Abstract

Click to increase image sizeClick to decrease image size Notes1 Chaim Perelman's work showed the Platonic roots of Modernist thought; see especially The Realm of Rhetoric. Latour's work is strong in terms of Modernism's impact on understandings of science.2 See Robert Hariman; Reyes, "The Swift Boat Veterans for Truth."3 I draw mostly on Rotman's more recent Mathematics as Sign because there one finds the clearest articulation of his approach.4 The issue of the relationship between informal and formal mathematical discourse, the discursive/argumentative strategies within each, and the rhetorical purposes of each remains an unexplored and potentially rich area for rhetorical analysis. See the "Potentialities" section that follows.5 For others who make this argument see William P. Thurston; Lakoff and Núñez; Imre Lakatos.6 This is, of course, a major issue in the mathematics education literature, where studies of student perspectives on math reveal two consistent themes: students perceive math as (1) abstract and (2) rule-driven. The point that we are building toward is that mathematics is not abstract or rule-driven by nature, but it can and often is taught as an abstract form of logical (rule-driven) reasoning. This pedagogical approach, it has been shown, does not allow the majority of students to identify with mathematics (see Boaler). Regarding computers and mathematics, an interesting phenomenon has emerged in the twenty-first century: powerful computers are analyzing enormous data sets and are producing complex mathematical formulas out of those data sets that even the best mathematicians cannot understand—they know they work to predict certain phenomena in the data set but they cannot give meaning to those predictions. The fact that computers can generate novel mathematical formulae significantly undermines the Platonic view of mathematics. See Rotman, Mathematics as Sign, 126–128.7 Lakatos's work reveals the importance of historical context and the dynamics of argumentation in mathematical innovation. See Lakatos, Proofs and Refutations.8 For insightful accounts of the emergence of Greek geometry and its debt to empirical, material features of the world see Michel Serres; Reviel Netz.9 To the skeptical reader who thinks math is only metaphorical at the basic level: Nearly half of Where Mathematics Comes From addresses more complex mathematics, offering analyses of the concept of infinity and of Euler's classic equation eπi = −1. A full treatment of these analyses is beyond the scope of this essay.10 Rhetoric of science scholars have extended Latour's argument in various ways. The number of scholars is too long to list here but one might profitably begin with John A. Lynch and Chantal Benoit-Barné.11 Analysis of rhetoric as constitutive has increased in many areas of rhetorical studies but remains a minority approach to the study of mathematical discourse. I develop this point in "The Rhetoric in Mathematics."12 These works build of course on previous scholarship on mathematics as deployed in other domains, including especially the domains of economics and statistics.13 Bernhard Riemann's concept of manifold, for example, comes to mind as a potentially beneficial way to advance our thinking about polysemy and subjectivity, for it emphasizes not only the discrete differentiations of meaning and identity but also their layered and continuous features. See Arkady Plotnitsky.