Kunskapsproduktionens ritualisering

I inlägget Vetenskap som vägvisare skrev jag att en viss uppsättning idéer om vetenskapen – på ett liknande sätt som idéer om demokratin – led ett sorts nederlag, grovt räknat under 1800-talet, och att de därigenom transformerades från att utgöra förändringskrafter till att utgöra kompromissbildningar. Från att ha representerats av en relativt mångfacetterad kör av röster i opposition, kom de att placeras i det moderna samhällets centrum. Jag skall här förklara varför denna process kan förstås som en process av ritualisering.

I det moderna samhället är kunskaper heliga. Detta kommer till uttryck genom att kunskapsproduktion utgör en av det moderna samhällets viktigaste ritualer. Den kunskapsproducerande ritualen har två väsensskilda sidor: kunskapsproduktion förstådd som lärande och kunskapsproduktion förstådd som forskning. Båda dessa ritualer förstås i metaforiska termer, som växande, skapande, frambrigande och upptäckande. Men medan lärandet förstås som väsentligen reproduktivt förstås forskningen som nyskapande. Lärandet är i det moderna en folklig ritual, påbjuden och obligatorisk. Forskningen är en ritual för en utvald elit. Lärandet utgör, kan man säga, en reproducerande upprepning av forskningens ursprungliga skapande. Tillsammans utgör forskning och lärande en liturgisk ordning, som demonstrerar och tydliggör för det moderna samhället vad deras värld består av och fungerar, liksom vilken plats som de enskilda samhällsmedlemmarna intar i denna värld – liturgin tydliggör hur varje enskild människa står i förhållande till kunskapen, i egenskap av “kunnig” – det vill säga en framgångsrik lärande, eller som “forskare” – en framgångsrik kunskapsproducent.

Det paradoxala med denna liturgiska ordning, och som är min poäng i fråga om vetenskapen, är att det moderna samhället neutraliserat lärandet och forskandet – förstådda här i en mer allmän, ickeritualiserad bemärkelse – genom att ställa dem i samhällets centrum som ritualer. I och med detta har innebörden av orden förändrats på ett genomgripande sätt.

Enligt en användbar definition av “ritualens form” – jag hämtar den från Roy Rappaports Ritual and Religion in the Making of Humanity (1999) – karaktäriseras ritualer av:

  • En praktik vars form mer eller mindre definierats på förhand, av andra än de som deltar i praktiken.
  • En praktik som är mer eller mindre invariant i tid och rum, det vill säga utförs på mer eller mindre samma sätt på många olika platser, på ett sätt som är relativt oföränderligt.
  • En praktik som är formaliserad, reglerad och övervakad och som ofta äger rum på en särskild plats enligt ett särskilt schema, en särskild rytm.
  • En praktik vars konsekvenser står i ett komplicerat förhållande till sin intention eller påstådda effekter.

Det är inte svårt att se att denna definition passar både lärande och forskning.

När denna typ av handlingar utförs förmedlas två sorters budskap. För det första förmedlas ett budskap om vad som finns i världen, hur världen fungerar, vad som är viktigt och så vidare. I fråga om lärande och forskning är budskapet att kunskap och kunskapsproduktion är viktigt och att världen är sådan som vetenskapen säger att den är; den säger att det är viktigt att ha kunskaper och att det är viktigt att det hela tiden produceras nya kunskaper; att kunskaper gör livet, samhället och världen bättre. Det är det första budskapet. För det andra förmedlas ett budskap om de som deltar i ritualen som säger hur de står i förhållande till kunskapen. Läranderitualen demonstrerar, genom de tecken som deltagarna frambringar (“svar”) hur framgångsrika de varit vad gäller “lärande” och hur mycket kunskaper de därmed “har” – där citationsteckningen syftar till att skapa distans till förgivettaganden rörande detta “ägande” av “kunskaper”. Forskningsritualen demonstrerar, genom den process genom vilken textprodukter examineras och konsekreras, hur mycket kunskap forskaren “producerat”. Medan den kunskap som blir resultatet av lärande antas husera inuti den kunniga människan, huserar de av forskaren producerade kunskaperna där ute, i världen.

Avgörande är här att lärande och forskning är aktiviteter som fyller en samhällsreproducerande och samhällsstrukturerande funktion (en förklaring i bilder finns här). De är initieringsriter och konsekreringsriter, med ett vardagligt språkbruk delar av kulturella sorteringsmaskiner. Detta gör att skrivande, inom vetenskapens ramar, inte syftar till läsning i en allmän bemärkelse, utan till en mycket specifik sorts räkning. Forskare skriver inte för att bli lästa, utan för att räknas, som forskare. De skriver för att deras texter skall räknas som kunskapsbidrag, något som är en förutsättning för deras sociala existens som just forskare. Det samma gäller eleven, som inte tar sikte mot lärande i en allmän bemärkelse, utan förmågan att producera de svar som gör att hon räknas som kunnig.

Det finns nu ett teoretiskt krux med denna förklaring. Kruxet består i att personer i det moderna samhället, liksom medlemmar i andra kulturer, vet mycket väl hur deras ritualer fungerar. De uppfattar inte “förklaringen” som ett tillskott av information. Och det är, givetvis, redan väl känt att elever “pluggar för provet” och att forskare skriver för meritering.

Med en idé som utforskats ganska grundligt inom psykoanalysen och psykoanalytiskt inspirerad filosofi kan man säga att ritualerna är genomskådade, vilket betyder att de flesta som delar i dem, om de stannade upp och tänkte till – något olika personer gör mer eller mindre ofta – skulle inse och för sig själva bli klara över att det de gör utgör ett ytligt regelföljande. Ibland talar man om detta fenomen i termer av cynism, men det är inte riktigt vad det är fråga om. När vi är artiga är vi till exempel sällan uppriktiga. Även när det gäller artighet är det möjligt att stanna upp och fundera över vad vi egentligen tycker och tänker om de vi umgås med. Ett “autentiskt” beteende skulle förmodligen inte vara så artigt – kanske allt för intimt, eller allt för kyligt och avståndstagande. När vi är artiga, till exempel när vi hälsar på varandra, deltar vi i en ritual, och de är inget cyniskt med det.

Det är på detta sätt som jag menar att man skall förstå både skola och vetenskap – som något man bara gör, på ett självklart sätt, som en av de saker man måste göra, som det går att reflektera över och kritisera – men som det är föga meningsfullt att kritisera och reflektera över, eftersom sådant bara ställer till problem och ändå inte leder till något gott.

Så fungerar ritualer; så bevarar de sin plats; så förhåller de sig till människors reflexivitet.

Utifrån denna analys kan man skilja mellan texter skrivna inom ramen för en ritual och som därför inte är tänkta att läsas utan för att fungera som tecken på kunskapsproduktion, och texter som är skrivna för att läsas och därmed förmedla något, från en person till en annan. Texter producerade inom vetenskapens ram är, kan man säga, biprodukter. De är en restprodukter av en social process. Och denna sorts texter ackumuleras därför i rask takt. Man kan jämföra denna ackumulation med den biprodukt som blir resultatet av lärande, nämligen svar, riktiga och felaktiga, på skolans tränings och examinationsuppgifter. Även dessa svar bär på en myt om användbarhet, men denna användbarhet ligger i den effekt deras produktion antas ha på producenten i form av framväxandet av ett litet stycke kunskap. Forskningsartikeln antas vara användbar i kraft av sitt kunskapsinnehåll som antas ha effekter – goda, förbättrande – på världen. Denna myt upprätthålls genom den aspekt av ritualens form som kräver att texter måste “referera” till publikationer för att ha möjlighet att upphöjas till publikation.

Ett användbart ord i sammanhanget är byråkrati. Inte alla byråkratiska procedurer kan förstås som ritualer, men skolans och vetenskapens ritualer kan förstås som byråkratiska. Och termen är användbar eftersom den skapar rätt associationer av maskinmässighet, regelföljande, och ytlighet.

Jag skall avsluta detta inlägg med en reflektion kring berättelserna i bibeln (Lukas 14:5, Matteus 12:11) som handlar om när ett akut problem uppstår på sabbaten då man inte får arbeta – en oxe, ett får eller kanske ett barn faller ner i en brunn och är på väg att drunkna. Jesus frågar om man då inte skulle rädda barnet, sabbaten till trots, och menar att detta är det rätta. Jag tolkar det som Jesus säger som att man skall vara medveten om att de ritualer man följer är just ritualer, att man skall vara klar över att de är genomskådade, och därmed också ha förnuftet i beredskap för att avgöra när det är dags att ta ett steg ut ur den rituella logiken – om det så handlar om ett akut problem, men också om ritualen är allt för plågsam, tar allt för lång tid eller kanske helt enkelt är för idiotisk för att tas på allvar.

Jag tänker att denna berättelse – som är så att säga epistemologisk – har en etisk motsvarighet i berättelsen om den barmhärtiga samariern (Lukas 10:25). Även här är utgångspunkten ett stycke kultur, förhållningsregler för sociala relationer. Jesus säger att man skall ha kärleken i beredskap, på ett liknande sätt som förnuftet, för att se när man skall ta ett steg ut ur de sociala konventionerna och istället agera utifrån en förutsättningslös kärlek, på samma sätt som man när det gäller brunnen skall agera utifrån ett förutsättningslöst förnuft, en förutsättningslös kreativ reflexivitet för att se till att problemet får en snabb och bra lösning.

Vad man tar med sig in i dessa situationer, dessa undantagstillstånd, har såklart till viss del formats inom den mer eller mindre ritualiserade kulturens ramar. Men det man gör när man klivit ut, är något annat än det man gör när man följer kulturens påbud och handlar ytligt.

I den väldigt bra boken On Critique (engelska: 2011, franska: 2009) talar den franska sociologen Luc Boltanski om de tillfällen då man stannar upp inför invanda handlingsmönster för “reflexive moments”. Den typ av handling som utgör regeln kallar han för pragmatisk. Den innebär tyst acceptans, trots glappet mellan handling och förnuft.

Ivan Illich menar att modernitetens ritualer är perverterad kristendom. Han berättar om detta i Rivers North of the Future (2005). Det paradoxala är att moderniteten fångat upp både förnuftet och kärleken, så som de kommer till uttryck i de två berättelser jag refererat, om brunnen och samariern. Men moderniteten vill göra detta handlande, det kärleksfulla och förnuftiga handlandet, till regel. Moderniteten har därmed ritualiserat både förnuftet och kärleken. Det jag skrivit om här kan förstås som förnuftsanvändningens ritualisering. Och det är det faktum att det är just förnuftet som utgör ritualens myt som – begripligt nog – gör den extra svår att “kliva ur”. När det som tidigare var existensen av en allsmäktig Gud som man tillfälligtvis skulle lägga åt sidan var det så att säga enklare. Nu säger ritualen att den själv är det förnuftigaste som finns. Och andra uttryck – som till exempel den här bloggpostningen, som är till för att läsas och därför aldrig kommer att räknas som ett kunskapsbidrag och därmed aldrig kommer att bidra till någon “meritering” inom vetenskapen – har på förhand diskvalificerats som “tomma” vad gäller förnuft och kunskap. Det förstås som åsikt och opinion.

Det är av denna anledning som jag menar att det är svårt att se vad för gott vetenskapen skulle kunna göra för förnuftet – den är ju i egenskap av ritual förnuftets själva motsats.

Vetenskap som vägvisare

Andrej Slavik vill göra motstånd mot den ekonomiska makten och undrar:

Min egen fråga gäller om och hur universitetet kan bli en del av en sådan motrörelse. Akademisk frihet i all ära, men som institution står universitetet – sträng taget, det moderna universitetet – givetvis inte fritt från den konflikt mellan demokrati och kapitalism som Streeck beskriver. Det är inte heller inbegripet i konflikten enbart till följd av yttre omständigheter – dess finansieringsformer, för att ta det mest uppenbara exemplet – utan också och framför allt eftersom det redan från början utgör ett politiskt projekt. I filosofiska termer: universitetet är implicerat, inte bara de facto, utan också de jure. Det handlar bara om att först förstå detta faktum och sedan agera därefter. Och nej, det är förstås inte så bara.

Andrejs förslag, så som det kommer till uttryck i Marknadens makt och universitetets möjligheter, är inte helt olik förslaget i det tidigare diskussionsbidraget Sex kontradisciplinära påståenden, nämligen att humaniora, samhällsvetenskap och konst skall slå sina kloka huvuden ihop och bilda en “kulturvetenskaplig koalition”: Humaniora bidrar med “idékritik”, samhällsvetenskap med “maktpolitisk medvetenhet”, konst med “taktiker och strategier” som gör det möjligt att “sätta kraft bakom orden i en post-demokratisk offentlighet som översköljs av oupphörligt stegrade informationsmängder i form, inte bara av texter, utan också av bilder och andra former av data”. Denna koalition skall lägga av med att bekämpa den positivistiska scientismens väderkvarna, ty:

Vad som behövs idag är faktiskt raka motsatsen: en återerövring av begreppet vetenskap, betraktat som ledstjärna för universitetet som samhällsbärande institution, ur ett medvetet och uttalat politiskt perspektiv.

Vetenskapen skall bli en politisk kraft som gör motstånd mot den ekonomiska makten, mot den nyliberalismens utbredning in i minsta skrymsle av det moderna livet som Wendy Brown beskriver i Undoing the demos.

Jag tänker lite annorlunda.

Jag är förbannat trött på vetenskapen. Vad är det egentligen för “vetenskap” som skall återerövras? Denna fråga skall förstås som en parallell till den fråga om demokrati på vilken Alain Badiou bestämt sig för att svara nej eftersom den för honom framstår som en form allt för snäv för att rymma den typ av frigörelse han tycker man bör sikta mot. Alla vet att de stater och överstatliga organisationer som idag kallar sig “demokratiska”, knappast lever upp till begreppet – att det på denna punkt finns ett ofta katastrofalt glapp mellan ideal och verklighet.trumanshow Den väg som den moderna ordningen pekar ut för förbättring är att minska detta glapp – men Badiou säger att detta aldrig kommer att lyckas, eftersom det är en väg som stakats ut av precis de krafter som aldrig vill se demokrati realiserad, som aldrig skulle acceptera demokrati realiserad. Vi måste därför, säger han, göra det oerhörda, och förkasta själva målet, själva idealet. Då ger vi oss ut i djupa vatten, givetvis; vi tar en mycket större risk. Vår moderna värld är ganska tajt riggad, kan man säga – och jag tänker här på The Truman Show och det entydiga budskap som installerats i resebyråerna i hans värld, Seahaven – mot idén att välja bort demokrati som ideal.  Och det är givetvis inte vad jag skall föreslå här.

Men vad med vetenskapen?

Vetenskapens neutralisering

Min förståelse av vetenskapen utgår från en sorts skapelseberättelse som stelnat för mig under läsande av diverse vetenskapshistoriska och filosofiska texter. Nyckelhändelsen i denna berättelse utspelar sig under första halvan av 1800-talet. Innan denna episod flöt det vetenskapliga samman med det konstnärliga, poetiska, etiska och det politiska. Vetenskapen var en förändringskraft, och dess naturvetenskapliga sida var i opposition, en underdog, fortfarande, som ville förändra samhället. Det var revolution och revolutionsförsök. Till och med kristendomen kunde ifrågasättas. Det var en öppen fråga vilken typ av nytt samhälle som det vetenskapliga, förnuftiga tänkandet skulle frambringa.

Men – så står det i min berättelse – revolutionsförsöken slogs ner. Förändringslustan kvästes. Ordningen återställdes.

Kvar blev en neutraliserad vetenskap, en vetenskap som fortfarande stod i framstegets tjänst, en vetenskap som fortfarande var utopisk – bara nu på ett lite annat sätt; ett sätt som inte var lika hotfullt. Den stod, kan man säga, för förändring “med måtta”. Med ledning av den tyska filosofihistorikern Herbert Schnädelbach och hans Philosophy in Germany 1831-1933 har jag punktat upp följande förändringar:

  • Empirisering. Från och med nu måste man som vetenskapare arbeta med ett empiriskt material. Det duger inte att sitta som filosof vid skrivbordet och bara tänka. Det är inte vetenskap. För tankarna kan driva iväg, allt för långt bort från verkligheten, sådan den nu en gång är.
  • Proceduralisering. Från och med nu förknippas vetenskapen med att följa en viss procedur, snarare än med ett visst “vetenskapligt” kunskapsstoff. Att vara vetenskaplig är att följa en metod, en på förhand utstakad väg som håller tänkandet på rätt kurs. Snarare än att som tidigare förlägga människans kompass inuti henne, i hennes personliga förnuft, flyttas kompassen ut till en regelbok, vad man men en antropologisk term kan kalla en ritual.
  • Dynamisering. Vetenskapen förstås från och med nu som en samhällsförändrande kraft, en institution i ständigt pågående förändring. Med denna nya form av vetenskap får det moderna samhället rörelsen som en omistlig del av sin självbild – en rörelse mot ett mål som per definition aldrig kan nås. Sanningen – slutpunkten – placeras bortom det fattbara och det nåbara.
  • Av-ontologisering. Vetenskapen tar ett steg tillbaka från sina tidigare anspråk på att säga hur verkligheten egentligen är. Inte ens den matematiska fenomenvärld som Kant förstod som människans lott ligger längre fast: allt flyter, och vetenskapens resultat förstås som “modeller”, approximationer.
  • Funktionalisering. Vetenskapen får från och med nu sitt främsta värde genom sin instrumentella användbarhet: modellerna möjliggör prediktioner, och dessa prediktioner möjliggör kontroll. Sanningen och verkligheten diskvalificeras som ovetenskapliga.
  • Av-politisering. Vetenskapen kopplas loss från politiken – och här har jag en fråga: kan man kanske säga att även den moderna politiken tar form i samma rörelse, det vill säga inom ramar som delvis utgörs av denna nya avpolitiserade vetenskap? Klart är att vetenskapen blev ett tjänstehjon.
  • Professionalisering. Och med detta blev det också rimligt för de nya staterna att hålla sig med en kader av forskare, som aldrig kunde hota politiskt, utan alla drog i samma riktning, mot det metodologiskt bestämda framsteget.
  • Av-personifiering. En sista förändring vars betydelse inte skall underskattas är att vetenskapen slutade vara ett projekt för enskilda tänkare (pace Einstein och kulten runt honom). Att arbeta vetenskapligt blev att underkasta sig vetenskapens krav och bli en expert vars legitimitet vilar just på att hon inte tänker själv, inte självständigt – och egentligen inte tänker alls, utan låter den vetenskapliga metoden verka genom henne – det vill säga att hon gjort sig till redskap för något större och antagligen bättre än det förnuft som alltid är så olyckligt färgat av den enskildes särart, hennes kropp, känslor, fantasier.

Denna vetenskap kan på ett sätt som skär genom antropologi, psykoanalys och historia förstå som en kompromissbildning: den är en förskjutning som möjliggör en verksamhet som på samma gång verkar för förändring och för stabilisering. Vetenskapen får, genom sitt nederlag, ett ritualistiskt moment – vilket är typiskt för kompromissbildningar; den blir till en produktion av sken, som skiner starkare än sin föregångare, men bara för att dölja att det mörker som står i dess centrum. Och som det kan gå med ritualer och kompromissbildningar, blev denna vetenskap så lyckad – politiskt, kapitalistiskt lyckad – att den började expandera, för vem vill inte ha ett sken av förändring som som garanterar att allt förblir som det är?

Efter detta nederlag fastställdes det vilken typ av samhälle som vetenskapen var en del av, nämligen ett kapitalistiskt samhälle. Liksom Badiou tänker om demokratin, tänker jag om vetenskapen: det är en förändringsväg som aldrig kan leda ut ur den ram som genererar vår tids olycka.

Väl att märka betyder detta inte att vetenskapen är ond; att den skulle bidra till olyckan – eller ens att den inte skulle bidra till något gott. Vad det betyder är att den utgör en kompromiss. Den representerar ett beskuret tänkande som på förhand tror sig veta att det inte bör tänka fritt, eftersom det då av naturen kommer att tänka fel. Detta är vad vetenskapen lärde sig under de där svåra åren på 1800-talet (tänker jag mig).

Science is the Enemy

Slavoj Žižek har skrivit att Demokratin är fienden:

We do not vote concerning who owns what, or about the relations between workers in a factory. Such things are left to processes outside the sphere of the political, and it is an illusion that one can change them by ‘extending’ democracy: say, by setting up ‘democratic’ banks under the people’s control. Radical changes in this domain should be made outside the sphere of such democratic devices as legal rights etc. They have a positive role to play, of course, but it must be borne in mind that democratic mechanisms are part of a bourgeois-state apparatus that is designed to ensure the undisturbed functioning of capitalist reproduction. Badiou was right to say that the name of the ultimate enemy today is not capitalism, empire, exploitation or anything of the kind, but democracy: it is the ‘democratic illusion’, the acceptance of democratic mechanisms as the only legitimate means of change, which prevents a genuine transformation in capitalist relations.

Jag tror att det samma kan sägas om vetenskapen i den mån man är ute efter radikal förändring, i den mån man vill handla politiskt. Vetenskapen expanderar, som en del av kunskapssamhället, det lärande samhället, det evidensbaserade samhället. Vetenskapen expanderar som en del av utbildningssystemet, det nya universitetet, där varje lektion är underställd lärandemål och lärandemetoder, och integrerade i program för anställningsbarhet. Vetenskapen är en del av det nät av regler, skillnader, procedurer, värden som breder ut sig och förändrar, förstorar och förstärker den moderna världen, det moderna sättet att leva. Att ty sig till vetenskapen kan inte vara något annat än att skriva under på och skriva in sig i detta nät. För vilka är annars de discipliner som skall åstadkomma förändringen? Har inte forskarna förtjänat sin plats genom att underkasta sig den vetenskapliga kompromissen, det vill säga lovat att inte tala sanning – eftersom den är ovetenskaplig; lovat att begränsa sina visioner till det vetenskapliga framåtskridandet?

På universitetet finns otvivelaktigt personer som kan utgöra en radikal förändringskraft. Men den förändring som behövs kan idag aldrig ske i vetenskapens namn. Vill man förändra måste man kliva ur den vetenskaplig dräkten, det vetenskapliga språket, och stå själv för det man säger. Vetenskapen kan inte föra en sådan talan.

Våga vägra vetenskapen

Snarare än en allians av discipliner tror jag på en allians av personer, som klivit ut ur vetenskapen för att göra något väsentligen annat, nämligen använda sitt eget förnuft. Tillbaks till Kant med andra ord – mycket hellre än ett återupplivande av en lobotomerad vetenskap. Moderniteten är besatt av vetenskapen, på ett liknande sätt som den är besatt av demokrati, ekonomisk tillväxt, hälsa, rasism, feminism och mänskliga rättigheter. På alla dessa punkter har den satt av, i full fart, som en idiot, på ett sätt som aldrig kan leda till målet. Och orsaken till detta är att den egentligen inte vill åstadkomma någonting. Den är fångad i sina kompromisser, som den måste realisera, pilla med, som den fascineras av – älskar att explodera i hatfulla utfall mot oliktänkande – älska sin egen rationalitet, sitt eget förnuft – sin kamp för det rätta och goda – för att hela tiden dölja för sig själva sina tvivel, sina dolda begär, sin verkliga förändringslusta, sin rasism, sin fascism, sitt sockersug. Det är en sorts masspsykos som moderniteten befinner sig i, en verklighetsflykt – och vetenskapen är en del av denna flykt.

Att ta ett steg tillbaka innebär att ifrågasätta modernitetens värden – varav vetenskapen är ett. Det är att avstå från att delta i modernitetens projekt av ständig förbättring och optimering i förhållande till på förhand givna mål.

Det hörs redan sådana röster. De är alltid undantag, och de framstår alltid som mer eller mindre absurda, utifrån den korkade modernitetens perspektiv. Det är en sådan röst man skall bli, som följer sitt eget förnuft, som bildat sig en egen uppfattning, som skapar sprickor i modernitetens förfelade förbättringsmaskineri, tvingar människor att ta ställning till sådant de inte vill tänka på.

För mig framstår Andrejs mångdisciplinära förändringsväg som lite för smidig, lite för rätt, lite för realiserbar; som en omflyttning av pusselbitar som redan finns där och som bara väntar på att söka forskningsmedel i en ny konstellation. Det är inte min grej att passa in på det sättet.

Politics, Pedagogy and Anthropology – Three perspectives on Education

This post is a response to a proposition, from Ditte, as to understand Education from the different perspectives of Politics, Pedagogy and Anthropology. I will start by explaining this proposition.

Starting with politics, this is basically a “naive” view of Education that takes the “official story” of education to be true. From this perspective, Education is a place where people learn stuff that they need to participate in social life, to become “citizens” of modern society. In school, thus, people acquire knowedge that are useful for everyday life, for work, for democracy.  To this can be added that tests in school actually measure amounts and quality of such knowledge, and that the actual documents – grades, exams – that are produced in the education system, as end points of a system of training, testing and grading, actually indicates the possession of the kind of knowledge that Education is intended to provide.

From this perspective, it makes sense to expand school for the purpose of increasing the amount of knowledge possessed by citizens. For instance, it may be considered that “life is more complex now”, and thus – given the idea that learning as knowledge production is proportional to time – it may be deemed necessary to increase the time spent in school. It also makes sense to increase time spent in school insofar as test results turn out bad, e.g. in PISA.

From the perspective of pedagogy, however, things are not that easy. Knowledge is still considered a prerequisite for everyday life and citizenship, but it is not clear that such knowledge is actually produced in school. In particular, it is not clear that tests actually indicates possession of the kind of knowledge that is actually sought for. Documents – grades, exams – are thus considered with suspicion from the pedagogical perspective. They are, always to some extent, indicative of nothing, empty. Pedagogy has developed elaborate theories of learning as develpment as transformation of subjectivity; pedagogy insist that learning is precarious and thus that time does not equal learning (as politics would have it). To the contrary, experts need to care for the proper performance of teaching for learning to occur.

While it is easy to understand why it makes sense to reform education, from the pedagogical perspective, it is not obvious why school should be expanded. The insistence on the need for reform is equal to the claim that experts are necessary for school to work properly.

The anthropological perspective, finally, considered education as a particular instance of an initiation rite. The “usefulness” of knowledge is not taken at face value, but rather interpreted as a “way of talking” about the prerequisites of modern adulthood. As Ditte put it:

Rituals are a three stage process beginning with a preparation state (seperation),  followed by a stage of transition (marginal phase) and ending with integration into society (agrgation phase).

The marginal phase contains ordeals and “surviving” these is to pass the test.

The ordeals are indicative of adulthood i.e. being a part of the oikos (what it takes to be part of the oikos varies).

The point now, of the anthropological perspective, is that we can interpret our expansion of the educational sphere as an expansion of a particular ritual. We somehow think that we need more the “product” of this ritual, i.e. knowledge; we are not satisfied with how it prepares youth for adulthood – this is how we interpret the “test results” of education. We thus “expand the marginal phase” of the rite of initiation.


I come here to think of a distinction I made in my dissertation, between the “outside” and “inside” of school. They largely correspond to how you describe politics and pedagogy. From the “outside” everything is very easy, things work basically as they should, school do what it is supposed to do. But from the inside it is quite the opposite – nothing works, everything needs to be reformed. Still, however, pedagogy is committed to the same fundamental assumptions about how school should work. The distance between ideal and reality is only so much larger “from the inside”. From the inside, too, the world of schooling is much richer, filled with images and theories, about how it should work, what works and not, what should be done, etcetera. In my dissertation I talked about a multiplicity of “sublime objects” that captures desire. From the outside school is just one large blob: education.

As I indicated already above, I find the question you raise about pedagogy and expansion interesting. Also, the question about the history of schooling – why it emerged, and the relationship between this initial expansion and pedagogy: Did pedagogy drive the expansion, or did it rather just accompany it?

The metaphysics of Grube’s mathematics education

In the last post I introduced the mathematics education of August Wilhelm Grube, who’s Leitfaden, first published in 1842 and the in six subsequent editions, was one of the most used textbooks in arithmetic in the second half of the 19th century. Even more importantly, his educational doctrine then stood at the center of the methodological discussion. In this post I will continue to use the book by Rolf Braun about Grube, here to bring out the philosophical influences and implications of Grube’s thought.

The general purpose of this post and the last one is to highlight the religious origin of modern mathematics education. The more specific purpose of this post is to exemplify the high level of philosophical sophistication of educational thinking in the 19th century, in particular in connection with elementary mathematics. I want to show here how on of the doctrines that were to lead on to those of modern mathematics education, were shaped by the heterogeneous and quite fascinating mix of philosophical ideas present in Germany in the middle of the 19th century.

Grube’s point of departure, I read in Brauns book was the following – and these are Grube’s own words:

The faith is the sense organ of reason, of the inward facing eye, whereby man becomes convinced of the existence of non-physical beings. This belief stands over the “knowledge” of mind, in that it is an act of reason (an act of the power of the soul to sens the super-sensible); it is thus beyond any demonstration, any evidence of the understanding, in that it contains immediate certainty in itself. (p. 70, in Braun, 1979, here and henceforth)

It if quite difficult to find a good translation of the expressions that Grube uses, that sounds well in German. And, at least to me, it is difficult even to understand what Grube means. It seems in a way that Grube operates in a world quite different from ours, and that this makes itself known in the difficulty of translation. What Grube actually writes is:

Der Glaube ist der Gefühlssinn der Vernunft, das em Innern zugewandte Auge, wodurchder Mensch vom Dasein nichtmaterieller Wesen die Überzeugung erhält. Dieser Glaube steht über dem ‘Wissen’ der Verstandes, denn er ist ein Akt der Vernunft (der das Übersinnliche vernehmnenden Seelenkraft); er ist damit über jede Demonstration, jeden Verstandesbeweis erhaben, da er die Gewißheit unmittelbar in sich selber trägt.

There are many entities and capacities here, that do not square so easily with what we secular moderns find present in the world. What, for instance, is the “Gefühlssin der Vernunft”? And that his the “eye” that looks inward? What are the “non-material beings” the presence of which we get convinced? What is a “soul power” that can sense the supernatural? etc. one can go on.

The point is that this is the “world” in which Grube’s mathematics education was conceived. While we are familiar with some aspects of it, namely those that have been handed down to us by generations of school teachers and textbook authors, what we see here are some quite other aspects, that we do not even understand.

But what Grube tries to say is that “belief”, in contrast to the kind of conviction that you can get by rational means, such as “proof”, is the foundation of “reason”, in the sense of the “reasonable” or “practical reason”. You cannot “find out” what is reasonable be means of rationality and demonstrations – it can only be founded on belief. Developing this theme, Grube writes:

Alles Wissen wurzelt im Glauben und geht, zur höchsten Entwicklung gelangt, wieder über zum Glauben, zu dem Punkte, wo Wahrheit empfunden, die Wissenschaft zur Angelegenheit der Herzens, zur Religion wird.

All knowledge is rooted in faith and becomes, as it reaches its highest development, faith once again, to the point where truth is felt, science becomes a matter of the heart, and becomes religion.

Grube saw as the ultimate goal of all philosophy to solve the “riddle of existence”, and this by understanding that God is the last and highest  unity of “being and thinking” and – as should be clear from the quotations above – he thought that this goal could only be reached through faith.

I think this is a rather unexpected philosophical context for mathematics education, and it puts Grube’s method in a new light. Religion is the basis of science, and science, in its highest stage, again returns to religion and becomes identical with it. Grube writes this only a decade after August Comte had published his book on “positive philosphy”, the origin of positivism. But while Comte wanted to replace religion with science, letting science become a “new religion”, Grube definitely wanted to keep religion, by arguing that science needed it as a foundation.

To be continued…

The Mathematics Education of August Wilhelm Grube (1816-1884)

I have argued, or tried to argue, for some time that modern mathematics education is not very much an “enlightenment” phenomenon, but to the contrary much more the consequence of a reaction against the enlightenment, that took place around the middle of the 19th century in Germany. This not only means that mathematics education is not primarily concerned with emancipation and science, but also that it has a deeply “religious” core. What I argue is that many of the central tenets of mathematics education can be traced back to certain forms of protestant Christianity, even though all religious language has now disappeared, since the movement of progressive education in the early 20th century.

My thesis is thus similar to what Max Weber and others have argued in relation to modernity at large: that its rationale can and should be understood as a secularized form of Christian theology. But I will be more specific, and talk only about mathematics education, as a combination of a set of practices, a way of talking about these practices, and an institutional form that gives it a role and function in society. One can say that I view mathematics as what Louis Althusser called an “ideological state apparatus”.

What I want to do here is to give some empirical evidence for this thesis. I will do that by translating extracts from and commenting upon a book, published in 1979, by a German named Rolf Braun about the educator and philosopher August Wilhelm Grube. After Adolph Disterweg, Grube was one of the most influential writers in the emerging field of mathematics education in Germany. In particular, he was  known for the “monographic method”, where teaching is focused on one number at the time. Grube’s only book on mathematics education, Leitfaden Fur Das Rechnen in Der Elementarschule. Nach Den Grundsatzen Einer Heuristischen Methode, was originally published in 1842. It became immensely popular and came out in (at least) six further editions, the last one in 1881. While his method was widely used (and is to some extent still used today!), it was also the subject of severe criticism. Importantly, however, the impact of Grube’s Leitfaden can be seen in his firm position in the discourse throughout the latter half of the 19th century, and to some extent even in the first decades of the 20th. Eduard Jänicke, a chronicler of the field of mathematics education as it was consolidated in the 1880’s, wrote:

It has been some time since Grubes ideas took hold and set fresh new roots into the soil of school mathematics (Schulrechnen). Only with the second edition of the Leitfaden (1852) did one begin to think through his thoughts, talk about them, implement them. Diesterweg gratefully welcomed the reform proposals; aspiring teachers sought to try them out; others used the given impetus and hastily wrote a new book on arithmetic à la Grube. On the agenda of teacher conferences and on the front of the teachers magazines was only one issue that stirred the spirits, which became the shibboleth and needed to be settled: Grube pro et contra. (Rolf Braun, August Wilhelm Grube – Mathematikunterricht und Erziehung, Peter Lang, 1979, p. 66 – henceforth, if no other reference is given, page numbers refer to this book).

Maybe a good starting point is the state of the discussion of education in the 1850’s, as characterized by Adolf Diesterweg. There were two sides, one who

wants to educate (erziehen) the human so that she fits with the state, the church, the family, etc. as these now happens to be, and thus take the impermanent and changing social institutions as the point of departure for the education. (p. 46)

the other side however wanted to

use psychology to determine the nature and proper state of the human and then base the aim and means of education on the result of this research. They expect from a generation educated in the spirit of the eternal concept of humanity, a constant activity of reform of social institutions. (p. 46)

We have here basically an opposition between on the one hand a conservative view of education as a means of introducing and adapting young people to society as it is and on the other hand a “progressive” view of education as a motor of social change. It should be noted that we are in the 1850’s, well before the “movement” of progressive education. And an important difference is that the progressive at this point in time was not yet secularized, but more or less deeply christian. Grube positioned himself between these two camps, and Braun suggests that this is the reason why he got such a big following in the 1850’s and 1860’s. (p. 47)

Introduction to Grube’s Educational Theory

The basic point of departure for Grube was to find a middle path between what was then called “formal” and “material” education. He found the way to do this in a principle of “aesthetic education”, inspired by indirectly by Friedrich Schiller. In the form Grube found it, the aesthetic education was focused on a “feeling for” and “theoretical insight in” language. Grube however applied these ideas on mathematics education.
Grube was dissatisfied by the tendencies of his day in education. He was critical of “modern education” that created “a rift, an inner gulf, a screaming disharmony”. He meant that modern education tears body and mind apart and “makes one-sidedness a rule and necessity in life”. The consequence of industrialization and specialization, Grube wrote, was that

people are intellectuals, artists, civil servants, craftsmen, farmers – all kinds of people, only not humans in the full sense of the word. (p. 51, my emphasis)

And contributing to this was also the atheism and materialism of the times. Grube wanted to mitigate the effects of all these tendencies with his “aesthetic” mathematics education.

Interestingly, Grube saw all of these tendencies of his day as effects of one underlying cause, namely “abstracting thinking” (abstrahierenden Denkens), in that it abstracts from the reality of things, and then only acknowledges the “law of thought”. Grube argues that this emphasis on thinking results in a “raw enjoyment in thinking” in that it makes “the subject to world”: “when the mind is intoxicated by its power, it replaces God himself”. He blames philosophy, and I suppose that it is philosophers such as Johann Gottlob Fichte that he is (implicitly) referring to. Grube sees the problems in politics, religion, in art and philosophy as caused by lack of depth of feeling and lack of unity between “heart and reason”. With his aesthetic education Grube wanted to achieve harmony between the spiritual and corporeal existence of the human being. He meant that this unity was reached in an “aesthetic state”. (p. 52)

Grube thought that this goal could only be reached through an object by which the pupil is moved, and it is in light of this idea that we can understand the rationale of the monographic method. I quote Rolf Braun:

The task of all teaching is thus for Grube to put the pupil in an aesthetic state in and through teaching. According to him, this is only possible when “each stage of the teaching rises to a finished and accomplished whole, so that the idea that permeate and enliven the teaching object can be felt”. Only then will the disposition [Gemüt] of the pupil be moved and not only individual capacities and powers of the pupil be addressed. Then the pupil will be put in an aesthetic state by the teaching object, that is, the teaching will be educational [bildungswirksam].

With this concept of the aesthetic, that Grube puts in the center of his educational theory [gemütspädagogik], he wants to acknowledge the necessity of letting the teaching object move the subject, the pupil, in her totality, that is, the pupil must be addressed “holistically” by the teaching object, so that all of her capacities are activated. However, the teaching object must in itself be suitable for causing this  aesthetic effect in the pupil.

What objects are suitable for having a “holistic” effect on pupils? What objects can “move the core” of a pupil? In fact, at the time, many different “objects” were used in teaching for similar purposes as those that Grube describes here, for instance stories from the Bible, and historical biographical sketches, that conveyed messages building character, or, in Grube’s terminology, moving the disposition of the pupil towards a unified whole. It is in light of this purpose of teaching, and the idea that the pupil should be moved by the object, that we should understand the monographic method and its focus on individual numbers. The numbers are to be treated in a way the puts the pupil in an “aesthetic state” and moves her by its inner properties.

But what is the teacher going to do if it is by the “object” that the pupil is to be moved? The teacher is to “lead” the pupil to let herself be moved. Some of the terms used at the time to talk about this was “the heuristic method”, “the socratic method” or the “katechetic method”. Its characteristic feature is that the teacher “guides” the pupil (as Socrates did with the slave Meno) by means of well chosen questions, rather than “lecturing” about the subject. One of the educators that influenced Grube wrote:

The form of the educating (erziehenden) teaching is developing, and to this end the teacher stimulates (erregt) the pupils, so that they enhance their power by their own efforts of searching for the answer. […] he thus puts the pupils in self-activity, in which they learn out of themselves.  […] The teacher supports the drive for learning (Bildungstrieb), that is, the desire and attention of the pupils, at the same time as he, perhaps unnoticed, always leads the way. (p. 58)

We can here see a specific instance of what is sometimes called the “pedagogical paradox”, arising from the incompatibility of two doctrines: on the one hand that the pupil should “develop”, freely, through “self-activity”, and on the other hand that this development should lead to a pre-determined goal of “Bildung”, character, moral and later also useful knowledge. The teacher has the complex task of “leading the way”, while never actually “showing” the pupils the way. The purpose of teaching is not the “movement”, but the effort needed to move oneself – it is the power of self-movement that is the be developed in education, and the teacher has to ensure that what is developed is a power with direction.

For Grube, and in connection to elementary mathematics education, this general doctrine concerning education meant that:

not technique and virtuosity in calculation can be the main thing, but rather, through calculation, the achieving of clarity of perception, integrity of judgement (Selbsttärigkeit im Beobachten), freedom in construction (Kombinieren) – put shortly, a mathematical education (Bildung), that is more than just skill. (p. 59)

Grube wanted the pupils to become independent, to get a “power” through the school and through the teaching, to manage the everyday life. But this could not be achieved through the already then common “word problems” of calculation applied to practical life. To the contrary – and somewhat paradoxically – Grube meant that education can only be “practical” insofar as it is based on the principle of the “formation of disposition”, what in German was called Gemütsbildung,  and on morality. Only when the education transforms the inner core of the pupil in the direction of morality would it be “practical”, as Grube understood this word.
This, now, is what I am getting at – that the discourse on mathematics education, its doctrines and theories, did not emerge as means to promote the goals of today, of “creativity”, ingenuity, effectiveness, entrepreneurship and the like – but to the contrary, as Grube here exemplifies, to make mathematics education into a rather conservative if not reactionary force, promoting morality and “depth of feeling”. Grube confuses matters by calling the possession of such capabilities “practical”; what he refers to is basically the capacity to stand back from practical life and perceive it in its “truth”, to see the “core” of things themselves, beyond what Heidegger would call their “readiness-to-hand”, and this core was for Grube, as for many of his contemporaries, deeply Christian.
Grube searched for a middle path between the “camps” in education, described above referring to Diesterweg. One way to describe these camps is in terms of subjectivism and materialism. There were then the two evils of present day mathematics education for Grube. The subjectivism derived its tenets from philosophy, from what in philosophical terms is called subjective idealism, that when applied to education wanted the subject to “make its own world”, through a kind of expansion of the mind propelled by “self-activity”. The materialism, on the other hand, could rather be seen as a force originating in the practical life and in what today would be called “economy”. It took the existing world, rather than the subject, as its point of departure, and had as its goal the adaption of the subject to the presently existing.
It is interesting to note how well this dichotomy fits with our present. The “subjectivism” of today is “progressive” education, in particular in the form it sometimes took in the 1970’s, influenced by the student revolts of 1968. In Swedish it is called “flumskola”, with its focus on the “inner” development of the children, unconcerned with the harsh realities of work and economy. The “materialism” is of course also massively present in the pressure from the economic sphere, wanting to shape education in its image.
Most important, however, is to note that  it is actually the “middle path”, of Grube and others, that dominates education today. It is a paradoxical and complex combination of the respective “cores” of on the one hand a subjective idealism that wants to expand the power of the subject indefinitely, and on the other hand, a materialist determinism, that takes as its sole point of departure the “necessities” of the already existing outside world of the market. This, I think, is why mathematics education – and the education system at large – stands to firmly in modern society. It is a “compromise formation”, making it (seemingly) possible to have two opposite things at the same time: on the one hand emancipation of the human subject – as expressed in educational theories deriving from German idealism and its romantic successors – on the other hand a practical reinforcement of social structures and hierarchies.

What we can see in Grube is the formation of an educational doctrine fitting this double and somewhat impossible goal.

Grube’s innovation was to use numbers as the “objects” that were to move the core of the pupils.  It is not difficult to see how they can fit very well with the intention of finding a middle path between the subjective and the material. On the one hand, mathematics was already associated with the inner core of humanity. A great philosophical predecessor is Baruch Spinoza, who in his Ethics considered “mathematical thinking” to be the only truly free thinking that humans were capable of. Before him, Descartes had said that when we have mathematical ideas in our mind, we have them, in some way, “in God”, that is, when we think mathematically, we think “like Gods”. Kant made geometry and arithmetic into “bridges” between the subject and the phenomenal world, and thus positioned mathematics equally in the core of humanity and as the essence of the (human) world. He did this in an attempt to make sense of the physics of Newton, and more generally, the idea of mathematics somehow “connecting” something deeply human with something essential of reality, is a founding idea of modernity. What is often forgotten is that this idea was, by way of “common sense”, fitted into a christian cosmology up to the very end of the 19th century. Thus, the inner core of humanity, the essence of the world, as well as the “bridge” between them, until then, were usually interpreted in relation to the presence and power of some kind of Christian divinity. From this perspective, mathematics could enter the education system as part of a “humanistic” curriculum, siding with the classical languages. On the other hand, mathematics has been conceived of as a tool for instrumental action. Thus its place in education could be argued for in two complementary ways, partly as a means of formation of the inner core of the pupil, to an ideal of “harmony” with something truly human, fitting the essence of what is truly human with the world, and partly as a “tool”, that can be used to “solve problems”, to manage the everyday and professional life. In this sense mathematics entered the education system in connection with industrialization and economy, as part of a package of new “useful” school subjects also containing the sciences and modern languages.

Grube’s educational theory intended to make sense of this “double nature” of mathematics. But he was firmly focused on the first aspect, which he saw as primary. If only the “inner core” of the mathematical objects were made to move the core of the pupils, he thought, they would surely also be able to perform the petty task of solving problems.

Grube conceived of the numbers as learning objects, in a way not too dissimilar to how this concept is used today, and these were to be approach aesthetically. He wanted to replace the “extensity of the many” with the “intensity of the example”, and called this the “principle of the examplary”. The simplicity and unity of the thing itself should form the point of departure for the teaching method. Then, Grube thought “the pupil will be capable of subsuming the many instances of the everyday life under the in this way appropriated concept”. (p. 63)

But while the method would surely, Grube thought, put the pupils in position to solve their everyday life problems, it was morality that was its main end. Grube wanted to pupils to “empathize” (einzuleben) with the objects around which the teaching circle, feeling and enjoying, in relation to these objects, their own knowledge and power grow, thus influencing their desire. “According to Grube, the teaching is morally effective when the learning leads to a will to learn”. Interestingly, this means that the moral effect of mathematics education does not lie in the transmitting of “moral or religious” doctrines, but in that “the performance of calculations leads to a will to perform calculations”. The attentive and emphatic activity of working with numbers is thus a moral end in itself, in its contrast with the superficial and fragmented life of industrialized modernity.

 

The making of the world

Today Ditte went to Porto to the ECER conference to present her work on the introduction of entrepreneurship in the Swedish school but also to do “my” presentation about the Ritual fabrication of mathematical knowledge. We have prepared a prezi together that can be found here, and a corresponding “handout” that I paste below:

The ritual fabrication of mathematical knowledge

Handout for presentation at ECER 2014

Sverker Lundin (sverker.lundin@gmail.com)
and
Ditte Storck Christiensen (dittestorck@gmail.com)

Slide 1

The presentation starts with an attempt to describe, in a way that everybody can agree on, some central aspects of mathematics education as part of the modern education system.
To the left we have the process that gives mathematics education its purpose: learning, that leads to (mathematical) knowledge, that can then be ”used” – whatever is put into that word – outside the education system, in everyday life and professional life.
To the right we have a formal process that we should all be able to agree exists in the education system as well. We have here assessment, grades and regulations for admittance – to further education and also to professions.
We then make some observations concerning these two processes that can be said to run in parallel in mathematics education as part of the education system.
First, we observe that the practice of learning is more or less the same as the practice of knowledge assessment. This observation is important because of the meaning that is ascribed to the results of such assessment. The purpose is to certify that pupils have knowledge that can then, by definition, be ”used” – in a the most general sense possible of that word – outside school. But the assessment takes place in school, in a practice almost indistinguishable from the practice of learning. This observation, of on the one hand the strong similarity of the practices of learning and assessment, and on the other the interpretation of such assessment as a certification of the presence of knowledge, the purpose of which is “use” in some other practice, is intended to raise questions, as to the reasonableness of the logic and rationality of this system.
Secondly, we observe that both the left and the right processes of education contain, as their last step, an attribute that endows their bearers with a certain “power” or a certain set of benefits. Knowledge can be “used” to solve problems and to comprehend – in whatever ways this use is envisioned. Grades can be “used” to get admitted to further education and to professions. We observe that these two kinds of “use” if thoroughly different, but still closely related in the education system. Furthermore, we can note here, that while the left kind of “use” is surely possible, we have very uncertain information about how, when and where it takes place. For the right kind of use, to the contrary, we know exactly how, when and where it functions.
Thirdly, we observe that the sameness between the practice of learning and the practice of use is a contentious question. From one perspective, the two practices are “the same”, so that for instance the problem solving in school can be seen as “use” of knowledge in the same way as problem solving outside school can be seen as “use” of knowledge. On the other hand, critical voices claim that the school practice is in fact not at all like life outside school, that it is “unrealistic”.
Generally, in this first slide, all but the bottom left part of the picture – “use” – is located inside the education system. It is the “use” that puts everything else into purposeful contact with, so to speak, the outside world. If this connection turns out to be a chimera, the whole business of education must seem misdirected. The only connection with the outside world that remains is the administrative system where grades is used as a means for segregation.
In this first slide, we note that the “things”, “entities” or “processes” to the left are, invisible, immaterial and crucial for the purpose of the education system. Furthermore they are what one might call precarious, in the sense that it is non-trivial not only to bring them about but also to confirm their presence. The processes and entities on the right, to the contrary, are what one might call concrete and profane. There is never any doubt when an assessment has taken place, a grading mark is unambiguous and systems for admittance are, if not transparent, so at least concretely there in their “mechanical” functioning.
Given this distinction, we want to say that the entities and processes on the left constitute a framework for interpretation that lends sense and purpose to the education system. With this description, we want to insert a wedge between what is obviously there in the education system, and this framework. We will then talk about the “making” of this framework. We do this by introducing another framework for interpretation, brought in from anthropology. We thus end up with another understanding of what takes place in mathematics education.

Slide 3

This slide presents the alternative framework for interpretation, that is, the framework that does not employ learning, knowledge and knowledge-use as tools for interpretation. The main point of this alternative framework is that it shows how frameworks-for-interpretation are brought into existence. Thus, what we want to focus upon is how it comes that mathematics education (and education in general) is interpreted in the way that it is. What we will say is basically that the education system in itself, because of its relationship between what is done and said, produces its own framework for interpretation. The education system determines, if not completely by itself so still largely, the conditions for its own interpretation. This, furthermore, should be seen as typical for the function of ritual in culture.
In the left of the slide we present what Roy Rappaport calls the ritual form. It is a set of properties of a certain type of activity. With Rappaport we claim that, if an activity has these properties, certain effects can be expected to ensue. These effects can furthermore be quite directly connected to the properties of activity.
To the right we have two such effects, that Rappaport calls the canonical and the self-referential messages, respectively.
The canonical message is the framework for interpretation. It is the set of entities and processes that “exists”, in the sense that they are present at hand for people who want to make sense of the world. They function as interpretive resources, as ways of talking about practice and experience. Thus, one can understand what takes place in a classroom as “learning”, or, possibly, a failed attempt to make learning happen.
The self-referential message connects these general “forms” of the world with particular people and particular situations. One can thus say that pupil A, since he scored well on a test, has knowledge, this then becoming an attribute of this person that sticks, after the test situation and in many cases even after school.
Three things are to be noted here. Firstly, that the general mechanism for the production of these two messages is action “as if”. This is a concept that is elaborated in psychoanalytic theory, and in anthropology, most comprehensively, we think, by the Austrian philosopher Robert Pfaller. The point is that if people act as if something is the case, this something becomes, in a specific sense that cannot be elaborated here, present and real. Secondly, it is to be noted that these two messages – the canonical and the self-referential – tend to support each other, so that discourse on particularities such as how much pupil X can be said to know based on her test score, contributes to the “realization” and “presentation” of the framework that is used in this discourse. The framework is thus not brought into existence by being talked about, but by being used for talking about and interpreting the world. Thirdly, that which is brought into existence, and made real and present by ritual activity is not rightly understood as “beliefs”. The question of what a “belief” is, is complicated, and the concept of “belief” has a problematic place in the history of modernity (see e.g. the work of Talal Asad or Ivan Illich). In particular, early modern anthropologists (e.g. 18th and 19th century) tended to interpret non-modern cultures in terms of a concept of “belief” modelled on protestant faith, where inner conviction is essential. Thus, it was assumed that the entities and processes brought into existence in ritual activity were “believed in” in this so to speak convictional way. To the contrary however, meaning produced in ritual activity is rather made “real and present” in the same way as we moderns relate to such things as love, history and blue. We do not usually find it interesting to ask about the “existence” of these things, nor do we “believe” in them – they are just parts of the world that we can identify, talk about and use as means for understanding. This, hence, is how the “world” of mathematics education should be understood – as present and real, rather than in any particular sense of the world existing.

Slide 4

Slide for explains how the framework of slide 3 can be “applied” as interpretive framework for mathematics education as presented in slide 1.
We present the activity of mathematics education as a ritual, fitting the definition of the ritual form. It is action “as if” a number of things were the case in the world. In particular, mathematics education takes place as if mathematical knowledge was crucial for understanding and managing life in modern society. It takes place as if the activity of problem solving in school was a necessary prerequisite for a problem solving is that supposedly prevalent outside school.

As we do this – and it should be noted how the presence and logic of this activity is ensured “mechanically” through conventions in a number of ways – we bring forth this mathematical and problematic world. One can say that the world inside school is designed to fit the interpretive framework of mathematics, learning and knowing. This framework is the only way to make sense of what takes place in school, and it is virtually impossible not to use it. We thus all contribute to the “making” of our modern world, as we participate in schooling.

Knowledge as substance. A shift of perspective. (on video 1)

I recently posted a series of 4 videos on YouTube with the title The Ritual fabrication of mathematical knowledge. On the first of these videos, my friend and colleague Roberto Baldino has responded in a mail. This response has now prompted me to translate the video into text to facilitate further discussion. This text thus follows, roughly, the path of the Prezi that I used when making the video.

The video starts with an attempt to describe what knowledge is. One could call this a “phenomenological” approach, but then that would presuppose a distinction between the phenomenon and the actual thing itself – and I do not want that. References here go to Bruno Latour and Graham Harman, and their way of analyzing things. I want to describe knowledge as something that basically exists – without commitment to any philosophical theory of how or why something like knowledge can exist the way it does.

But it is perhaps necessary, already at the beginning, to sort of reveal what will come later, namely an attempt to explain how it comes that knowledge “is” or “seems to be” what it is. This explanation will take discursive practice as its point of departure. Given that this is the explanation that will come, this first step can hopefully make sense as a description of that which calls for an explanation.

On the other hand, what I take as my point of departure for my description of knowledge is exactly practice, so that what I talk about is more exactly what knowledge must be for our practice to make sense. I thus aim, one could say, to clarify what must be the “point of departure” for our practice, if this practice is to make sense. This operation is actually very much what Max Weber thought should be the aim of social science. So, at least I am in good company trying to do this.

Thus, for our practices that relate to to knowledge to make sense, knowledge must be in a particular way, and the first slides of the video attempts to describe this.

Thus, firstly, knowledge must of course exist. A lot of activities in modernity would not make sense if there was no such thing as knowledge. But already this is a nontrivial fact, because knowledge belongs to the group of entities, for which it is not so easy to say how, or where, they exist. I think the question of the existence of knowledge is related to the question of the existence of “truths” and “values” – that goes back, I have read, to the proto-neo-kantian Hermann Lotze. I did not want to do into that in the video though. The point is just to make clear that this question, about how knowledge exists, is legitimate, non-trivial, valid.

Secondly, it seems that knowledge can exists “in”, on the one hand people, on the other hand text. I derive this claim from the facts of education and of research, that is, from the existence of purportedly rational institutionalized activities. The end product of education is knowledgeable people, the end product of research is scientific knowledge “residing”, as I suppose one could put it, in texts.

It may seem unimportant that we talk about the result of education and research using the same word, but my very point is that this is important indeed. I will claim that we derive the rationale for many aspects of these activities (of education and research) for what appears to be taken as properties of a substance or entity; properties of knowledge as if knowledge was a substance or entity. Knowledge brings together and “makes sense” (literally) of practices, of institutionalized cultural activity.

What more with knowledge?

There is a logic of its production – again, this taken from how it related to practically, discursively. What is educational theory if not a discussion about the conditions under which knowledge emerge, the conditions under which learning takes place – and here what emerges is the particular “mode” of knowledge that exists in individuals.

Learning is thus intrinsically connected to knowledge as the name for the process by which knowledge is brought into existence. And more specifically it seems useful here to talk about “individual-born” knowledge as the result of learning. (While text-born knowledge in a corresponding way is the result of research.)

But, alas, learning is an invisible process, and it is precarious, in the sense that it is only retroactively that one can say if it has occurred.

Here, again, I derive these claims about learning from how it is related to in practice and talked about. The complaints about the failures of education, what is that if not complaints that the proper procedure has not been followed, so that “nothing happens”, besides that which is obviously visible. So, what I am getting at is that education is an attempt to make present a process which brings an invisible entity or substance into existence, residing in an individual.

I hope it is clear, now, that the purpose of this “describing” is to make what is taken for granted in modernity seem rather exotic. So, this is quite a common procedure for social science or philosophy, to try to make the common seem interesting and fascinating. That is what I want to do for knowledge and learning, and the other practices of the education system (and, eventually, for science).

So, going on, we suppose that quantities of this knowledge-substance can be measured…

We seem to relate to different “kinds” of knowledge (mathematical, etc)

And we suppose, obviously, that this substance can “do stuff”, that it can endow its bearer with some sort of power.

And, clearly, we make signs of the quantity we take individuals to have of the substance, and have organized our culture so that these signs too, as it were, endow their holders/bearers with a certain “power”.

My point now is that this name – “knowledge” – is not innocent. It does things. Again, Latour can be a reference. We can say that it has “agency”. It should be obvious that we, as humans, in a sense have “made” knowledge what it is – as a name for the result of education, and, incidentally, also the name for the result of research. It may seem that it just makes good sense to treat this result as if it was an invisible substance, and treat its emergence as if it was a precarious invisible process, etc.

This would be a vision of modern culture as transparently rational, functional, purposeful.

My contention is that this is not at all the case. To the contrary do these properties, of knowledge and of learning, transcend our culture, in the sense that they are referred to as causes of and rationales for culture. Looking at what we do and what we say, it seems very much as if we thought that knowledge was not something that we have made, just a useful way of talking, but rather that it demands things from us. This state of culture is called “heteronomy” by Cornelius Castoriadis, whom I think is useful here to point out the difference I am after. Knowing, and acting on the knowledge of the fact that we can choose, in a way, the properties of our culturally constituted substances and entities, would be what he calls “autonomy”. And he thinks that is the proper state of (modern) culture.

So, knowledge is a sort of autonomous counterpart of the consciously cultural – such as political parties and Christmas. Knowledge is partly “nature”. But, as nature, it has peculiar properties; properties tightly interwoven with culture. If it is “nature” it is a nature that puts tight constraints on “cultural possibilities” – for instance making the education system indispensable, making science and research indispensable, and even making mathematics education indispensable.

From another perspective, it thus looks very much like ideology…..

But it is not critical theory that I want to turn to to “explain” this existence of knowledge in modernity, but rather ritual theory. I think, basically, that this theory can say much more about what goes on here. And I intend to demonstrate that in the next post, about video 2.

A want to reply to some comments from Roberto Baldino.

I refer to Ernst Cassirer and his concept of “symbolic forms”. Cassirer’s philosophy originates in neokantianism of the Marburg variety. Their problem was how to reinterpret Kant in light of the fact of scientific progress. Kant thought that science was stable, and thus sort of built Newtonian physics into the mind of humanity. What is a human, and what is the world, if our scientific conception of the world is in a constant state of change? Cassirer found it useful to see the world as the result of a twofold process of subjectification and objectification, resulting in minds relating to objects. This process is cultural, and Cassirer was very interested in the many ways culture can bring worlds into existence, worlds, and minds relating to these worlds. He was very attentive to the role of language in culture! He thought that modernity was special however, and thought that our culture should be placed at a later stage in a history of human progress. He would probably not have liked my attempt to portray knowledge as just any simple “symbolic form” on par with Gods, spirits, whatever.

When I say that knowledge is a substance, I mean that, in modern culture, it is treated as if it was a substance. But – and this is perhaps where it gets tricky – this does not mean that it is not a substance. We have here a point that the gang of post-modern theorists of science have had to repeat over and over again: just because something is “constructed” or “made” or “constituted”, this does not mean that it does not exist. It does exist! Thus, knowledge does exist, and it is a substance in modernity. But it is only a substance in modernity. When a school is built and an education system established in a previously non-modern location – it starts to make sense to talk about people there to have more or less knowledge, when they go to this school as learning or not learning, as their practices as knowledge use. But we have then brought modern culture to them, as a way of organizing life, as a way of viewing the world and – interestingly – constituting the world (with objects such as knowledge, airplanes, atoms and quarks, plastic and politics), as a way of understanding what a human is and what makes a human valuable – etc.

It is as such that I say that it is brought into existence through learning and certified through knowledge assessments and peer-review. With this, I say something about this culturally instituted form (perhaps Castoriadis is a good reference here, he uses the term instituted). I do not say anything whatsoever about what people can or cannot do, besides what comes from the fact of being attached or not attached to the sign of having knowledge – making you, if we follow that reasoning here strictly, also actually having it, as long as you move inside the culture in which it is recognized and operated with. Here “recognized” is a reference to Pierre Bourdieu and his concept of “symbolic capital”, which quite obviously makes sense in relation to different kinds of knowledge. The “move inside” is a reference to Bruno Latour and his argument about networks and science, technology and theories only “working” as part of networks. In this sense, knowledge only “works” as part of the network constituted by the education system and for text-borne knowledge – science.

It is exactly right to call this first phase of the analysis, the “descriptive” part, the purpose of which is the clarify what actually takes place here, what must be assumed, for an over-identification with a power-discourse/practice. The intention is to make it seem absurd, by just clarifying what it is. I do not here put forward any critique! I do not feel that I need to. But what is very important here is why this is the case. Why is it, that just clarifying what one could call a “symbolic structure” can be a threat to that very structure? And here, as you rightly point out, psychoanalysis, of the zizekian or pfallerian variety, has the tools that are needed to understand. The thing is that we relate to things such as knowledge always partly unconsciously, always never completely focused, so to speak: the properties of knowledge reside in practice, they fit the definition of a collective unconscious fantasy, as Zizek calls it, it is “seen through” in a sense that Pfaller describes in detail and that I used in my “Hating school” article. And it can only exist as such, as partly unconscious, as (partly) seen through. That is why this operation of making visible and clarifying, is critical in itself, in a quite interesting and fascinating way.

Lastly, concerning the inclusion in the analysis of the my own act of analyzing/talking/criticizing – it seems like a characteristically modern/modernist gesture to complain about an analysis that it is not reflective enough, positioning yourself at a higher level of reflection, including also yourself in a more comprehensive way. I agree that there is a point to this, and that zizek et al have pointed that out usefully. And in my analysis, this extra inclusion, so to speak, plays a crucial role. The basic structure of the discourse on education is that everybody that speaks, speak on behalf of science – from a position that is before hand excluded from the analysis. Mathematics, basically, is always taken for granted as a stable ground, as obvious, and it is there, on the side of mathematics, that people like to see themselves, talking about boring, stupid, failed education. We then get what I call the “standard critique”. I take a step back, and consider also science (mathematics, knowledge – as in the video and the text above) as part of that which needs to be explained. But sure – it is of course possible to complain again, about the new position where I (like to) find myself. And this is then the critique directed at the field of science studies, STS, ANT, SSK, etc. those who try to study and understand science from a position that does not take the demarcation of science for granted; it is claimed that this position is self-refuting etc. which is just stupid bullshit because it does not realize that people have been thinking, talking, inquiring, understanding long before this monolithic ritualized nonsense-producing capitalism-mongering “science” that we have today emerged in the 19th century.