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

(paper).

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. 471What 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. 475While 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. 476Although 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. 478It 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. 479Likewise,

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. 487Ours 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