms fnaturalnumbers. But thisdistinctioneing bit morecomplicated hanthe abovementioned will eave it for notheroccasion. What I have intendedhere is merely o show thepossibility f eliminating ome of the paradoxeswhichmanylogiciansnowadays seem to have accustomed hemselves o insuch a degreethat they almost considersuch anomalies asestablishedmattersof course. As far as my memory ervesme, Lord Russell somewhere ays that " paradoxes are theexperimentsf ogic". I don't agree. To mymindparadoxesare rather" traps of logic ", and I don't like to see logicianstrapped-not evenin theirowntraps. I, therefore,ave triedto destroy omeof thesetraps. Whether have succeededornot I leave to you to decide. But shouldmy presentpapermerely erve as a warning gainstthetraps, nd as a reminderofbeing cautious, shouldconsider ven suchmodesteffectsnotbeing quiteunsatisfactory.UniversityfCopenhagen

jorgensen _ some reflections on reflexivity

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