Sal Restivo
Rensselaer Polytechnic Institute



*[J]ust as the oppressor, in order to oppress, needs a theory of oppressive action, so the oppressed, in order to become free, also need a theory of action.
Paulo Freire*
This abstract sketches the basic objectives of the plenary lecture. The lecture is based on the sociological theory of mathematics outlined in my paper, "Mathematics, Mind, and Society (MMS)". In my lecture, I will briefly summarise my theory of mathematics, and then clarify the basic terms of my argument: mathematics, mind, society, and anarchist theory. My objective in this lecture is to begin the process of extracting, refining, and developing a politico-theoretical framework and agenda that is at least implicit in MMS and has been slowly emerging in my work over the last twenty years or so. By "politico-theoretical" I mean to link theory, practice, and power. This is tricky in the sense that properly understood, theories are or engage worldviews, so they are or are integral with forms of discourse and practice, that is politics and power.
  *At the moment in which you say, Look, but now I invite you to be responsible!, immediately they think in opposition that your hypothesis is not rigorous....we have to fight with love, with passion, in order to demonstrate that what we are proposing is absolutely rigorous. We have , in doing so, to demonstrate that rigor is not synonymous with authoritarianism, that 'rigor' does not mean 'rigidity.' Rigor lives with freedom, needs freedom. I cannot understand how it is possible to be rigorous without being creative.

For me it is very difficult to be creative without having freedom.

Without being free, I can only repeat what is being told me.

Paulo Freire*
Mathematics represents and embodies human labor; and human labor is always social labor. Even when I sit and think alone, I am performing social labor because the language of my thoughts and emotions is given to me by my society and culture, and even the very self and consciousness I experience in this (as in every other) situation are social because given to me and sustained in and for me by everyday social interactions. This principle of the pervasiveness of the social is very little understood. It is the basis for understanding mind and consciousness as socio-cultural products and processes. Even the brain is socially constructed. The significance of the social fact that minds and brains are not independent, free-standing entities and that independent, free-standing individuals are illusions has not yet reached into the social worlds of education (although some progress in this direction has clearly been made among those attending this conference).


*By perpetuating the school as an instrument for social control and by dichotomizing teaching from learning, educators forget Marx's fundamental warning in his third thesis on Feuerbach: "The educator should also be educated."
Paulo Freire*
Society is symbolically useful in my title, but does not convey the central idea I want to emphasize, that our selves are structured and re-structured, produced and re-produced, in moment-to-moment social interactions during the course of our everyday, everynight lives. These interactions are, in fact, ritualized and linked (in what Randall Collins has called "interaction ritual chains"), and these rituals and ritual chains are the crucibles in which we make and re-make our selves and our cultures. We could, then, say that mathematics, like language, and like any symbolic system, represents the product(s) of sets of interaction ritual chains.


*Just as there is no such thing as an isolated human being there is no also no such thing as isolated thinking.
Paulo Freire*
My conception of theory reflects my anarchist objectives. The craft or practice of theory is widely misunderstood.. It is, properly practiced, a subversive activity; indeed, it may be the most subversive activity humans are capable of. From an anarchist perspective (and here I follow Brian Martin), "Ideas are central to social struggles. Most of the intellectual work in government, corporations and universities is too technical or obscure to be of any value for popular use, or else, like advertising, it is manipulative. Are there ideas and methods of thinking that are specially suited for developing insights and strategies to challenge hierarchical systems? How can "theory," thinking systematically, become a popular pastime rather than an elite pursuit?" The sociologist Charles Lemert has in fact argued that "Everyone can do [theory]. Everyone should do more of it. Responsible lay members of society presumably would live better - with more power, perhaps more pleasure - if they could produce more social theories." We need to help ourselves and others understand the power - the critical and subversive power - of theory, and to help eliminate the idea of theory implied in such statements as "It's only (or merely) theory," "It's fine in theory, but not necessarily in reality," and the idea that somehow theories worth the label are constructed in vacuums out of nothing, without any grounding.


*Dialogue in any situation (whether it involves scientific and technical knowledge, or experiential knowledge) demands the problematic confrontation of that very knowledge in its unquestionable relationship with the concrete reality in which it is engendered, and on which it acts, in order to better understand, explain, and transform that reality.
Paulo Freire*
Finally, I need to explore the anarchist agenda. To begin with, I follow Peter Kropotkin's conception of anarchism as one of the sociological sciences. For the moment, I can only outline some of the basic ingredients of the anarchist agenda. In my lecture, and in the paper that will generate that lecture, my objective will be to integrate this agenda with the general sociological theory that has guided and grown out of my work on mathematics and science. This integrated agenda will form a foundation for reforming and rethinking mathematics and mathematics education. Fortunately, I have the advantage of being able to draw on a recent issue of Social Anarchism in which several contemporary anarchists outlined their versions of the anarchist agenda. I have adapted their program as follows:


The Anarchist Agenda

1.Human and ecological contexts for human survival with dignity and integrity.

2.The self is a social structure, community dependent and inter-connected.

3.Promoting diversity in selves and communities.

4.To transform bureaucracies into worker organized and operated organizations.

5.To strengthen popular involvement in and control over mass media.

6.Demarchy: local networks of volunteer based functional groups, dealing with various community functions including education.

7.Anarchafeminism: bringing the anarchist movement to bear on male domination and the oppression and suppression of women.

8.To search for and implement alternatives to state-market political economies.

9.Developing networking into a strategy for social action.

10.Challenging taken-for-granted ideas about material and intellectual property, and promoting non-ownership and collective usage; the rejection of property, consumerism, and commodification.

12.Facilitating organized nonviolent action in and by communities.

13.Promoting science and technology for the people, alternative technosciences.

14.Theory as a subversive activity

15.Intellectually and theoretically, the rejection of transcendence, immanence, and psychologism.

16.The complexity of the world requires that anarchists avoid become enclavists, and instead work in consort with other activists for social change.

17.The anarchist tool kit should be part of a larger variegated toolkit of strategies, skills, tactics, and technologies for social change.

18.Anarchists should practice heterodox borrowing of ideas, perspectives, strategies, theories, and technologies.

19.Anarchists should avoid dogma in theory and practice.

20.Anarchism is a form of life.

In my lecture, I will begin the process of developing and applying an anarchist sociological theory to the problem of rethinking mathematics and mathematics education as social constructions. Some of the questions participants might care to consider are: