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.

  

Stabilizing measures: Method and Market

A central feature of method in modernity, as it was conceptualized in the 19th century (see Gaukroger’s The Emergence of a Scientific Culture, p. 30), in particular in the social sciences (see Schnädelbach Philosophy in Germany 1831-1933) is that it is designed to create change, but at the same time, not any change but the right kind of change, described as “scientific progress”.

This is a peculiar idea! That you can sort of have a machine, something that works without thinking, in a way, constantly and persistently producing a particular kind of new. The thing is that this idea is founded on an ambivalent image of the power of human imagination. Because – why is method needed? Why not think freely? Because, as individuals, we are imperfect, fallen, ridden by idiosyncratic needs and desires – and thus we need to be checked. But still – we have something in us that opens up for the kind of change that we should really want, that is: progress.

There are many ways of thinking about the constitution of this method – sometimes including creativity (as Popper did), sometimes just depending on “rational” rule-following. However one conceives of it – the only way to make sense of method is through this split vision of the power of individual human subjects, as partly “fallen”, partly “godlike” (se Michael Allen Gillespie would have put it in The Theological Origins of Modernity).

From a sociological perspective, we can get another understanding of method, namely as a way of providing constant, non-revolutionary change. And this “explanation” of what method really does for us, fits well with the sociological circumstances under which it rose to prominence in Europe, that is, after the unruliness of the first decades of the 19th century. In the sociological level, the idea of “scientific method” can be seen as a compromise.

The point here – in this post – is that method has an interesting counterpart in the concept of the entrepreneurial spirit and the entrepreneurial self. Andreas Reckwitz accounts for the emergence of this, as he calls it, “dispositif” in modernity, becoming hegemonic recently, after the 1980’s.

What we have here, perhaps, is another complementary way of keeping human creativity and fantasy in check. This time, not through the imposition of law – as method does – but through the creation or establishment of a fabricated environment, to which the individual must adapt to survive.

Method, in a way, also constitutes such an environment, through invariant and stable mechanisms for control, ensuring that method “has been follows” – thus putting the process of change in a sort of ritual setting (following here the definition of Roy Rappaport).

For the entrepreneur, this “control” is instead taken care of through the dynamics of the market, if market is understood in a wide sense as the conditions for getting a “following” in the present state of culture: we think here of e.g. Twitter, Facebok, Youtube, whatever – where the conditions for success are determined by the “state” of this market, an always difficult to determin “readiness of the new”, which, when it is satisfied, results in the “viral” – the Internet variation of the theme of success in the market.

Here, as an individual, you are completely free to think, say, do and produce whatever you like. Importantly, however, culture and society will not be threatened by these creations, as long as their “impact” is determined by this market logic. To have an impact, you must act on the market, in the double sense of the word of putting your product on the market, and adapting it to what you think is the “desired of the market”. The successful entrepreneur follows this constantly shifting, but in another sense invariant and stable, desire, always satisfying the need and desire that at this particular moment had a potential for emerging. He does then, not, obviously, think and create freely, but as an instrument of this market logic.

There is an interesting parallel between these areas: In science, as in the market economy; the brilliant scientist, as well as the successful entrepreneur – are described as thinking outside the box. But in fact, what is valued is having a sense for exactly the walls of the box, never leaping outside, but rather coming up with new things that can be stuffed inside it. A marxist would call this box capitalism. But perhaps it is better to talk about it in a somewhat wider sense, leaving the question of what explains what more open…

That the market is a “box” is of course already known – the point in this post is the connection between market and method – as stabilizing measures in modernity, complementing each other in putting our modern culture in a constant state of checked transformation.

Connecting to previous posts, these checks on culture, are connected to the image of growth of our two favorite substances, knowledge and money. Our way of talking about and understanding the reason for the necessity of method and market, is in terms of this growth. We are attached to these substances, and as long as we conceive of change in terms of their growth, our culture will be kept in order.

Thus – two easy (?) ways of changing direction is to let go of any of these processes of growth, economic or scientific.

/Sverker & Ditte

How I work

The idea of approaching education from its outside – and yes, there is something like education that can be addressed from different positions and thus explained according to other ways of perceiving school activity –  arose when proceeding from studying analytical philosophy to undertake studies in philosophy of education. These new surroundings provided my very first real encounter with the assertions of pedagogues.

From my time as a student of analytical philosophy, I was quite accustomed to the strictness and high demand for strong arguments characterizing a tradition always concerned with justified beliefs. So when later entering the field of Pedagogique, where “no questions are asked”, I faced the effects of the environment that brought me to expect this stringency from every scientific discipline. You might say that a “work related injury” made me constantly ask questions to which no answer was ever thought of. Education is good, knowledge is assessable, learning is emancipating and so on… thatand nothing else is the truth.

However, between an education in analytical philosophy and one of philosophy of education a few courses in anthropology and ethnology most fortunately happened to squeeze in. Introducing the concept of ritual as a kind of transformer and stabilizer of social relations, I was inspired to look at our “modern” society as constituted according to the same mechanisms as so called, “primitive” societies.

After my eureka moment at the Department of Cross-Cultural and Regional Studies (ToRS) decided to depart from complete symmetry dismissing the existence of any qualitative difference between how one or the other social collective takes form. Hereafter, neither justified beliefs nor pedagogical assertions were considered by me as matters of truth, they could only be matters of ritual. Basing any approach to a subject – that be knowledge assessment or the development of entrepreneurial spirits – on complete symmetry left little room for anticipating rational or irrational behavior and so on while these categories, like many categories, are produced by ritual and part of the logoipertaining to the performances that occurs with it.

Looking to a principle of symmetry is not every anthropologist business. The principle should therefore not be taken to count for all of anthropological research. For example, it is quite common to find anthropologist escape the principle of symmetry by comparing other collectives to their own, judging their activities to be as rational as the western ones and thereby making everyone modern (presented in the image of us). I think this is the case with much of today’s established anthropology of education. But a more crucial reason for establishing a new branch of anthropology, is the lack of self awareness that causes anthropology to refrain from describing the modern society from the outside, that’s is by same approach as we describe foreign cultures. Anthropologists are all too loyal to the modern norms and values. 

Representing this the “loyal course of investigation”, someone by the name of Catherine Pélissier (not familiar to me but still an anthropologist out there) closes in on the subject assuming the existence of “flexible individuals capable of teaching and learning”. In her article from 1991 (Annu. Rev. Anthropol. 1991. 20:75-95) Pélissier claims that “Learning and teaching are fundamental, implicitly or explicitly, to human adaptation, socialization, culture change, and, at the broadest level, the production and reproduction of culture and society.” and even that “teaching and learning – the social processes involved in constructing, acquiring, and transforming knowledge – lie at the heart of anthropology.”

If you consider the claims mentioned above, what Pélissier means by “teaching and learning” is not initiation via ritual in any neutral (descriptive) sense. Instead the sentence refers back to the pedagogical myths themselves, holding that education is emancipation through the development of reason and/or of knowledge and this is exactly how teaching and learning are approached (taken for granted) by anthropologists of education. I wish to change that. Instead of solving problems pertaining to the idea of the necessity of schooling (or education), I will investigate how school is constituted and maintained as a modern ritual and dwell on the consequences of our faith in education. What thoughts and actions underlie this institution and makes it endure during the pressure of time. This is the approach I call Anthropology of Education and Research.

Resources:

Anthropologists sensitive to the principle of symmetry, such as Mary Douglas and Roy Rappaport.

Ethnologues of the kind that philosophers name critics of culture are often approach as leftists, Marxists and other bad things. To me they will be resources of great importance for understanding the place of school in modern our society. These sharp critics, and especially Luc Boltanski and Robert Pfaller, have great insight into the workings of ideology on the body and mind of modern man&woman.

Researchers with an interest in what constitutes the mysterious Social but still not “really” anthropologists, such as Bruno Latour, has noticed the above mentioned lack of self awareness when it comes to own familiar anticipations that takes for granted the existence of smart and stupid, scientific and non-scientific, as according to western measures and as the precondition for welfare (growth).
Other researchers that has touched upon the development of modern dichotomies and their durability, among these Philippe Aries and Theodor Porter and a good deal more, are welcomed resources.

Actual research:
During 2011-2014 I undertook the task of “explaining” what went on when entrepreneurship was transformed and made into pedagogical entrepreneurship, as part of a process of introducing entrepreneurship in the educational system of Sweden.

Using ritual theory as a mean of understanding the process, I followed the concept “entrepreneurship” in its change from being a matter out of place, to being a matter of concern and finally a matter of fact

Though the product of the institutionalized work (performed by the government, The National Agency for Education and research faculties) invested in the transformation was what is known to us as “pedagogical entrepreneurship”, appears as an evident solution to the problem of living in a time of change, a great deal of ambivalence is involved in stabilizing this new concept.


Now it may seem paradoxical that ambivalence is what constitutes pedagogical entrepreneurship, but seen in the light of ritual theory it is only “normal” to reach stability through a process that creates ambivalence. From ambiguity (where it is impossible to straighten out a situation or to categorize a thing), a certain balance can be attained. We are dealing with a form of tension that place us in a performative “limbo”.

Four types of critique in modernity

Continuing the last post, education is clearly an area of social life where thing can easily go wrong, and thus efforts – institutionalized, stabilized, geographically invariant – are made to avoid this. I said that the discourse of learning and knowing is the way we moderns talk about this precariousness of education. Not only are measures in place serving to keep education “on track”, this keeping also contains accounts of that which should be avoided, referring to examples, as often contemporary as historical. These account take the form of critiques. They move over the border line between desirable practices (and outcomes) and other practices that for various reasons tend to occur instead. They explain why the desirable is to be considered as such, and vice versa.

What I want to do here is to relate this form of critique, in a kind of ideal-typic fashion, to two other forms, and then draw some conclusions from the structure emerging from the comparison.
Perhaps one can describe modernist critique in terms of an opposition between stable tradition and progress. I think here of the 17th and 18th centuries, and the enlightenment project to transform culture so as to reflect the true nature of humankind, as rational. This is a critique with self confidence, aiming at a particular goal that it believes in.
Opposite to this kind of critique we have its traditionalist counterpart. It takes aim at the goal of modernity, a culture or a society reflecting what it takes to be essentially human, that is: rationality, claiming that such a culture is not a worthy goal of change; that it is better to keep that which is, for instance Christianity, certain traditional forms of morality, etc.
The thing now is that this simple opposition is insufficient for understanding the form of critique typical for modern education and – I think – more generally for present day modernity. The critique typical for education is neither modernist, nor traditionalist. It must rather be seen as a sort of compromise formation in the sense that Robert Pfaller characterizes religious rituals:
Schematically, I think what happens is that the ideal of rationality, in a wide sense of the word, were starting to become a cultural-transforming force in the 18th century. Or, from another perspective, enlightenment, modernity, process was at least the discourse connected to cultural transformation – nothing said about underlying causes. Western history, at this point in time, came to a state of cultural disorder – historians talk of an “age of revolution” between 1775 and 1848. It is in this period that I think the “compromise” took shape.

The emergence of this compromise is connected to the opposition between danger and safety or risk and security, as discussed by Ivan Illich in The Rivers North of the Future. Through mechanisms difficult to understand, as what was at the same time a reaction against and an affirmation of, the ideal of modern process, culture found a way to at the same time secure progress, and secure itself against disordering transformation.

It was at this juncture that education and research took shape. The crucial point I want to make here, is how it was at this point that what is recognized as the “pedagogical paradox” became a prominent feature of modern culture, that is: the paradox of how it is possible to at the same time want the child to “develop freely” and nevertheless impose external goals to this development. This pedagogical dilemma is just a particular instance of the more general problem, of how it is possible to have stable and invariant institutions, the purpose of which is cultural transformation. But that is what education and research purports to be.

It is in the formation of these institutionalized activities that ritual theory starts to become useful for understanding modernity, and it is no coincidence that it is exactly at this point that “science” begins to replace “religion” (see for instance the first part of Stephen Gaukroger’s The Emergence of a Scientific Culture) as what one could perhaps call the “center of the imaginary”  (thinking of Cornelius Castoriadis) of modernity.
I contend that this ambivalence towards modernity is particularly visible in the formation of modern mathematics education, making mathematics education a paradigmatic case for understanding this crucial aspect (the ambivalence) of modernity.

Mathematics was introduced partly as opposed to the then prevalent school subjects of classical languages and christianity – as part of a new curriculum focused on science, also including modern languages.
But it was also introduced as a strictly christian subject – drawing on the central place of mathematics in theological discourse since the 17th century. For sure, this place of mathematics was always more or less contested within theology – but now, the theological interpretation of mathematics opened up for a compromise, sort of affirming christianity, through its potential antagonist, modernity and modern science and mathematics. While this needs further study, it seems very much like modern mathematics education – the characteristic classroom practice, its textbooks, its central doctrines concerning learning and knowing, took form, not as a part of secularizing progress, but to the contrary as part of the reactionary politics following the 1848 attempts at revolution. Mathematics education was established and used, quite consciously, as a means to ensure orderly conduct of the citizenry – as part of a christian curriculum.

***

What happened quite soon, as we know, and in the very process of establishing these conglomerates institutions of science and christianity, was that the christian part of the “explanatory discourse” of education was dropped (see Michael Allen Gillespie’s The Theological Origins of Modernity). The form of the activities can nevertheless still be understood as compromise formations; as both stabilizing culture, and contributing to its transformation.
Typical for critique in education is thus on the one hand a belief or faith in modernity and progress, but on the other hand an often unarticulated “faith” in the means by which this progress is to be achieved, severely limiting the range of options available for transformative action. It is a faith, one could say, in “modern tradition”, where the education system has not replaced the church and Christianity as that which has been handed over to us by previous generations. The operations of the “drop” of christian discourse has made it possible to see this institution as, in a way, in itself “modern”, thus immune to modernist critique.

Given this characterization of the critique “of education”, it is possible to point to some alternatives.

Firstly, a most important alternative to the education-immanent “compromised” critique of tradition, is to (re)widen the scope of critique, to possibly include also those institutions that today purport to “safeguard” progress – that is, education and (as I have not talked to much about in this post) research. This, I take to be a strategy in accordance with the analysis of modernity presented by Hans Blumenberg: essentially positive to progress, but not necessarily to how we try to realize this goal.

Secondly, it is of course possible to reject the compromise for the opposite reason, that is, for its partial affirmation of the modern ideal of progress driven by rationality. I take this to be the stance of for instance Nietzsche and Heidegger and their followers. But it seems also problematic, in a special way, because the very critical stance, the attempt to transcend the culture of which you are part, seems to be uniquely modern. Thus, as others have already observed of course, this “breaking free” of the “ideology” – as it would then be characterized – of rationality and progress, can also be seen as a logical step within the history of modernity. From this perspective, the only non-modern stance possible would be one of (possible “seen-through” in Robert Pfaller’s sense) conformity, to modernity as it happens to be, in its constant process of self-transformation. And in that sense, most moderns would thus qualify as non-moderns, confirming the thesis of Bruno Latour.

Thirdly, I think it worth mentioning a strange version of the ritualization of the progressive stance, namely the ritualization of its opposite, critique of modernity. It is very popular, for the moment, to be critical of “post-modernism”, but nonetheless, in a particular sense I will contribute to that critique. I think here of the production of variations on the themes set by philosophers such as Nietzsche, Heidegger and Adorno from within the “compromised” institutions of education and research. In the same sense sense and for the same reason that critique of “tradition” expressed within education and research will never actually lead to substantial transformation of culture, the same goes for critique of “rationality” (or modernity or progress), expressed within these same institutions: it will never make modernity any less modern.

***

Given this analysis – I welcome critique and comments – it seems to me that the most reasonable stance to take towards modernity – a modernity of which we are all already part and shaped by – is to affirm its basic stance of openness towards change to the better, and, perhaps even a certain ambition to participate in the achievement of such change. On the other hand, what must be rejected, is the idea that this ambition can be delegated to an institution, be that education, research or politics. Nothing can be excluded from critique beforehand. Faith must be put in something non-material, not existing, a sort of force, potentially present for any human being. This means that the forms of the project must be constantly renewed, always with the possibility of error and failure.