Review Essay. Stranger Relations: The Case for Rebuilding Commonplaces between Rhetoric and Mathematics by Mitch Reyes

This is a review of:

Pandora’s Hope: Essays on the Reality of Science Studies, by Bruno Latour.
Cambridge, MA: Harvard University Press, 1999. 324 + x pp. $29.74 (paper).
Science in Action: How to Follow Scientists and Engineers through Society, by
Bruno Latour. Cambridge, MA: Harvard University Press, 1987. 274 pp. $27.55
Ad Infinitum: The Ghost in Turing’s Machine: Taking God Out of Mathematics
and Putting the Body Back in: An Essay in Corporeal Semiotics, by Brian Rotman.
Stanford, CA: Stanford University Press, 1993. 203 + xi pp. $22.46 (paper).
Mathematics as Sign: Writing, Imagining, Counting, by Brian Rotman. Stanford,
CA: Stanford University Press, 2000. 170 + x pp. $21.77 (paper).
Where Mathematics Comes From: How the Embodied Mind Brings Mathematics
into Being, by George Lakoff and Rafael Núñez. New York: Basic Books, 2000.
492 + xvii pp. $26.99 (paper).

This looks very interesting indeed, considering that the reading list features several of my key texts.

How did math become the “purest” countervailing
force to rhetoric—the former celebrated as the language of truth, the latter reduced
to strategies of manipulation? And what are the consequences of the division—the
estrangement—of rhetoric and mathematics, not just for our academic understanding
of each but also for our views of their respective roles in society?
These are just some of the questions that scholars, in spite of conventional
wisdom, have recently begun to ask. They have done so because there are real
repercussions—intellectual, pedagogical, sociocultural—to maintaining the polarized
status quo. p. 471

What is at stake in the campaign to rebuild commonplaces between rhetoric and
math? From the literature surveyed here, nothing less than a major transformation
in thinking about rhetoric, mathematics, and culture. Out of Bruno Latour’s
work—especially Pandora’s Hope and Science in Action—we can locate an early moment of rupture between rhetoric and mathematics in Plato’s Gorgias even as
we build on his alternative actor-network approach. Out of Brian Rotman’s semiotic
analysis—progressively articulated in Signifying Nothing, Ad Infinitum, and
Mathematics as Sign—we can begin to see the deep seeded and often unconscious
commitment to Platonic realism in contemporary mathematics, how it systematically
conceals the materiality of mathematical discourse, and how we can re-enliven
that materiality through semio-rhetorical analysis. And out of George Lakoff’s
and Rafael Núñez’s Where Mathematics Comes From we learn of the conceptual
metaphors at the roots of mathematical thinking.We will use these books as coordinates
for plotting a course toward more recent studies of rhetoric and mathematics
that explicitly interrogate the role of rhetoric in mathematical practice. p. 471-2

I think that uncritically accepting Lakoff & Núñez is tricky, but still, this is an exciting paragraph.

The organizing principle of Platonic Realism is that mathematical objects exist independently
and a priori of human cognition.Mathematical symbols are, accordingly,
more or less adequate representations of ideal mathematical objects, and the purpose
of doing mathematics is to discover “objective irrefutably-the-case descriptions
of some timeless, spaceless, subjectless realm of abstract ‘objects’” (Mathematics as
Sign 30). From this perspective, mathematical symbols should function as transparent
referents for real mathematical objects and their relationships and should have
no function beyond that… p. 475

While this perspective may have some psychological benefits—enabling those
operating from within it to see their work as pure and absolute—it also has some
real deficits when it comes to understanding mathematical practice. Like the realist
style so familiar to rhetorical scholars in other domains,2 mathematical realism
immediately denies the materiality of mathematical discourse. […]

But how, asks Rotman, can we account for the movement from mathematical
practice to mathematical knowledge? By what means do mathematicians capture
their supposedly presemiotic thoughts? And what is the mathematician’s relationship
with the a priori realm of mathematical objects? Plato answers with reference
to the soul and a metaphysics of reincarnation; Gottlob Frege, one of the founders
of formal logic and a preeminent mathematical realist of the twentieth century, does
not do much better… {…]

For Frege and Plato and other mathematical realists, Rotman argues, the means
of production of mathematical knowledge are hidden because the constitutive
work of the mathematical sign is systematically denied. p. 476

Although we have only scratched the surface, two important rhetorical insights
emerge from Rotman’s work at this point: first, the structure of mathematical persuasion
within the practice of doing mathematics begins to take shape and, second,
the forms mathematical discourse takes and their consequences begin to emerge. p. 477

“Presented with a new proof
or argument, the first question the mathematician . . . is likely to raise concerns
‘motivation’: he will . . . seek the idea behind the proof . He will ask for the story that
is being told, the narrative through which the thought experiment or argument is
organized.” (18).Why, one might ask, are these ideas absent from the mathematical
proofs they animate? Because they exceed the strict boundaries of formal logical discourse
sanctioned within formal proofs (what Rotman calls “the Code”).4 Rotman’s
argument here, and other scholars have made a similar point, is that one can know a
proof, reproduce all the steps, even explain why those steps follow logically fromone
another, and yet fail to understand the meaning and significance of the proof.5 p. 478

It is precisely the Person—who is finite, lives outside the formal mathematical
code, and has access to the ideas that motivate mathematical theorems and
proofs—that Platonic realism denies. That denial brings us to our second rhetorical
insight: although Platonism protects a faith in mathematics as absolute, it also
shapes conventional mathematical discourse in profound ways. Consider the conspicuous
absence of indexical terms (“I,” “now,” “here”), for instance, in most
mathematical texts; or the omnipotent voice of command (the imperative mode);
or the lack of contextual explanation of the concepts considered (Mathematics as
Sign 121). […] Yet if
one desires to communicate the actual practice of doing (rather than memorizing
and regurgitating) math and hopes to offer an understanding of the meanings of
the concepts mobilized in mathematical statements, then one needs to attend to
the creative, constitutive force of mathematical discourse that Platonic realism renders
invisible and that only now is beginning to come into view through Rotman’s
analyses. p. 479

For rhetorical scholars, the good news is that several old friends traffic with
Rotman’s reanimation of mathematical discourse: the meaning and significance
of a mathematical statement comes not from its infallibility—the establishment of
which is the purpose of formal logic—but from its meta-Code. Suddenly we see
that contextual knowledge—rhetorical, historical, sociopolitical—of mathematical
concepts is central to understanding them, without which one can execute a problem
or a proof (as a computer might) and yet not have the slightest inkling of the
meaning or purpose of that execution.6 Equally problematic, one who encounters
Platonically inspired mathematical discourse is likely to see it as an inert, abstract,
rule-driven system of formal logic instead of a fascinating, evolving, contextually
situated, creative practice of thinking and writing. The arts of mathematical innovation
lie in the nexus between thinking/scribbling and the argumentation that these
“thought-scribbles” give rise to within one’s mathematical community. p. 479

Rotman shows that mathematical meaning comes—through the Person—from the
meta-Code external to formal mathematical discourse, but what are the analytic
strategies available to scholars—short of talking to “the Person”—to tease out the
different ways meanings get produced in mathematics, to study how they circulate,
and to analyze how they influence mathematical practice? p. 480

Next there’s some potentially useful critique of Lakoff and Núñez, then Latour:

Mathematics, Latour contends, underwrites the worlds of capital and technoscience
not because it is true in some transcendental sense but because it enhances
capacities to mobilize traces, stabilize relations, and accelerate combinations.p. 486

Latour’s arguments, when combined with the work of Rotman, Lakoff, and Núñez,
bolster the case for developing links between rhetoric and math. Far from the language
of pure reason, through Latour we begin to see mathematics as the web that
weaves the world of technoscience, as a discourse that rewrites the networks it represents,
and as a vehicle that concentrates power. Mathematics, then, is inherently
public and political—all the more so for the efforts that seek to insulate it from
these very domains. Mathematics must be understood in light of the networks and
relations it renders, the ways it simultaneously concentrates and conceals power,
the means by which it translates the objects of its gaze, the productive metaphorical
structures it uses, and who we become when we do math. Each book we have
reviewed suggests the viability and the benefits of critical rhetorical study of mathematics;
each book also calls for more sustained inquiry. p. 487

Ours would not be an effort to reduce mathematics to rhetoric, but rather to
enhance understanding of math as a discursive formation that enables, strengthens,
weakens, and creates relations between humans and nonhumans. Mathematics
is a socializing force that can articulate nonhumans into sociability with humans
and thus radically transform collectives. In order to attend to these new, complex,
and fast changing collectives we will need not only to trace the materiality of mathematical
discourse but also transform our own traditional humanistic theories of
rhetoric. p. 489




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