7 - Routines: How We Mathematize

Summary

We are what we repeatedly do. Excellence then, is not an act, but a habit.

Aristotle

The rules of formation operate not only in the mind or consciousness of individuals, but in discourse itself; they operate therefore, according to a sort of uniform anonymity, on all individuals who undertake to speak in this discursive field.

Michel Foucault

If the meaning of words is in their discursive use, Wittgenstein's exhortation “to let use teach us meaning” makes perfect sense and may even appear tautological. It is by reproducing familiar communicational moves in appropriate new situations that we become skillful discursants and develop a sense of meaningfulness of our actions. The all-important regularities to be found in any discourse are the focus in this chapter.

Meaningfulness from repetition

In chapter 4, communication was defined as a collectively implemented activity that, when observed over time in its diverse manifestations, displays repetitiveness, and thus patterns. The repetitiveness is the source of communicational effectiveness. If I know how to react to a given action of an interlocutor, it is because I was exposed to a similar situation before and am now able to implement an action quite similar to the one that was performed then.

Discursive patterns are multifaceted and intricately interrelated. Words and symbols are combined into utterances; the utterances, through their structural commonalities and through their recurrent coappearance in discourse, solidify into stable associations of communicational actions and re-actions; these latter associations, in turn, are coupled with sets of situations and practical deeds that, from now on, will occasion their use.