In 1591, François Viète published In Artem Analyticam Isagoge (Introduction to the Analytic Art), which presented a new way of writing equations that “constituted a radical departure from the traditions of ages” (Dantzig, 2007/1930, p. 89). Viète proposed that all given parameters be represented by consonants and all unknowns by vowels. So, instead of writing 5?2 + 4? + 7, one would write BA2 + CA + 7. Some years later, in his Géométrie, Descartes chose to use the first letters of the alphabet for parameters and the last letters for unknowns: AX2 + BX + 7, a simple improvement that, most likely through its easily visualized polarity, made the new system more intuitive. But the radical step had been Viète’s.
The new notation allowed the paraphrasing of any equation into numerous equivalent forms (Dantzig, p. 90) and made it possible to speak in terms of classes, or “species” of equations, as Viète’s phrase, “logistica speciosa” acknowledges. This reconceptualization thus cleaved algebra definitively from arithmetic: the former was calculating with types and the latter (the logistica numerosa) with individual numerical coefficients (Kline, 1980, p. 122). By rendering abstract all terms in the equation, this tidy new notation also made the arithmetic restrictions concerning negative and complex (e.g., √- 1) numbers irrelevant. “In vain, after this,” notes Dantzig, “will one stipulate that the expression a – b has a meaning only if a is greater than b, that a/b is meaningless when a is not a multiple of b, and that n√a is not a number unless a is a perfect nth power. The very act of writing down the meaningless has given it a meaning; and it is not easy to deny the existence of something that has received a name” (p. 91).
Viète’s discovery is a fine example of what the cognitive psychologist Annette Karmiloff-Smith (1992) has called explicit “representational redescription”. Viète’s discovery is also a compact and useful metaphor for thinking about how writers choose to name the concepts they wish to discuss, and how carefully considered redescribing of key concepts, objects, or persons, can enhance their readers’ understanding and appreciation of the argument.
Recently I have come across three examples of very effective concept redescription in non-fictional exposition. The authors reject the accepted name of a concept or person for reasons that make good rhetorical sense. The new names they have chosen to work with allow the reader to engage in the equivalent of escaping the workaday cognitive operations required by the logistica numerosa for the more exotic, forbidding, and fruitful cognitive terrain of the logistica speciosa. In this installment and the next, we will look at how redescription enhances arguments in texts from different disciplines.
As a first example, let’s consider the “placebo effect”. There is a large literature on this effect, with contributions from a number of fields. The word “placebo” is commonly defined as a sham treatment given to trick patients into believing that they are receiving a medically active substance or treatment. In his book on the subject, the medical anthropologist Daniel E. Moerman (2002) claims that the term “placebo” has been used to refer to an overly broad range of phenomena and that it should be abandoned, or reserved only for control-group responses in clinical trials (p. 4). Moerman argues that the placebo effect is precisely not the effect of the placebo (p. 14), but a response to the meaning fashioned from the patient’s involvement with the medical personnel and institution. He therefore redescribes the “placebo effect” as the “meaning response”, and defines it as “the psychological and physiological effects of meaning in the treatment of illness” (p. 14). This redescription allows his concept to include placebos that cause negative effects (i.e., nocebos), thus enlarging the concept (as did Viète’s new procedure), but it does much more than that. He wants to shift the grid so that the central concept is in an entirely different semantic neighborhood, thereby reorienting the argument so that the reader has both a better view of the newly-defined important sights and an enriched set of implicatures and connotations to enhance her experience of those sights. His new term highlights the patient’s role in the process, and ties in closely with his hermeneutic perspective on the heretofore narrowly medicalized studies and theories concerning placebos and their effects. The new term thus broadens the semantic network of the reader, encouraging ideas that might not have been born of the older term and its cognitive and emotional networks.
But one might ask at this point: Is such concept redescription really like the move from the logistica numerosa to the logistica speciosa, and not just a sort of euphemism? Perhaps somewhat like saying “pre-owned” instead of “used” to sell more cars? I shall insist that the argumentatively effective concept redescription is not like euphemism, in which a rather drab or disagreeable concept is made to sound less drab or disagreeable through the use of a funny or aesthetically pleasing word or phrase. In fact, in the examples discussed here, the writer uses a less aesthetically pleasing word that moves away from singularity and toward conceptual extension. This redescription better captures the referent that the writer has in mind, and pries the concept away from the sparkle of the term commonly accepted in discourse on the subject. In our first example above, the Latinate term “placebo” (meaning, “I shall please”) certainly holds more allure than the Old English-derived “meaning”. But taking some of the shine off of the first concept is necessary to have the reader focus on the wider conceptual field of the second term, and on the claimed more extensive and profound psychological effects. What successful concept redescription most often does for an argument is to allow the reader to mentally place the concept alongside others of its species, which have been ignored by, downplayed by, or simply not detectable in the presence of the earlier term -- logistica speciosa.
As a rhetorical choice, Moerman’s presentation of the new term “meaning response” is quite effective. One improvement that could have been made in the exposition would have been to refrain from using the word “placebo” subsequent to his presentation of the new term. Perhaps the interleaving of the two terms is undertaken in the text to remind the reader of the contrast between the two terms. Or perhaps the writer senses that there is more to be gained than lost in this particular case by allowing the two terms to be juxtaposed throughout the text. However, as we will see in next week’s examples, there is much argumentative power to be gained by boldly presenting one’s new term and never (or almost never) looking back.
Dantzig, Tobias. (2007/1930). Number: The language of science. London: Plume.
Karmiloff-Smith, Annette. (1992). Beyond modularity: A developmental perspective on cognitive science. Cambridge, MA: The MIT Press.
Kline, Morris. (1980). Mathematics: The loss of certainty. New York: Oxford.
Moerman, Daniel E. (2002). Meaning, medicine and the ‘placebo effect’. Cambridge, UK: Cambridge University Press.
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