5 - The brittleness of the orange equilibrium

Summary

I want you to remember that words have those meanings which we have given them; and we give them meanings by explanations.

Ludwig Wittgenstein (1960, p. 27)

The proof…changes our concepts. It makes new connexions and changes the concept of these connexions.

Ludwig Wittgenstein (1956, p. 166)

Mathematical economists are members of an interpretive community (Fish 1980), and it is sometimes suggested that the creation of mathematical texts in economics is associated with that community's desire to avoid serious issues of interpretation: Mathematics is thought to produce a text that allows little or no variability in a reader's response (e.g., a real number is not a metaphor). My argument, however, will show that a mathematical text established one of several competing interpretations and forced readers to select one image from a set of images; mathematical work has, in at least one case, shifted economist-readers' use of a word.

At issue is the word “equilibrium” and how its meaning evolved in a sequence of papers published between 1939 and 1954. Although “equilibrium” is a term that appears in the hard core of the neo-Walrasian program, and “hard core” suggests linguistic fixity, that connotation is misleading. I am not, of course, interested in the “true” meaning of equilibrium. I am instead interested in how an interpretive community read the word “equilibrium” over a fifteen-year period. In McCloskey's terms (1983,1986), one must examine the rhetoric associated with some writings about equilibrium.