Brian Rotman’s (rhetorical) approach to math

Rotman’s project is interesting because it directly engages not only the question of persuasion, but the question of the construction of mathematical objects through mathematical language. This is interesting to me because, as I argue in my Master’s Report, “Unlike other sciences and public discourses, whose arguments proceed from shared assumptions or agreed upon perceptions of the natural world, mathematics begins with writing that performatively posits abstract fictions” (46). For Rotman, as for Reuben Hersh and Phillip Davis and countless others, mathematical knowledge is rhetorical: rough, approximate consensus arrived at through specialized, yet inexact, language, and argument among those familiar with its specialized terms. But Rotman also recognizes the aspect of mathematical language that differentiates it from natural language, in general, and from the special, altered subsets of it used in other sciences. Although neither Rotman nor Mitchell Reyes, who brought Rotman to the pages of Quarterly Journal of Speech, seems especially attuned to the uniqueness of this quality, they both appreciate the constitutive, constructive nature of the mathematical signifier.

In my Master’s Report, I was looking to Brouwer for an account of math that would bring it into line with the theories of performative language articulated by J.L. Austin, Derrida, Shoshana Felman, and/or Mikkel Borch-Jacobson. I was only partially successful. Brouwer left me hangin’. Rotman comes even closer than Brouwer, but also misses the mark. His account of math makes its signs constructive and creative but not performative in the post-Austin sense.

But Rotman’s account of math is definitely rhetorical. Here’s how it works:

1. Rotman’s starting point: “Mathematics is an activity, a practice” (7).
2. Three interrelated agencies, Person-Subject-Agent are at work in mathematical activity; the activity is primarily communication; and the agencies are, therefore semiotic (to Rotman) or rhetorical (to “us”).
3. Mathematical assertion and proof are two essential mathematical activities: the assertion is a prediction and the proof is a process of persuasion.
4. When the Person asserts and proves, he (sic) “scribbles/thinks,” thereby becoming the “scribbling/thinking” Subject.
5. The Person-as-Subject makes a prediction about his (sic) own future, about what would be true if the (Person-as-)Subject manipulated signs infinitely, if he (sic) repeated certain scribblings again and again.
6. The Person-as-Subject writes a proof to persuade someone/s (the Subject for Rotman…, maybe the “they” or the “we” for me) that the prediction is valid (true?). The proof is a thought experiment and the writing that it is inextricably linked to. Each step of the written proof, i.e. each discreet act of writing performed by the Subject, corresponds to some imagined action performed by the Agent in the thought experiment. *(We’ll eturn to this briefly.)
7. The Subject is persuaded to accept the prediction by writing the proof and, thereby, executing the thought experiment (as the Agent-imagined-by).
8. Rotman adds that, along with this mechanical logic to persuade the Subject, there must be what C.S. Pierce calls a “leading principle.” The leading principle, which is related but not reducible to the proof, persuades the Person. An important feature of the leading principle is that it explains the relationship between the Subject and the Agent. “Precisely in the articulation of this relation lies the semiotic source of a proof’s persuasion. [...]. It is the business of the underlying narrative of a proof to articulate the nature of this resemblance” (19).When an assertion is validated, “it is the Person who, by being able to articulate the relation between Subject and Agent within a thought experiement, is persuaded that a prediction about the Subject’s future encounter with signs is to be accepted” (24).

*Brief return: The writing/thinking Subject imagines the Agent to act. The Subject “must act indirectly and set up an imagined experience-a thought experiement-in which not he but his Agent, the skeleton diagram of himself, is required to perform the appropriate infinity of actions” (17). So what are the actions of the Agent? It seems that the Agent manipulates (virtual) signs. If this is the case, then th Agent must write and think… right? But is that problematic? Does it imply the existence of a Virtual Agent? Does he (sic) do something else? Something more or less?

Leaving aside the potentially problematic details of the Agent’s activities, the preceding is Rotman’s account of mathematical language in action, of communication by transactions with mathematical sign. It is his rhetoric of math, which explains how people with bodies and imaginations interact with meaningful material signs in order to produce knowledge, which then influences their perception of and future interactions with material reality.