1This paper focuses on the relationship between quantifiers and worlds of reference (world of fact vs world of hypothesis) in economics discourse. The corpus examined includes samples of different genres in the area and has been collected to study language variation across genres. The analysis is meant to explore whether quantifiers play a different role in these two worlds of reference, whether these co-occur differently in the various genres of economics discourse and whether they tend to occur in any specific moves or acts that characterise the structure of textbooks as against other genres.
- 1 Textbooks and their role within scientific discourse have received greater attention since Kuhn’s c (...)
- 2 Various features have been studied: the use of metaphors (Henderson 1982, McCloskey 1985, Klamer 19 (...)
2Economics textbooks have recently received particular attention from a variety of perspectives interested in economic discourse.1 The issue has been tackled by economists interested in the rhetoric of enquiry like McCloskey (1985, 1994) or Klamer (1987, 1990), by economists interested in problems of teaching economics like Henderson (1987) or Brown (1993) and by applied linguists like Dudley-Evans (1990, 1993), Tadros (1985), Hewings (1987, 1990), Meriel and Thomas Bloor (1993) and Swales (1993), most of them involved in making economic texts accessible to students who are not native speakers of English.2
3The notion of world of reference plays an important role in the epistemology of economics. Economic reasoning is often presented in terms of possible worlds: discourse follows a logic of ramification determining the range of possibilities that emerge from a state of affairs. Economics as a science proceeds not only by representing what happens in the actual world, but primarily by exploring what could have or could not have occurred in actuality. The frequent recourse to references to hypothetical (or fictional) worlds in economics discourse has deserved attention from a variety of points of view, including methodologists of economics, philosophers, epistemologists, rhetoricians, sociologists or historians of economic thought. These have variously articulated the distinction (or the interplay) between theoretical reasoning, speculation, mathematical abstraction, possible worlds, metaphors on the one hand and empirical techniques, data, facts, history (and stories) on the other.
4The issue has an obvious interest for the study of economics discourse and its genres because of its connection with a highly interesting feature of language: factivity. Language can project its ideational meaning on to different plans, as belonging to different worlds: the world of fact and the world of hypothesis. Many linguists concerned with economics textbooks — such as Tadros (1985), Henderson and Hewings (1987, 1990), Hewings (1990) — have accordingly drawn attention to how often economics reasoning is not based on what is presented as fact, but on hypothetical, speculative examples.
- 3 Myers has variously dealt with the problem in a series of studies devoted to the rhetorical strateg (...)
- 4 The issue is central both to Klamer’s analysis of the first 12 editions of Samuelson’s Economics (K (...)
5The issue of factivity plays a particularly important role in a genre like the textbook, because of its didactic, educational aims. Myers (1992) argues that while we might be led to believe that a particular statement finds its way into a textbook because it is a fact, it is the reverse which actually occurs: textbooks typically add ‘factive’ certitude to the phenomena being described, by avoiding hedging, by lack of references to the primary literature, by a wide use of simple present and a massive use of cross-references.3 What textbooks seem to hide is the dialogic nature of economic science, the widely recognised argumentative nature of economics, its discursive structure — what McCloskey calls economics as conversation.4 Myers draws attention to an interesting paradox of textbooks: the very same features that make them easier for students to read
may make it harder for them to deal with other text types they encounter later in a scientific career [...] because they get no sense of how facts are established. (1992: 13)
6My paper is meant to explore whether any similar remarks could be made about the use of quantifiers in economics textbooks, especially if considered in relation to their world of reference. Exact quantification can be regarded as part of the ethos of the academic community of economists, but the complexity of empirical data often leads textbook writers to offer “simplified” versions of reality, either by making highly inexact (but effective) generalisations about the real world or by presenting hypothetical model-worlds with their ideal numerical data.
7It is my belief that the expression of quantity could be regarded as a highly relevant category in the description of economic discourse but it does not seem to have received adequate attention from the point of view of applied linguistics, apart from Channell’s studies on approximation (Channell 1990, 1994). Economists have indeed discussed the varying role of mathematical and statistical proof in economic argument from the point of view of the rhetoric of science. McCloskey (1985), for example, devotes the whole of Chapter 8 to “the unexamined rhetoric of economic quantification” (138), criticising the widely held belief that numbers are objective and conclusive and insisting on the fact that they can only be interpreted in relation to some socially agreed standard, accepted by the speech community (141). He does not, however, pay any specific attention to the verbal representation of quantity or to the relative role of quantitative argument as against other types of argument.
8The present paper focuses on the roles played by quantifiers in a few genres of economic discourse, and studies the relationship between their definite/indefinite nature and the factual/non-factual nature of the world of reference of the moves or acts in which they tend to occur.
9The reflections presented in this paper are based on two kinds of corpora: a corpus of selected chapters from economics textbooks and a comparative corpus of works written by Paul Samuelson.
10The textbook corpus — which I have designed in order to analyse a wider variety of features — collects selected chapters of 10 standard introductory textbooks: the introductory chapter, a chapter on micro- and a chapter on macro-economics.
- 5 See the list of the textbooks in Appendix.
11The texts were chosen on the basis of a variety of criteria. They were all major works whose authority is established by their longevity (they have all undergone various editions and regular revisions) and by their being included as set reading texts or reference texts in reading lists for University students (and A-Level students).5 The authors of these texts often announce that their books have been written as basic introductions to economics; the readers are therefore assumed to be new to the field and both readers and writers are certainly aware of the conceptual distance between them.
12The comparative corpus consists of a small number of works by the same author, namely Paul Samuelson. The main focus of the analysis is on the two major genres of the textbook and the research article. Extracts from Samuelson’s well-known Economics are compared with a selection of research articles published by Samuelson in professional journals or books; the analysis also includes a small number of articles written for non-professional magazines and newspapers.6
- 7 The comments written for newspapers and magazines, of course, are not taken as representative of “e (...)
13A comparison of works by the same author seemed to offer the best perspective for a study of language variation across genres. A totally different “tenor” of the interaction between writer and reader will usually require different language options to be taken and the same author will usually realise a different “implied author” when writing different genres.7
14The choice of the specific author is basically determined by the paper’s focus on textbooks and by the unquestionable influence exerted by Samuelson’s Economics in setting “the standard for post World War II textbooks” (Klamer 1990: 130) with its now fourteen editions. The restriction to a single author, however, and to Paul Samuelson in particular, necessarily has a number of disadvantages of which I am well aware. One may object, for example, that authoritative — “paradigm setting”— figures like Samuelson may in fact be very self-confident in their assertions and therefore be lacking in the traditional self-effacing strategies of most scientific writers. This is certainly true of Samuelson, but it does not seem to have implications in the area of quantifiers. The variation we may notice across genres, moreover, might just be Samuelson’s own view of the difference between them, and this — authoritative as Samuelson’s may be — certainly cannot make any claim to general validity. Samuelson does not represent the whole field of economics, but he may well be taken as representative and highly influential in the area of American neo-classicism, with its emphasis on the exploration of possible models, rather than on empirical work. I do not therefore make any claim to general validity. My attempt is rather that of presenting a case study and reading it in the light of the observations previously made on a corpus of textbooks.
- 8 The distinction most commonly adopted in semantics is along the three lines, a) factuality, involvi (...)
15The distinction I take as a starting point is that between what is presented as the world of fact and what is presented as non-fact or counter-fact, both included under the cover-term of “hypothesis”.8 My distinction between world of fact and world of hypothesis follows very much Sinclair’s distinction between fact and fiction. On the one hand we have utterances where speaker and hearer believe that “what is averred corresponds to a state of affairs” in the world of fact (Sinclair 86: 44). On the other hand we have utterances where this correspondence is irrelevant, such as the one presented in example (1), where a shift to the world of hypothesis is clearly signalled by the initial imperative of the second sentence (my italics):
(1) A production possibility frontier joins together the different combinations of goods and services which a country can produce using all available resources and the most efficient techniques of production. Assume for simplicity that a country produces only two goods, food and cloth. (Hardwick, Ch. 1)
- 9 For a discussion of these and other issues with reference to the distinction between world of fact (...)
16The distinction between fact and hypothesis is not always so easily clear-cut. Sinclair (1986) argues that utterances that are simultaneously fictional and factual — cases of verisimilitude — are cases where we do not know the stance of the writer with reference to actuality and that in these fictional status takes preference over factual. Predictions and quotations would be obvious examples of speech acts where these problems might arise.9 I have normally considered these as “world of hypothesis” whenever there was some explicit element of authorial “detachment” from the projected text, as can be seen very clearly in example (2).
(2) A common mistake in studies of cause-and-effect relationships is the post hoc fallacy. A classic example of the post hoc fallacy is the belief held by the medicine man in a primitive society that both witchcraft and a little arsenic were necessary to kill his enemy. (Samuelson, Ch. 1)
17The most prominent function of hypothetical moves consists in providing examples or illustrations for the generalisations put forward by the author. Hypotheticality signals like assume for simplicity signal to the reader that any questions about actuality are unnecessary and irrelevant and that the information is merely exemplificatory. Hypotheticality is thus a discourse device used by the writer
to narrow down the gap between his conceptual world and that of the reader, so that the reader will be able to understand the generalisation that emerges from the hypothetical statements. (Tadros 1985: 48)
- 10 The question becomes particularly relevant if the overall status of the text is allowed to obscure (...)
18The shifts between the ideal world and reality, between fact and hypothesis, however, may well be a source of reading problems for students if they are unaware of the shifts and how they should be interpreted.10 These are therefore marked by various signals. The most obvious will be explicit signals of hypotheticality, but it will also be important, of course, to learn to recognise signals of shifting back to the world of fact.
- 11 Tadros (1985: 43) lists two structures: if + NP + VP (past verb), +NP + VP (past modal) and if + NP (...)
19Many signals of hypotheticality are discussed by Tadros (1985) in her study of “prediction”, i.e., of the signals that involve a commitment to (“predict”) the occurrence of particular linguistic events. She lists verbs like assume, suppose, consider; if-sentences,11 expressions like let NG be NG, use of fictitious characters or places. When trying to consider hypotheticality at large, in its widest spectrum of situations and functions, the variety of signals increases, to include for example both a verb like take and a modal adverb like hypothetically. Other examples from my corpus are: say/let us say, imagine, consider, use of modals like may or will, often combined with references to the writer’s or the reader’s cognitive or expository procedures: let us illustrate this by considering, we can see this in a simple numerical example, a simple example will illustrate this, to show this, we can now understand...
20Co-textual features become particularly relevant when the hypothetical moves extend over longer sections of text often including a number of shifts from one world to the other: a hypothetical example might be established in a table, so that any backward reference to that table might imply a shift to the hypothetical mode which was only signalled at the beginning. In Samuelson’s chapter on cost analysis, for example, most data are basically related to three hypothetical situations: an anonymous firm described in the first sections of the chapter and two further examples representative of different sectors of the economy (Farmer Gomez and Hot Dog Ventures, Inc).
- 12 Henderson and Hewings (1987: 54) notice that Samuelson and Nordhaus make constant use of all other (...)
21Most explicit signals, moreover, will only be interpretable as such within general or specific conventions of economics discourse, i.e. with reference to the whole discourse community or to a specific approach within the discourse community. Expressions such as everything else constant or all other things being equal - usually presented and discussed explicitly in introductory chapters - conventionally allow economists to work under hypothetical experimental conditions.12 Other metadiscursive expressions such as for simplicity or a numerical example, a simple example are normally used to introduce a simplified version of reality, reducing the number of factors to be considered or their numerical attributes. A similar function might be played by in a closed economy or even by under perfect competition, when the reader believes that perfect competition is an ideal abstraction.
22The issue of quantity and its expression seems to play an important role in this shift from one world to the other: indeed it is often the determining factor, as the analysis has shown.
23Quantification as a semantic phenomenon can be seen to involve various categories, often including all sorts of scalar sets, from modals to adverbs of frequency and duration. Though recognising the presence of quantitative meaning in these expressions, I have deliberately decided to restrict my analysis to expressions of quantity within the noun group. These still involve a much wider class of elements than would normally be referred to as “quantifiers” in logic, in formal semantics or even in most grammars.
24Quantifiers can be preliminarily defined — in a stricter sense — as determiners whose meaning expresses some notion of quantity - adjectives or pronouns used to say how much of something there is. In Lyons’ words, “a determiner tells us which member or which subset of a set of entities is being referred to; a quantifier tells us how many entities or how much substance is being referred to” (1977: 455).
- 13 The notion of “extracting” an item from a set dates back to Culioli’s studies (1970, 1975), where a (...)
- 14 Though well aware of the status of the indefinite article in terms of a theoretical description of (...)
25Irrespective of the formal means by which they are expressed, we are dealing here with the expression of two different notions: the notion of identity (within the process of identification of referents) and the notion of quantity (within a process of “quantification” of referents). In actual forms the two notions are at times inextricable, although we might at least try to specify which of the potential meanings of an expression are actualised and which receive major emphasis. The indefinite article, for example, undeniably carries an element of quantification (of singular quantity) together with the meaning of “indefinite identity”. It “extracts” one item from a set of discrete items (such as the one normally associated to a countable noun).13 Its complex meaning potential, however, is not always fully activated; though carrying a meaning of “singular quantity”, a/an is normally primarily a marker of indefinite identity. We may regard one meaning as normally foregrounded against the other, though recognising that some contextual features may indeed contribute to activating the “singular” meaning, e.g. in “the real wages of a person move only a percent or less from month to month” (Samuelson, Ch. 32).14
26The question at issue here is not which definition best suits grammatical or semantic theory. It is rather which definition best helps determine how economists quantify the “Things” they refer to in their textbooks. I have therefore adopted a notional approach to the problem, whereby all lexical variants of the standard closed class quantifiers are considered. This means considering the ideational rather than the logical structure of the noun group, in Hallidayan terms, or recognising — as most notional grammars do — that, although the quantity nouns might look like the head of a noun group, they function semantically like the closed-class quantifiers.
27I will therefore use Quantifiers —in a wider sense— to include all the elements in the noun group that refer to quantities and amounts of things, irrespective of their syntactic class or function:
28• general determiners (the so called “closed-class quantifiers”) like some, enough, few, many, more, all.... in all their constructions;
29• “open-class quantifiers”, including adjectives like certain, numerous, various and a large class of phrasal quantifiers consisting of a noun of quantity followed by of, like lots of, plenty of, a great deal of...;
30• numbers and fractions.
- 15 From the point of view of the experiential structure of the noun group (Halliday 1985), Quantifiers (...)
- 16 From the point of view of the texture of texts, we can follow Martin’s description of the identific (...)
31This variety of elements can play a number of different roles within the structure of the noun group15 and within the texture of texts.16 Various mechanisms can be seen in example (3) below, where one is used as Deictic to present a first reference (R1), whereas second (R2) and third (R3) are used as Numeratives and combine with other determiners to create an element of relevance phoricity by presuming a superset of sources (R1, R2, R3) and the first two identifies a further set (R1, R2) by virtue of both quantity strictu sensu and order.
(3) Why the difference? One source of the discrepancy was a more optimistic administration forecast for economic growth. [...] A second source of the difference concerned interest rates. [...] A third adjustment partially offset the first two. (Dolan, Ch. 11)
32The distinction commonly hypothesised between definite and indefinite also needs clarification. Definite and Indefinite have been applied both to the notion of identity and to the notion of quantity and the two notions are not always clearly distinguished: what we are interested in here is not the fact that many is used to signal indefinite identity, but rather the fact that it refers to an indefinite (or inexact) quantity.
33The distinction between definite and indefinite or exact and inexact, however, gets blurred if we consider quantifying as a discourse process, rather than some sort of extra discoursal, abstract entity. As already noticed by Halliday (1985: 163), in moving from system to text, an exact numerative expression may be made inexact by submodification or by the use of approximators and inexact numerative expressions may be exact in the context.
34The contextual definition of an inexact numerative expression is a complex issue which cannot be tackled here. Examples (4) and (5) show different ways in which quantification may be “implicit”: the notion of quantity may be an implicature of another textual element or may be carried over“ in an anaphoric chain.
(4) To illustrate technical efficiency, let us consider two bicycle manufacturers. One uses a large number of workers and many machines to produce 1,000 bicycles. The other uses fewer workers and fewer machines to produce the same number of bicycles. (Wonnacot, Ch. 1)
(5) Where (∆)goods are complementary a change in the price of one of them will cause a change in the demand for the other. (Stanlake, Ch. 14)
35The problem of approximate quantities, on the other hand, cannot be ignored. Approximating constructions such as those in examples (6) and (7) are very common.
(6) [...] between 1950 and 1969, a “rising tide was lifting all boats.” Average family income was rising by about 40 percent (even after adjusting for inflation). (Samuleson, Ch. 1)
(7) If all the British people were content to live at the level of an Indian peasant, all our wants could be easily satisfied with one or two hour’s labour each day; we would not experience scarcity. (Stanlake, Ch. 1)
36The notion of approximate quantities and of vague language (Channell 1994) presents an only apparent clash with common expectations about economics. Economists —as also shown by Channel (1990)— make extensive and careful use of approximations in academic writing, though also providing many examples of precise numbers and dates. Economists often designate intervals of numbers rather than precise numbers or quantities, by using approximators like about, around, nearly, almost, or by specifying upper or lower limits of quantities with expressions like at least, at most, etc. Expressions such as millions of or dozens of can also be considered approximations, where at least some numerical order is suggested. Approximating quantities with round numbers is another strategy. In economics there are certain established conventional approximations which function as the “unmarked form”: British GNPs, for example, are usually counted in millions of pounds, not in pounds and pennies, as can be seen in example (8). There are fields of economics, therefore, where approximation is the standard official measure.
(8) In 1987 its(GNP)value was £ 354 378 m. (Stanlake, Ch. 17)
37On the other hand there may be —though not very common, especially in economic analysis— exact numbers that turn out to be an approximate representation of a very wide range of values, as in example (9), where hyperbole is at play.
(9) [...] economics tries to figure out the 1001 puzzles of everyday life. (Samuelson, Ch. 1)
38But —and this is I think one of the most distinctive features of economics textbooks and argument— there are often round numbers that would be interpreted as approximations in the world of fact, but they are intended to count as exact values. The thousand bicycles in (4), for example, can only be interpreted as a definite, exact value, because the world of reference is not that of fact, but that of hypothesis.
39Both approximate and indefinite quantities draw attention to the pragmatic dimension of discourse, to the role of context in utterance interpretation and in particular to the role played in interpretation by the set of assumptions in the hearer’s / reader’s mind - assumptions deriving from a wide variety of kinds of background knowledge: encyclopaedic information, cultural knowledge and assumptions derived from his / her processing of the environment and of earlier parts of discourse. The reader of an academic textbook - however “introductory” that is - has to supply several cultural assumptions in order to identify the intended meaning. And Quantifiers play an important role in this, both at micro-level (where the intrinsic content of all semantically vague terms used in the utterance has to be enriched) and at macro-level, where they are part of a constituted set of methodological assumptions, of an agreement as to what empirical evidence is relevant to a claim, how evidence is to be produced, represented and applied in the situation.
40We can thus identify three basic ways of referring to quantities in economic discourse:
41• “exact” quantities will be those that find a numerically exact definition (or follow conventional approximations that are not perceived as such in the context: they may be regarded as “approximations we live by”);
42• “approximate” quantities will be those where intervals are referred to with reference to some numerical value(s), which works either as a limit of the interval or as a reference point;
43• “indefinite” quantities will be those where no reference to numerical values can be established.
44The analysis of the textbook corpus has focused on the running text. Though well aware that most quantitative data are actually provided in tables, charts and graphs, I meant to explore whether Quantifiers tend to occur in any specific moves or acts that characterise the structure of economic genres.
45Economics textbooks make extensive use of general-specific patterns where general statements about economic reality and its processes are usually either preceded or followed (or both preceded and followed) by supporting examples or illustrations, in a pattern that might be represented like this:
- 17 For further information on the study see Bondi (1996).
46Examples and illustrations can be classified according to whether they are presented as belonging to the world of fact or to the world of hypothesis. The relationship between the two may vary, but most textbooks tend to provide a striking majority of hypothetical examples.17
47Considering the possible combinations of Quantifiers and worlds of reference, the analysis has drawn attention to two basic situations:
48a) the use of indefinite (and approximate) Quantifiers in generalisations about the real world, as exemplified in (10)”
49b) reference to definite quantity in speculative reasoning about possible worlds, as exemplified in (11).
(10) During any period in which the nation’ s per capita income increases, most Americans benefit, but a few are hurt. (Wonnacot, Ch. 23)
(11) Say a firm is producing 1000 hard disks for a total cost of $10,000. If the total cost of producing 1001 disks is $10,015, then the marginal cost of production is $15 for the 1001st disk. (Samuelson, Ch. 8)
Attention can also be drawn to:
50c) the metadiscursive (text-structuring) use of references to definite quantities for expository purposes.
- 18 Tadros (1985: 14), adapting Winter, identifies these as “enumerables” in her discussion of enumerat (...)
51Exact numerals are often used to pre-modify nouns with a metadiscursive, text-structuring function. These can be either discourse self-reference nouns like example, definition, chart, table, chapter, paragraph etc. or “metacognitive nouns”, i.e. nouns referring to the cognitive tools of exposition or argument, like advantages, aspects, elements, principles, techniques, roles, reasons etc. The two categories of nouns18 —when considered from the point of view of the language system— refer to procedures of language and reasoning and they can both be used in discourse to refer to sections of the text itself, as shown in examples (12) and (13).
(12) The first part of this chapter concentrated on the major concepts for measuring costs. But how do business firms actually measure costs? And what kinds of costs do economists include in their calculations? This section explores these two questions. (Samuelson, Ch. 8)
(13) Two elements of a balance sheet require mention: inventories and fixed assets. In both cases the difficulties arise because these assets are used up or consumed over time. (Samuelson, Ch. 8)
52These examples of references to the structure of discourse often account for a large proportion of references to the world of fact, thus leaving an interestingly low number of exact quantifiers referring to the world of economic reality. The tendency, once again, should obviously not be regarded as typical of economics at large, but may be considered characteristic of economics textbooks and of mainstream economics textbooks in particular.
53The three configurations above can be variously related to the different discourses that constitute a textbook: the discourse of the discipline and the discourse of teaching.
54The frequent use of metadiscursive Quantifiers gives great prominence to the interaction between writer and reader, and particularly to the way the writer as teacher guides the reader as student by providing a map of the text and of the discipline.
55The choice of Quantifiers with reference to the world of fact contributes to building up the view of reality that is mediated by the text. The use of indefinite and (fewer) approximate estimates —though not necessarily representative of the whole of academic writing— suits the argumentative purpose of the writer, who presumably wants the reader to focus on general trends, on relationships between forces and factors, rather than on their specific features.
56The use of exact Quantifiers in hypothetical moves most clearly contributes to this process of abstraction from the complexity of reality. The most prominent function of hypothetical moves consists in providing examples or illustrations for the generalisations put forward by the writer: a simplified model of reality allows the reader to concentrate on rules and general laws, rather than on the complexity of empirical data.
57The use of quantitative expressions in textbooks seems to me strictly linked to the wider rhetorical structures of textbooks, which are quite heavily based on general-specific patterns and on argumentative-expository procedures based on particular cases: examples, illustrations and analogies. A wider range of argumentative and expository procedures in other genres would therefore imply that a different pattern of combinations should be expected.
58The comparative analysis involved a small corpus of materials from a variety of works by Paul Samuelson. It was meant to explore whether the different situations outlined above play a different role in the various structures of the genres considered, depending on the role relationships in which writer and reader are involved. The starting point was the claim —supported by the analysis of the wider textbooks corpus— that the issue of quantification plays a major role in the choice of either factual or hypothetical references.
59Intuitively, however, the choice between the two worlds of reference could also be influenced by another major factor: the theoretical or applied nature of the matter at issue. We would expect economic theory to make more frequent recourse to hypothetical speculation than economic analysis of current issues.
60The distinction plays different roles in the different genres. Samuelson’s Economics is basically an introduction to theory, with only a few chapters on current problems. His research articles are mostly theoretical in nature, although they also provide contributions to a history of economic thought. The few comments analysed present a variety of perspectives.
61The analysis has centred on Samuelson’s textbook and has been partially supported by quantitative data as to the types of Quantifiers used. Quantifiers in the Samuelson corpus have been classified according to the two basic parameters discussed above: their numerical value (Exact/Approximate/Indefinite) and their world of reference (factual/hypothetical). Metadiscursive uses of quantifiers have been marked as a separate factual category, so as to be able to study if there was any consistent variation across genres or areas of interest.
62Approximation has proved to play a minor role in Samuelson’s texts, representing only 3.34% of the occurrences of Quantifiers. Relative frequencies do show great variation across genres. Approximations represent 2.95% of all Quantifiers in textbooks, only 0.73% in articles and a relevant 11.01% in comments. The minimal incidence of approximation in Samuelson’s theoretical articles may be related to his vast use of abstract mathematical reasoning.
63The clearest patterns, however, appear when considering the whole corpus from the point of view of exact Quantifiers and their relation to the world of reference.
64The analysis of the two editions of Samuelson’s textbook has shown similar patterns in the two books, both in terms of the role played by the various kinds of Quantifiers and in terms of the expected “theory vs current problems” distinction.
65When compared to “current problems” chapters, theoretical chapters do not present a higher incidence of hypothetical Quantifiers in general, but they do present a higher incidence of hypothetical moves where exact quantifiers play a major role. Exact Quantifiers account for the vast majority of Quantifiers used with reference to the world of hypothesis, both in the 1976 and in the 1992 edition (actually showing a marked upward trend, from 60.67% to 73.41%). In chapters on current problems, the mean is much lower (42.73%). The use of tables and graphs accompanying the verbal text —and offering an additional wealth of quantitative data— does not show relevant variation across the two approaches.
66The analysis also shows some consistent patterns within the theoretical chapters. Table 1 focuses on the role played by exact Quantifiers in the chapters from the two editions considered. It is based on the analysis of four chapters, including 1120 occurrences of Quantifiers. The values are not reported as statistically significant; they are only meant to support to the claim made about the major role of exact Quantifiers within the world of Hypothesis.
Table 1. Exact Quantifiers in theoretical chapters (%)
A = the proportion of exact Quantifiers to the whole set of Quantifiers with reference to the world of hypothesis
B = the proportion of exact Quantifiers to the whole set of Quantifiers with reference to the world of fact
C = the incidence of metadiscursive occurrences of exact Quantifiers with reference to the world of fact
67Exact Quantifiers do not only account for the vast majority of Quantifiers used with reference to the world of hypothesis: they consistently show higher frequencies within the world of hypothesis than they do within the the world of fact. Here they also present a very high proportion of metadiscursive uses, which leaves very little room (ranging around 20%) for exact quantification of extra-textual referents in the world of fact.
68Research articles show a different trend. The formal language of abstract mathematical reasoning becomes decidedly dominant and the use of exact Quantifiers appears to play a lesser —and less consistent— role in the verbal text.
69A preliminary quantitative observation can be made by comparing the data in Table 1 with those in Table 2. This is based on the analysis of the first subset of research articles, which is made of 8 articles and includes 803 occurrences of Quantifiers. The articles were all written in the 1970s and deal with topics that can be related to those dealt with in the chapters considered in Table 1.
Table 2. Exact Quantifiers in research articles (%)
70The clearest trend shown by the data regards a more restricted use of exact Quantifiers. A more detailed analysis of the values of each article would also show that their role is somewhat less consistent: the pattern according to which exact Quantifiers play a lesser role within the world of Fact than they do within the world of Hypothesis is still the dominant pattern, but one one of the articles follows the reverse trend.
71The most interesting feature can be noticed when considering the use of exact Quantifiers in hypothetical moves. Hypothetical examples and illustrations are drastically reduced, to show that the intended reader needs no “reinforcement” and no didactic mediation through the use of simplified numerical data. The reader is supposed to share the mathematical background of the writer and the burden of the writer’s argument is mostly carried by logical reasoning on the basis of an abstract model. This model is often established by an opening hypothetical move which creates the premises for the whole argument, as in the following example.
(14) Assume two goods (say soybeans or manufacturers, or soybeans and “money”, in the sense of abstract purchasing power over the composite goods and services that make up the non-grain totality of the standard of living.
Assume two periods (say, now and next year).
Assume 2N persons, who are identical in their tastes, incomes and equal endowments in the two periods of both goods... (Proof That...)
72The example above shows that, beyond the mere quantitative reduction, there is in fact an important qualitative change in the role played in research articles by exact quantifiers in hypothetical moves. Rather than building up illustrations to facilitate the reader’s understanding of a complex reality, these moves establish a simplified model of reality as a basis for the whole reasoning.
73An analysis of more recent articles, chosen to represent a wider range of topics and approaches in the author’s production, shows a lot of quantitative variation. This would not allow any generalisation as to the role played by exact Quantifiers within the two worlds of reference. The overall impression is confirmed, however, that the most significant variation is qualitative rather than quantitative: exact quantifiers with reference to the world of hypothesis are meant to establish a model (a scenario) for the whole argument rather than to provide simplified examples.
- 19 In A Long-open Question ..., for example, exact quantifiers represent 61.36% of Quantifiers within (...)
- 20 In The Overdue Recovery of Smith’s Reputation..., for example, exact quantifiers represent 38.89% o (...)
74The corpus is obviously too small to provide material for further generalisations but at least two tentative observations can be made. First, the use of mathematical demonstration may at times become so dominant as to produce the impression of two parallel texts grafted on to each other by means of numerous metadiscursive references.19 Second, the only articles that present a massive use of indefinite Quantifiers are also the ones that can be seen as contributions to a history of economic thought (whether presenting a re-evaluation of Smith’s work or focusing on the debate on monetarism) rather than on theoretical demonstration of Samuelson’s own position.20 This somewhat confirms a relationship between the communicative purpose of the writer and his choice of a specific combination of quantifiers and worlds of reference.
75The small corpus of comments published in non-professional journals is even less representative of a genre. Comparison with the rest of the corpus is also made more difficult by the fact that it has not been possible to establish an acceptable equivalence in terms of issues dealt with.
76The data show great variation and not many clear trends appear. The role played by exact Quantifiers seems to vary a lot, depending on the nature of the comments. The role of exact quantifiers in hypothetical moves, for example, ranges from 78.57% when dealing with matters of economic policy, to 60.32% when dealing with the history of economic thought and to 42.64 when dealing with some purely theoretical issues.
77We may notice, however, that comments generally present a much wider use of exact Quantifiers in hypothetical moves than in references to the world of fact (an avergae of 55,35% as against 35,09%). This pattern can be related to the similar pattern found in textbooks and therefore connected to the popularizing aim of the comments.
78Similarity of quantitative patterns, of course, does not necessarily imply similarity of pragmatic and argumentative functions. Exact Quantifiers used with reference to the world of hypothesis do not always take up the rhetorical function we have seen in textbooks. When dealing with matters of theory, they may indeed realize simplified hypothetical examples to illustrate general laws, but the majority of occurrences are found in modalized or projected statements.
79The extract below provides an example of exact Quantifiers in a modalized statement. The statement draws out the practical implications of the main claim made in the comment, which supports the increasing concern for a measure of economic welfare (NEW) as against a measure of economic growth such as GNP.
(15) It’s up to us, the public. If we will it, we can give up half a percent of conventional GNP yearly growth, in order to achieve perhaps an extra quarter of a percent rate of NEW growth. (From GNP to NEW)
80The limited choice of articles does not allow any generalization. It still serves our purpose, mainly by showing two things: a) a greater focus on economic analysis normally implies a higher use of quantification with reference to the world of fact and of approximations and b) a greater conceptual difference between reader and writer often induces a wider use of exact – simplified – quantities in hypothetical moves.
81I would like to conclude by briefly pointing out the implications that can be drawn from my analysis in the field of EAP. These may be presented on the guidelines suggested by Halliday (1987) for the field of educational linguistics in general and later adopted by many others. Halliday identifies three main areas in discussions of language learning: learning language, learning through language and learning about language.
82As for the first area, that of learning language, I believe my analysis supports the claim for a genre-based approach to the language syllabus and for students’ exposure to a variety of genres. Though focused on a specific language feature and its relationship to some specific moves, the analysis has provided an example of the qualitative if not quantitative role played by language variation across genres in the field of economics discourse. ESP and EAP language materials based on a restricted range of genres —and this often means restricted to specialist textbooks— do not only misrepresent the rhetoric and the communicative purposes of the special interest area, but they also offer a partial representation of how some key concepts find their verbal expression in the variety of genres that make up the discourse areas that may be relevant to the students’ curricula.
83This leads us to the second area to be considered: the area of learning through language. An analysis of the characterising features of a genre offers material for learning about the cultures and ideologies which inform the target language and its uses. The different roles played by factual or hypothetical argument in different approaches to economics or to scientific exposition itself, for example, can be the object of interesting comparative analysis.
84The most important implications, however, seem to me those that can be included within the area of learning about language. Language awareness —irrespective of the role we think it might play as part of learning language— can play an important role in developing critical reading skills. Students of economics could become much better readers by developing an awareness of the forms and functions of both quantification and model building and by learning to understand the different role they play in the different genres, according to the different communicative purposes and to the different “tenors” of the interaction.