JS Lect 1: The Rhetoric of Numbers: Qualitative Research into Quantification
THE RHETORIC OF NUMBERS:
QUALITATIVE RESEARCH INTO QUANTIFICATION
[OHP0 from BBC Today program, 16 th Feb, 2005]1
There is a very famous saying, attributed to Benjamin Disraeli if you are British, and Mark Twain if you are
American:
[OHP1 of quotes]
“There are three kinds of lies: lies, damn lies, and statistics” (Disraeli, or Mark Twain).
And this is what this lecture is about. What I want to talk to you about today is not about how to do
quantification, or about how to construct measures. (We are awash with measures, numbers, quantifying
assessments of all kinds.) Instead, I want to talk more about how to ‘deconstruct’ them, about how they can be
(and often are) used ‘rhetorically’ – that is, used to persuade or influence people in the decisions they take in
their lives.
Why are numbers so important? What do they convey? The mere presence of numbers tends to speak of rigour
and objectivity, of an ‘in touchness with reality’, of a kind of ‘scientific certainty’. It was William Thomson
(Lord Kelvin), a pioneer in thermodynamics and electricity, who said in 1891:
“When you can measure what you are speaking about, and express it in numbers, you know
something about it; but when you cannot measure it, when you cannot express it in numbers,
your knowledge is of a meagre and unsatisfactory kind. It may be the beginning of knowledge,
but you have scarcely, in your thoughts, advanced to the stage of science” (Lord Kelvin,
1891).
This may be so in the physical sciences, but is it so in human affairs, in which people’s actions are so much
more a matter of their relations to the unique circumstances of their performance? Consider, by way of contrast,
Freud’s (1964) lament about the relative absence of scientific paraphernalia and jargon in his work: “I have not
always been a psychotherapist,” he said:
“Like other neuro-pathologists, I was trained to employ local diagnoses and electro-prognosis,
and it still strikes me myself as strange that the case histories I write should read like short
stories and that, as one might say, they lack the serious stamp of science. I must console
myself with the reflection that the nature of the subject is evidently responsible for this, rather
than any preference of my own. The fact is that local diagnosis and electrical reactions lead
nowhere in the study of hysteria, whereas a detailed description of mental processes such as
we are accustomed to find in the works of imaginative writers enables me, with the use of a
few psychological formulas, to obtain at least some kind of insight into the course of that
affection” (Freud, 1964, pp.160-161, my emphasis).
These words of Freud – to do with providing “detailed descriptions,” not so much of hidden, inner mental
processes as such, but of people’s outward expressions of them in their interactions with the others around them
– can give us a clue to the “Rhetorical” approach to qualitative research that I want to introduce to you today.
[OHP2 - lect outline]
What I’m going to talk about today: 1) the quantitative attitude; 2) the “turn to rhetoric;” 3) Everyday
quantifying practices; and 4) two examples of “quantification rhetoric.”
So... before turning to the nuts and bolts of what is entailed in conducting a “Rhetorical Analysis” in a particular
sphere of human communication, let me first make a number of introductory remarks about “the quantitative
attitude” and its history, and then about the renewed respect for the study of Rhetoric in the recent “turn to
rhetoric,” and what we now think can be achieved by a rhetorical analysis – for, after all, we often here the
phrase that so and so’s talk is “mere rhetoric,” i.e., it is thought to be pretentious, insincere, or intellectually
vacuous talk. What happened to change this attitude?
1
The “quantitative attitude.”
[OHP3 of Plato and Descartes]
If I had to choose just two statements that set the scene for the “quantitative attitude,” I would first choose this
statement from Plato (1974). In book ten of The Republic, he remarked upon the ease with which we can be
deceived or misled by appearances, and suggested that, “measuring, counting, and weighing have happily been
discovered to help us out of these difficulties, and to ensure that we should not be guided by apparent
differences of size, quantity and heaviness, but by calculations of number, measurement, and weight... and these
calculations are performed by the element of reason in the mind” (p.432).
To this statement by Plato, I would add one by Descartes, from his Discourse on the Method of
properly Conducting One’s Reason and of Seeking the Truth in the Sciences of 1637. There he noted that:
“These long chains of reasoning, quite simple and easy, which geometers are accustomed to
using to teach their most difficult demonstrations, had given me cause to imagine that
everything which can be encompassed by man’s knowledge is linked in the same way... [thus]
there can be nothing so distant that one does not reach it eventually, or so hidden that one
cannot discover it” (1968, p.41).... [and with such a method] it is possible to arrive at
knowledge... [by which we can] make ourselves masters and possessors of nature” (p.78).
And for a long, long time we have thought of proper thinking as calculation, as what it is to be properly rational
– hence, Lord Kelvin’s claim.
But let me say this about what we might call The Quantitative Way of Seeing: If we are going to count things up,
to quantify them, we must be able to see them as distinct entities; as not, so to speak, ‘shading into’ one another,
so we are unclear as to where one entity ends and another begins. For things to be countable, they must have
their own self-contained identity, and not depend for their identity – like, say, the parts of a living body, arms,
legs, ears, eyes, etc., on being related as parts to a larger whole.
[OHP3a - quantitative way of seeing]
In other words, countable entities must exist as “externally” related to one another – while the living parts of a
body would be “internally” related to each other.
Thus we can see that, the process of measurement – of necessity – divides whatever it is “measuring” into units
which are external to one another, separate but juxtaposed.
Whatever is “measured” is thereby spatialized in conception into a string of units juxtaposed along an imagined
line which effectively constitutes a scale. In practice, a measurement consists in comparing whatever is to be
measured with this scale, and counting the number of units which correspond. This means that wherever science
is concerned with measurement, the particular aspect of nature involved has first to be prepared quantitatively.
This entails dividing it into a set homogeneous parts that are intellectually superimposed on nature like a grid or
scaffolding. Nature is then seen in the perspective of the framework, which is not part of nature at all, but is
really an intellectual re-arrangement of nature that reduces it to the purely quantitative i.e., to parts which are
external to one another.
It certainly gives us power over nature, but it has the effect of separating us from nature in such a way that we
cease to experience nature directly. We can control and organize nature according to our will, but the price for
this is that we begin to experience ourselves as being separate and essentially different from nature, while nature
in turn begins to seem lifeless and empty.
A consequence... the thoughts we embody in measurement are only applicable to dead phenomena for no living
thing can be thus fragmented without dying. For the parts making up a living process depend on their already
existing relations with each other if they are to remain living. Quantitative forms of thought are entirely
appropriate to the inanimate world, but quite inadequate for apprehending life.
Clearly, there is a whole sphere of study here in itself... and this is, eventually, to be a lecture of rhetorical
methods of analysis... so I won’t continue this line of thought here. But do look at Dorothy Smith’s article on
Theorizing as Ideology – based on Marx and Engel’s three tricks for the construction of ruling illusions – posted
on the LearnServ.
2
The turn to rhetoric in the late 80's early 90's
The “quantitative attitude” was all very well when we believed in the possibility of obtaining a “one true and
fundamental view” of the “real world out-there.” But in the 1980's many changes began to occur, in many
different spheres – the era of Postmodernism, Deconstruction, Feminism, and so on. Simply put, you could say
that we became a bit more reflexively self-aware of our own ‘collective involvements’, our own ‘active doings
in relation to those around us’, in our processes of investigation. Perhaps more influential than any other piece
of writing in effecting this change, was Kuhn’s (1962) Structure of Scientific Revolutions – with his claim that
scientific discoveries did not spring as a virgin insight into the head of a brilliant individual, but occurred only to
members of a “scientific community or school” that shared a “paradigm” – a shared “way” or “set of practices”
based on “same accepted examples of actual scientific practice” (p.10)*. “Discovery commences,” said Kuhn
(1962),
“with the awareness of anomaly, i.e., with the recognition that nature has somehow violated
the paradigm-induced expectations that govern normal science” (pp.52-53).
*{Later, he was to adopt the term “disciplinary matrix” – Kuhn, 1970, p.182.}
[OHP4 of Kuhn and Garfinkel quotes]
In other words, what Kuhn brought to our attention was the existence of a whole set of shared “background
expectations” which were constitutive for us of what we (in the past) had simply called our “observations,”
background expectations that we had, until that time, utterly failed to notice.
As the importance of these unnoticed background expectations is central to all our work here – and bringing it
into view is a central part of what is involved in doing rhetorical analyses – let me add a comment of
Garfinkel’s (1967) here, about the “seen but unnoticed” character of such paradigm-induced, background
expectancies. He remarked that, in conducting their investigations, sociologists commonly noted the everyday
features of a circumstance, and formulated a problem for investigation in terms of such features – in a moment
we’ll be examining crime and cancer statistics. But, “just as commonly,” he noted,
“one set of considerations are unexamined: the socially standardizing, ‘seen but unnoticed’,
expected, background features of everyday scenes. The member of the society uses
background expectancies as a scheme of interpretation. With their use actual appearances are
for him recognizable and intelligible as the appearances-of-familiar-events. Demonstrably he
is responsive to this background [i.e., we can ‘see’ people being responsive - js], while at the
same time he is at a loss to tell us specifically of what the expectancies consist. When we ask
him about them he has little or nothing to say” (pp.36-37).
But what Kuhn did not bring out in his talk of paradigms, was the contested and argumentative nature of the
whole ‘seen but unnoticed’ background in terms of which all scientific inquiries are conducted.
Again, there is a whole history to be recounted here. But I will set the scene here with just one reference:
Billig’s (1986, 1987, 1991a &b) account of arguing as thinking, is central for us here, as it immediately moves
us a way from the thought that there is, somewhere, a one true view to be found to the view that there are a
number of true versions of a state of affairs.
[OHP5 - Billig quotes]
For Billig, a central hero in the history of rhetoric is Protagoras – all of whose writings have unfortuately been
lost, but whose views come down to us in the Platonic dialogue called Protagoras. About Protagoras, Billig
(1991) remarks:
“One of Protagoras’ most famous sayings was the maxim: ‘In every question, there are two
sides to the argument, exactly opposite to each other.’ The saying was almost certainly
derived from Protagoras’ experiences in the law-courts... [where] in every case there would be
a prosecution and a defence, propounding directly opposite views... [But] there is also a
psychological implication to Protagoras’ maxim that there are two sides to every question.
The saying draws attention to the human capacity for critical thinking, which is based on the
faculty for negation. We possess the capability to resist arguments by inventing the counterarguments which constitute the inevitable other side to each question” (pp.46-47).
The potential two-sidedness (or more-sidedness) of all our claims to truth, gives rise to one of Billig’s most
important concepts – he formulates it thus, in terms of a lecturer (like myself) giving a lecture (a supposed piece
of reasoned dsicourse!):
3
“The lecturer who constructs a case, or argument, will give justifications for the case, in order
to foresee and deflect potential criticisms. Counter-views will be criticized either implicitly or
explicitly, as the lecturer attempts to exclude the opposing views to the main argument of the
lecture.. As the words leave the lecturer’s mouth, they struggle to do battle with those other
words which the lecturer is rejecting, and which might well be circulating in the minds of the
audience.
From this, it could be suggested that we cannot understand the meaning of a piece of
reasoned discourse, unless we know what counter-positions are being implicitly or explicitly
rejected... In the same way, we cannot understand the attitudes of an individual, if we are
ignorant of the wider controversy in which the attitudes are located. In other words, the
meaning of a piece of reasoned discourse, or of an expressed attitude, does not merely reside
in the aggregation of dictionary definitions of the words used to express the position: it also
resides in the argumentative context” (p.44).
In other words, although we might use numbers I our talk, and numbers might seem (‘on the face of it’) as
utterly neutral or as utterly factual as one can get, we will find that people are making subtle choices as to how
they can best present their numbers in making their case.
We will look at three forms of the qualitative analysis of quantification: studies of everyday quantification
practices; studies of metrology; and studies of `quantification rhetoric'. We will spend rather more time on the
last of these three.
1. Everyday quantifying practices:
[OHP6 - D&H quote, Lave quote]
We might think that mathematics is beyond the reach of rhetoric. But look at the papers and books by Davis and
Hersh (1983, 1986, 1987). Without going into the detail of an example ‘proof’ they examine, I can give the
flavour of their analysis with the following quote – to do with how the “prover” makes use of the notion of
“generalization.” They point out that:
“In step 1, a typical person is selected and named. Since it is a typical person, it is not
specified which person it is. The idea is that if one reasons about a typical person, and uses
only the characteristics which that person shares with all other persons, then one’s deductions
will apply to all persons (line 10). Should it not be verified, then, as part of the proof, that only
those characteristics have been used? What are the formal criteria for so doing? By raising
such questions, one can force the proof into deeper and deeper levels of justification. What
stands in the reason column now, the single word “generalization,” is pure rhetoric” (p.67).
This area of work includes cross-cultural analyses of quantifying practices, some of it going under the name of
'ethnomathematics'. Thus, for example, we discover that at the level of the basic concepts of quantity and
aggregation, languages can differ. (To study this further, see Helen Watson (1990) Investigating the social
foundations of mathematics: natural number in culturally diverse forms of life. Social Studies of Science 20:
283-312, and Whorf, B.L. (1956))
Other work has been done on how adults deal in practice with what, if they were still in school, would be called
‘mathematical problems’, but as Jean Lave (1988) – who is the most prominent writer in this area – finds, are
not able to apply the generalized knowledge they gain in the classroom very well in real-life contexts. She has
looked at how supermarket shoppers calculate best buys; how dieters, without the aid of kitchen scales, estimate
the appropriate weight of cottage cheese for lunch; and here’s an example from a Brazilian market boy:
[The subject is a twelve-year old boy manning a stall selling coconuts. He is approached by a customer who is a
researcher]
Customer: How much is one coconut?
Boy: 35.
Customer: I'd like ten. How much is that?
Boy: (Pause) Three will be 105; with three more, that will be 210. (Pause) I need four more. That is . . . (pause)
315 . . . I think it is 350.
Why doesn’t the boy just add a ‘0’ to 35 and get 350? Because he’s used only to dealing with 2's and 3's at a
time, and he works with what’s familiar to him.
4
But just how should we state numerical things? Where, actually, is the basis for our measurements? Standard
metres, standard kilograms, standard second? How do we know whether our instruments measure what they are
supposed to measure? What is, for instance, is the true, actual, real, second?
[OHP7 on second and USA GNP]
[Encarta quote on Time]
Time: For centuries, time has been universally measured in terms of the rotation of the earth. The second, the
basic unit of time, was defined as 1/86,400 of a mean solar day or one complete rotation of the earth on its axis.
Scientists discovered, however, that the rotation of the earth was not constant enough to serve as the basis of the
time standard. As a result, the second was redefined in 1967 in terms of the resonant frequency of the cesium
atom, that is, the frequency at which this atom absorbs energy: 9,192,631,770 Hertz (cycles per second). 9
billion, 192 million, 192 thousand, 631 hundred, and 770 Hertz
So our simple standards are subject to the most intense and continuous scrutiny in the search for ever greater
stability, and ultimate accuracy. This work of redefinition and the general maintenance of all the millions of
standards with their associated chains and hierarchies is extremely costly.
“In 1977, the US government spent 6% of the GNP on measurements.” (from O'Connell 1983: 166, n.1)
This, however, can be put in other ways [uncover OHP7 step by step]
As:
$105,373,940,000
or:
105.4 billion dollars
or:
well over a hundred billion dollars
or:
$4,214.9576 per capita
or:
more than four thousand dollars for every man, woman and child in America
In other words, there is a whole “lexicon” of numerical expressions.... which leads us very nicely into the third
form of the qualitative study of quantification:
2. First example - Criminal Statistics:
From Elaine Campbell The rhetorical language of numbers: the politics of criminal statistics. Journal of Radical
Statistics, Autumn, 2000, vol, 75 (http://www.radstats.org.uk/journal.htm)
In a moment into some of the “rhetorical” features of Elaine Campbell’s (2000) account of “criminal statistics.”
But first, here’s how she sets of out the range of possible of numerical expressions:
[OHP8 -lexicon of num exps and non-num]
A lexicon of numerical expressions
Seven different kinds of numerical statements appeared in these newspapers’ coverage of the ‘rise in crime’.
1.
Proportion – by far the most common mode of expression: ‘2 per cent increase in sexual offences’;
‘two-thirds of all robberies’; ‘24 of the 43 police force areas’.
2.
Frequency – proportional statements were buttressed by such statements as: ‘350 attacks per 1,000
5
population’; ‘six times more likely’.
3.
Precision – commonly used numerical forms were often precise - for example, ‘2.2 per cent’; ‘5.2
million’; ‘663,800 offences’; ‘population of 4211'; ‘36.9 offences per 1,000 homes’.
4.
Overall magnitude – some newspaper texts employed a quantification mode: for instance, ‘the rise of
115,000 recorded crimes brings the total to 5.2 million’ – although this form was much less marked
than proportion, frequency and precision.
5.
Equations – a few statements took the form of equations: e.g., ‘offences have risen by 29% or 70,000’ ;
‘there were 406 offences of violence, or a rate of 2.9 per 1,000’.
6.
Approximation – there were many instances of the use of approximation which included statements
such as ‘nearly 6%’; ‘more than half of the total’; ‘fewer than 10%’; ‘roughly 16 per cent’.
7.
Combinatorial modes – in addition to these discrete modes of quantification, there were expressions
facilitating comparisons and contrasts across different forms of numerical expression: e.g., some
statements combined precision with equation, magnitude and approximation - ‘crime grew by 8.7 per
cent or 80,285 offences to a total of over 1 million’; others combined approximation with magnitude,
equation and proportion - ‘offences top the million mark with an 80,000, or 9% rise in offences’.
Moreover, The Times (19/01/00) displayed a series of league-tables and maps adding an elaborate visual and
spatial dimension to the numerical expressions which appeared in the main body of the text. Indeed, as Potter et
al (1991: 343) suggest – as we shall see – visual displays function as ‘parallel commentaries’ which reinforce
textual numerical expressions.
But she also notes that a number of non-numerical expressions were used to give qualitative meaning to
numerical statements.
Thus, the different manifestations of ‘rising crime’ across offence types and police force areas/BCUs were
variously evaluated as:
‘slight’
‘sharp’
‘marked’
‘significant’
‘relatively small’
‘very low’
‘huge’
‘only’
‘typically’
‘predominantly’
‘rarely’
‘usually’
‘few’
‘mainly’
and ‘just’
Similarly, press reports utilised non-numerical quantifiers to position numerical statements on a spectrum of
extreme cases to show, for example, the ‘biggest’, ‘largest’, ‘worst’, ‘smallest’ and ‘least’ instances of a ‘rise in
crime’.
The rich lexicon of non-numerical quantifiers give sense to the numerical forms, and increases the range of
possibilities for inserting ‘number’ into argument.
How is this kind of “discursive architecture,” as she calls it, put to work to produce specific argumentative
(rhetorical) effects?
[OHP9 - Campbell example]
I have time to take only one example:
“Offences increased by 2.2 per cent in the year from October 1998 to September 1999. There
were 114,000 more offences taking the total to just over 5.2 million. Fraud and forgery, sexual
6
offences, thefts from the person and violence against the person all rose.... The figures make it
clear that increases in the Metropolitan and West Midlands force areas were largely
responsible for pushing up the national total. In the Met, crime grew by 8.7 per cent or 80,285
offences to a total of over 1 million. In the West Midlands there was an increase of 16 per cent
or 48,755 offences” (The Daily Telegraph, 19/01/00).
1.
2.
3.
4.
5.
6.
Consider, the first phrase: ‘Offences increased by 2.2 per cent’ – this is a precise proportion which
conveys a sense of ‘smallness’ about the rise in recorded offences. Juxtaposed with a total of ‘just over
5.2 million’, it has the effect of shifting the focus onto an altogether different order of ‘number’. The
contrast between the ‘smallness’ of ‘2.2' and the ‘millions talk’ of the totality constructs a minimal
picture of ‘rising crime’. Moreover, the approximation combined with the precision of ‘just over 5.2
million’ implies a level of magnitude beyond which counting is rendered pointless.
The insertion of the equation ‘114,000 offences’ is, then, crucial to bridging these extremes of number;
expressed as ‘hundred(s) of thousands’, readers are actively encouraged to see the rise in crime as
‘substantial’ rather than ‘small’.
The text then goes on to list those offences which have risen over the previous year. The absence of
any reference to property crime (such as burglary, thefts of and from vehicles, vehicle interference,
criminal damage, handling and theft from shops), suggests that the list is designed to be read as
emblematic rather than complete.
At the same time, the list makes no reference to the relative rate at which these offences have risen. The
absence of quantifiers here suggests that the overall rise in crime, rather than the detail of it, is of
primary analytical concern.
Indeed, since the article claims that ‘the Metropolitan and West Midlands police force areas were
largely responsible for pushing up the national total’, this is the only ‘fact’ which needs to be
demonstrated quantitatively. Thus, a combinational numerical expression is introduced which
establishes that ‘Met crime’ has increased by 8.7 per cent (ie. four times the overall increase of 2.2 per
cent); that this equates with 80,285 offences (ie. over two-thirds of the ‘absolute’ rise in recorded
offences); and that the ‘Met’ total is so high that it can only be approximated as ‘over 1 million’.
By suppressing all quantifiers of decreasing crime levels across different force areas (as well as offence
categories), the rhetorical effect is to exaggerate the rise in crime and lay the primary responsibility for
it onto two specific force areas.
3. Quantitative Rhetoric:
The final example I will discuss is taken from Potter,J., Weatherell, M. & Chitty, A. (1991) ‘Quantification
rhetoric - cancer on television’, Discourse and Society, 2, 3: 333-365.
[OHP10 - PWC questions]
In setting up their study, they note that in the past, they have found it useful to think about how discursive
claims are formulated in terms of two distinct questions:
1.
2.
How is discourse organized to appear factual? – that is, how is it made to seem that what is being
claimed is nothing to do with personal opinion, but is solely a matter of “letting the facts sapeak for
themselves,” a matter of simply depicting what is “in fact out there” already.
How is factual discourse used is the accomplishment of specific activities? – that is, how is talk about
facts used to win an argument.
It is this last question that PWC want to discuss in their article. (I will discuss the first question in my last
lecture – to do with what is involved in writing science.) As they put it:
“Instead of thinking of quantification accounts as more or less accurate renditions of some putative reality, we
should view them as designed for their robustness in an argumentative arena” (p.337).
When studying the construction of quantification accounts, they suggest, it is useful to make a further distinction
between two sorts of constructive processes – hence, two questions:
(1) what should be, or is being, counted? [e.g. for this case: cancers; types of cancer; types of curable cancer;
cures];
(2) how should it be, or is it being, counted? Or, to put it another way, how should some realm of objects or
concepts be constituted by linking them to a set of numbers? – note the “quantitative way of seeing” discussed
above!
PW&C study a TV programme critical of the work of cancer charities – the Imperial Cancer Research Fund and
7
Cancer Research Campaign.
The programme makers utilised a series of figures designed to suggest that the work of these charity-supported
research programmes had been rather unsuccessful.
One of the ways in which they did this was to construct a doubly-quantified contrast between those cancers that
were ‘effectively curable’ and those that were not.
[OHP11 - Overall Extract 1]
Let us just look at the first bit of commentary, and partition it up into three segments:
Commentary: “The message from these scientists is clear — exactly like the public — they hope their
basic research will lead to cures in the future — although at the moment they can't say how this will
happen. In the meantime their aim is to increase scientific knowledge on a broad front and they're
certainly achieving this.
But do their results justify them getting so much of the money that has been given to help fight cancer?
When faced with this challenge the first thing the charities point to are the small number of cancers
which are now effectively curable.”
Scientists are good guys. But... The challenge is mounted. The charities try to rebut it by saying that some (a
“small number,” says the commentary) are now curable. This commentary embodies a “preformulation” 2.
The first strand of this contrast is the suggestion that the number of types of cancer that count as ‘curable’ is
small.
For now, I just want to point to a few features of how these forms of quantification are used in the context of the
programme-makers’ argument about the unsuccess of cancer research.
In this extract, a spokesperson for the CRC is shown and heard — though the surrounding commentary
successfully undermines what he has to say.
[1st Kemp passage: read]: Kemp: The outlook for individual suffering from a number of types of
cancer has been totally revolutionized. I mean for example – children suffering from acute leukaemia –
in old days if they lived six months they were lucky – now more than half the children with leukaemia
are cured. And the same applies to a number of other cancers – Hodgkin's disease in young people,
testicular tumours in young men, and we all know about Bob Champion's success.
Note the use of ‘a number of’ and ‘for example’ here. These formulations are designed to give the impression
that the particular cases mentioned are members of some larger set.
But in the ensuing commentary, they are treated as the complete total, and a small one at that – only “three.”
(Shortly before this point in the film, we have been given the figure of “around 200" as the total number of
different types of cancer, hence “three” would be 1½% of the total!)
Commentary: But those three curable types are amongst the rarest cancers – they represent around l
percent of a quarter of a million cases of cancers diagnosed each year. Most deaths are caused by a
small number of very common cancers.
The second commentary entails a claim that these few – i.e., three – curable kinds happen to be “amongst the
rarest;” that is, relatively few cancer sufferers suffer from the ‘curable’ kinds as opposed to those cancers which
are both more common and more intractable.
The commentary then proceeds to the second strand of constructed smallness: that of the rarity of these types.
[2nd commentary passage: read] Note the careful choice of quantifiers here: “around 1 percent of a quarter of a
million cases.”
Clearly, this quantity could be expressed in any number of ways; as “2,500 out of a total of 250,000,” for
example. Rhetorically, the phrase that was used, again works to build up the case for smallness, through
maximising the contrast between the definitively tiny “1 %” and the largeness of “million;” even if only a
quarter of this famously big quantity.
At the start of this section of commentary, a scrolling table headed: ‘Annual incidence of cancer’ is shown in
8
which the contrast is made yet again.
[OHP12 – table of cancer incidence]
Here, the three curable cancers are shown in yellow while all the others (implicitly non-curable) are in white.
Thus, both their forms of relative smallness - in terms of numbers of cancer-types and of numbers of cancersufferers - are displayed.
The first kind of smallness is displayed by the relative infrequency of yellow bands; while the second (the
claimed `rarity' of these cancers) is displayed by the disappearance of yellow altogether as the list, ordered in
terms of increasing commonness, reaches its climax.
Before we leave this piece of analysis, here's an alternative account of the cancer charities' success given by the
same Dr Nigel Kemp, who we have just seen treated so badly, perhaps, by the nasty programme makers
(admittedly, this section of Kemp's interview was not transmitted):
[OHP13 - alternative account of numbers]
An Alternative Account of the Success of Cancer Research: “... each year in the United Kingdom two, roughly
two hundred and sixty thousand people get cancer. Each year er, roughly a hundred and sixty thousand people
die from cancer, so there's a difference of eighty thousand, and eighty thousand is one third of two hundred and
forty thousand ... so one could say that one's sort of a third of the way there... So there’s been some progress...”
(p.349).
[OHP14 - more recent table of survival rates]
Alternative (more recent) table:
Estimates of relative survival rates, by cancer site*
% survival rates (and their standard errors)
5 year
10 year
15 year
20 year
Ranked from best to worst:
Prostate
Thyroid
Testis
Melanomas
Breast
Hodgkin's disease
Corpus uteri, uterus
Urinary, bladder
Cervix, uteri
Larynx
Rectum
Kidney, renal pelvis
Colon
Non-Hodgkin's
Oral cavity, pharynx
Ovary
Leukemia
Brain, nervous system
Multiple myeloma
Stomach
Lung and bronchus
Esophagus
Liver, bile duct
Pancreas
98.8 0.4
96.0 0.8
94.7 1.1
89.0 0.8
86.4 0.4
85.1 1.7
84.3 1.0
82.1 1.0
70.5 1.6
68.8 2.1
62.6 1.2
61.8 1.3
61.7 0.8
57.8 1.0
56.7 1.3
55.0 1.3
42.5 1.2
32.0 1.4
29.5 1.6
23.8 1.3
15.0 0.4
14.2 1.4
7.5 1.1
4.0 0.5
95.2 0.9 87.1 1.7
95.8 1.2
94.0 1.3 91.1 1.8
86.7 1.1 83.5 1.5
78.3 0.6 71.3 0.7
79.8 2.0 73.8 2.4
83.2 1.3 80.8 1.7
76.2 1.4 70.3 1.9
64.1 1.8 62.8 2.1
56.7 2.5 45.8 2.8
55.2 1.4 51.8 1.8
54.4 1.6 49.8 2.0
55.4 I.0 53.9 1.2
46.3 1.2 38.3 1.4
44.2 1.4 37.5 1.6
49.3 1.6 49.9 1.9
32.4 1.3 29.7 1.5
29.2 1.5 27.6 1.6
12.7 1.5 7.0 1.3
19.4 1.4 19.0 1.7
10.6 0.4 8.1 0.4
7.9 1.3
5.8 1.2
3.0 1.5
81.1 3.0
94.0 1.6 95.4 2.1
88.2 2.3
82.8 1.9
65.0 1.0
67.1 2.8
79.2 2.0
67.9 2.4
60.0 2.4
37.8 3.1
49.2 2.3
47.3 2.6
52.3 1.6
34.3 1.7
33.0 1.8
49.6 2.4
26.2 1.7
26.1 1.9
4.8 1.5
14.9 1.9
6.5 0.4
7.7 1.6
5.4 2.0
6.3 1.5
7.6 2.0
2.7 0.6
2.7 0.8
* Redesigned table based on Hermann Brenner, "Long-term survival rates of cancer patients achieved by the
end of the 20th century: a period analysis," The Lancet, 360 (October 12, 2002), pp.1131-1135. Brenner
9
recalculates survival rates from data collected by the U.S. National Cancer Institute, 1973-1998, from the
Surveillance, Epidemiology, and End Results Program.
Those who do the tutorial on this paper will find that this TV account did not go unchallenged!!!
Conclusions:
What I hope we can see from all theses examples, is that the language of quantification, not solely the
processes and practices of weighing, measuring, and counting (Plato), provides an important resource for
constructing a specific argumentative point of view. In other words, the language of quantification –
conventionally viewed as ‘neutral’, objective’ and ‘hygienic’ – is a rhetorical medium through which social
statistics are made meaningful, and different political standpoints are expressed. What I also hope, is that we
have made some beginnings at outlining some methods – a vocabulary of useful terms – for conducting a
rhetorical analysis aimed at bringing to light the often “seen but unnoticed” background of expectations against
which we formulate of claims to truth.
References:
Billig, M. (1987) Arguing and Thinking: a Rhetorical Approach to Social Psychology. Cambridge: Cambridge
University Press.
Billig, M. (1991) Thinking as arguing (an inaugural lecture). In Ideology and Opinions. London: Sage
Publications.
Billig, M. (1991) Ideology, Rhetoric and Opinions. London: Sage.
Davis, P.J. and Hersh, R. (1983) The Mathematical Experience. Harmondsworth: Penguin Books.
Davis, P.J. and Hersh, R. (1986) Descartes' Dream: the according to Mathematics. Sussex: Harvester Press.
Davis, P.J. and Hersh, R. (1987) Rhetoric and mathematics. In Nelson, J.S, Megill, A., and McCloskey, D.N.
(Eds.) The Rhetoric of the Human Sciences. Madison: University of Wisconsin Press, pp.53-68.
Descartes, R. (1968) Discourse on Method and Other Writings. Trans. with introduction by F.E. Sutcliffe.
Harmondsworth: Penguin Books.
Freud, S. (1964) Studies in Hysteria, Standard Edition, vol.2. London: Hogarth Press.
Garfinkel, H. (1967) Studies in Ethnomethodology. Englewood Cliffs: Prentice-Hall.
Kuhn, T.S. (1962) The Structure of Scientific Revolutions. Chicago: University of Chicago Press.
Lave, J. (1988) Cognition in Practice: mind, mathematics and culture in everyday life. Cambridge: CUP.
Plato (1974) The Republic, trans. with an introduction by Desmond Lee (second edition, revised).
Harmondsworth: Penguin Books.
Plato (1974) The Republic, trans. with an introduction by Desmond Lee (second edition, revised).
Harmondsworth: Penguin Books.
Potter,J., Weatherell, M. & Chitty, A. (1991) ‘Quantification rhetoric - cancer on television’, Discourse and
Society, 2, 3: 333-365.
Watson, H. (1990) Investigating the social foundations of mathematics: natural number in culturally diverse
forms of life. Social Studies of Science 20: 283-312.
Whorf, B.L. (1956) The relation of habitual modes of thought and behavior to language. In Language, Thought
and Reality: Selected Writings of Benjamin Lee Whorf. Ed. J.B. Carroll. Cambridge, Mass: M.I.T.
Press, pp.134-159.
Supplementary reading:
Smith, D. (1974) Theorizing as ideology. In Ethnomethodology, edited by Roy Turner. Harmondsworth:
Penguin, pp.41-44.
Notes:
1
Error! Main Document Only.Today Program, 8.34 am, Radio 4, Weds 14th Feb, 2005
Caroline Quinn interviewing Douglas Bachelor, head of the league Against cruel Sports
Int:
Good morning... What do you make of the recent Mori Survey done for the BBC Country File which
suggests that support for a hunting ban here in England and Wales has fallen from 2/3 to below 1/2?
10
DB:
Well, it didn’t actually say that, what it said was that the number of ‘don’t knows’ had increased
substantially, that the proportion of of people who were for and against was roughly unchanged, and
they weren’t asking quite the same question and they asked last time,... [so the result...
Int:
Well,[... I think, are we talking semantics here. Last time it was about a speculative ban, this time its
about a real ban...
DB:
Well, what you had was 2 to 1 against hunting, and 2 to 1 in favor of a ban. All that’s happened in the
meantime is that the number of ‘don’t knows’ has increased. The number of people in support of
hunting had increased by 2%, so you could hardly say that there was a big move towards hunting and
against the ban.
Int:
Well I don’t want to bandy statistics with you. Lets look at what you’re doing these current days...
2.A “pre-formulation:”
In the formulation at the start of the passage the scientists are glossed as increasing knowledge but being rather
uncertain about how this will lead to cancer cures. This provides an opportunity to pose one of the programme’s
central questions: ‘Do their results justify them getting so much of the money?’
PW&C’s discussion works on the assumption that within the narrative logic of the programme, it is
necessary to show at least a case for giving a negative answer to this question. For them the interest is in the
way quantification is deployed to accomplish this rhetorical goal.
They start with the first gloss on the limited success in cancer cures: ‘When faced with this challenge
the first thing the charities point to are the small number of cancers which are now effectively curable.’
This gloss embodies what in rhetorical terms can be called “a preformulation.” That is, in the course of
formulating an argument at the same time it formulates an expected counter-argument (cf. McHoul, 1987;
Mulkay, 1985; Potter, 1984).
Here the argument is that cancer-funding has provided few results and the as yet to be delivered
counter is that there are cancers that cancer-funding has helped cure.
A preformulation can achieve two rhetorical goals:
$
$
1) First, it can make the subsequent response seem predictable or hackneyed.
2) Second, and most importantly, it can construct the counter-argument in a weak manner or a manner
that highlights difficulties with it. As such it acts as a frame for reading the counterclaim (cf. Smith,
1978).
In effect, the gloss provides instructions as to how to read what comes after it in such a way that it falls into line
with the argument of the film rather than the subsequent speaker. In this case, the content of the gloss is a nonnumerically quantified version of success in cancer cure: it is effective with a ‘small number’. How small is not
elaborated at this point; yet it important not to see ‘small’ here as a vague or imprecise term. Although ‘small’
does not operate as an absolute number outside the context, wit] context it indicates an evaluative and
quantitative contrast. That is, provides more information than a specific abstract number would have.
Following this preformulated version, the actual claim, made by Nigel Kemp, is inserted. This starts by
talking of a number of cancers however, here ‘effectively curable’ is replaced with the stronger ‘totally
revolutionized’ and the ‘small’ is missing from ‘small number’. It could argued that ‘number’ on its own is
relatively neutral with respect to implied quantity. However, while ‘number’ can be more than ‘small’ it is
genera modified in contexts where a substantial proportion is implied: e.g. a large number, a substantial number
(cf. Levinson, 1987). Thus ‘number’ on own, in a rhetorical context such as this, is probably heard contrastively
as not large or substantial, although perhaps not as small as ‘small’. Follow this preliminary gloss specific
instances are given. Here stronger quantitative claims are made: ‘more than half’ childhood leukaemia victims
cured; ‘the same applies’ to Hodgkin’s disease and testicular tumours. can note here that one of the interesting
features of the counting ti appears in this listing in that having narrowed the field from a large number of
cancers to a small number of selected ones, Kemp can provide much larger numerical formulations of
effectiveness.
11