Structuralists would be most likely to endorse which of the following statements?

Contrastive Linguistics

The first major paradigm of language-acquisition theory was the behaviorist–structuralist school which was informed by the contrastive hypothesis. This was built on the observation that learners with common mother tongues developed similar difficulties with specific foreign languages. The general principle of the hypothesis was that difficulties in second- or foreign-language learning were caused by structural differences between the mother tongue of the learner and the language to be acquired. The hypothesis had two degrees (Wardhaugh, 1970). The strong version claimed to be able to predict the difficulties of learners on the basis of a contrastive analysis, that is, a systematic comparison of the structures of the two languages involved. The original contrastive hypothesis was closely related to structuralist linguistics and its emphasis on langue (Lado, 1957). The view on learning was that of behaviorist psychology. Language was considered a set of habits, and second-language learning was a task which primarily involved a change of habits. The mother tongue of the learner would, in its capacity as a set of habits, interfere with the learner's new language (Weinreich, 1953). Contrastive analysis of entire languages were planned and carried out. Depending on the structural salience of the features involved, contrastivists also found that they were able to determine different degrees of difficulty. James (1980) suggests that contrastive analysis can be used by curriculum planners and teachers in their preparation, but not necessarily as a wholesale explanation of difficulties. Based on studies of learners' actual difficulties, however, a criticism of the contrastive hypothesis developed. It was found that difficulties predicted by contrastive analysis sometimes never appeared, and in other cases, difficulties arose which contrastive analysis did not explain. Furthermore, so-called errors came to be seen as necessary steps in the acquisition of a language (Corder, 1967). Many error analyses were carried out in order to shed light on real-life difficulties of learners. In some cases, the characteristics of the target language (L2) appeared to be more important than the mother tongue (Hyltenstam, 1978). The focus soon shifted to the study of the L2 performance of the learner as a language in its own right, a so-called interlanguage (interlingua or approximative system, Richards, 1974). An interlanguage has a grammar which follows universal principles just like any other grammar; it is just more variable. This understanding of language differed from traditional structuralist linguistics. Interlanguage studies further led to theorizing over the patterns of acquisition of second-language learners. This theorizing was likewise far removed from the behaviorist view of learning, it concentrated on cognitive aspects of language acquisition.

2.1.2.3 Structuralism

Probably the most well-known platonist response to the non-uniqueness argument — developed by Resnik [1981; 1997] and Shapiro [1989; 1997] — is that platonists can solve the non-uniqueness problem by merely adopting a platonistic version of Benacerraf's own view, i.e., a platonistic version of structuralism. Now, given the way I formulated the non-uniqueness argument above, structuralists would reject (4), because on their view, arithmetic is not about some particular sequence of objects. Thus, it might seem that the non-uniqueness problem just doesn't arise at all for structuralists.

This, however, is confused. The non-uniqueness problem does arise for structuralists. To appreciate this, all we have to do is reformulate the argument in (1)–(5) so that it is about parts of the mathematical realm instead of objects. I did this in my book (chapter 4, section 3). On this alternate formulation, the two crucial premises — i.e., (2) and (4) — are rewritten as follows:

There is nothing “metaphysically special” about any part of the mathematical realm that makes it stand out from all the other parts as the sequence of natural numbers (or natural-number positions or whatever).

Platonism entails that there is a unique part of the mathematical realm that is the sequence of natural numbers (or natural-number positions or whatever).

Seen in this light, the move to structuralism hasn't helped the platonist cause at all. Whether they endorse structuralism or not, they have to choose between trying to salvage uniqueness (attacking (2′)) and abandoning uniqueness, i.e., constructing a platonistic view that embraces non-uniqueness (attacking (4′)). Moreover, just as standard versions of object-platonism seem to involve uniqueness (i.e., they seem to accept (4) and reject (2)), so too the standard structuralist view seems to involve uniqueness (i.e., it seems to accept (4′) and reject (2′)). For the standard structuralist view seems to involve the claim that arithmetic is about the structure that all ω-sequences have in common — that is, the natural-number structure, or pattern.24 Finally, to finish driving home the point that structuralists have the same problem here that object-platonists have, we need merely note that the argument I used above (section 2.1.2.2) to show that platonists cannot plausibly reject (2) also shows that they cannot plausibly reject (2′). In short, the point here is that since structures exist independently of us in an abstract mathematical realm, it seems very likely that there are numerous things in the mathematical realm that count as structures, that satisfy FCNN, and that differ from one another only in ways that no human being has ever imagined.

In my book (chapter 4) I discuss a few responses that structuralists might make here, but I argue that none of these responses works and, hence, that (2′) is every bit as plausible as (2). A corollary of these arguments is that contrary to what is commonly believed, structuralism is wholly irrelevant to the non-uniqueness objection to platonism, and so we can (for the sake of rhetorical simplicity) forget about the version of the non-uniqueness argument couched in terms of parts of the mathematical realm, and go back to the original version couched in terms of mathematical objects — i.e., the version in (1)–(5). In the next section, I will sketch an argument for thinking that platonists can successfully respond to the non-uniqueness argument by rejecting (4), i.e., by embracing non-uniqueness; and as I pointed out in my book, structuralists can mount an exactly parallel argument for rejecting (4′). So again, the issue of structuralism is simply irrelevant here.

(Before leaving the topic of (2) entirely, I should note that I do not think platonists should commit to the truth of (2). My claim is that platonists should say that (2) is very likely true, and that we humans could never know that it was false, but that it simply doesn't matter to the platonist view whether (2) is true or not (or more generally, whether any of our mathematical theories picks out a unique collection of objects). This is what I mean when I say that platonists should reject (4): they should reject the claim that their view is committed to uniqueness.)

Componential or Paradigmatic Structures

It was with Goodenough and Lounsbury's adaptation in 1956 of “componential analysis” from structuralist phonology that something like genuine or full-fledged structural models were introduced into studies of kinship terminological systems. These were distinctive feature analyses in which the goal was to find the minimal set of features that were necessary and sufficient to distinguish the referents of kinterms in a given system from one another. These were attempts to model the semantic structure of kinship terminologies, and existed within a wider context of concern with analyzing semantic structure in general; the conception of structure and how it related to behavior was taken from structural linguistic analyses of phonological systems (especially Prague, but also see Zellig Harris's work within the Bloomfieldian tradition).

One result of componential work in kinship was the realization that semantics differs from phonology in important ways having to do with the function of the systemic entities, the role of features, and the degree of constraint of the relevant universe. A second result emerged when it was realized that native speaker assignments of relatives to kin categories did not depend on distinctive features (unlike the phonological case where features do govern assignments), but on a relative product “calculus” of the “he's my mother's brother, so that makes him my uncle” sort. The distinctive features found in a componential analysis of kinterms are, in fact, dependent on prior knowledge of how the relatives are related (genealogically, say); that is, they are defined in terms of kinterms, rather than vice versa. But, there exists considerable evidence that people use such distinctive features in sorting kinfolk, behaving toward them, and so forth. There still exists some question concerning the degree to which the distinction in kinship between the means by which entities are defined and the features by which those entities are associated with related thought and behavior is normal for some wider set of semantic systems—or is unique to the special domain via which people receive their basic social locations or identities.

These realizations posed basic questions about the nature of semantic structure and its modeling. Componential analyses of a densely populated and complex domain such as kinship yielded empirically powerful structural models, as shown in the classic studies of Wallace and Atkins in 1962 and Romney and D'Andrade in 1964. But, attempts to describe and formally model the system used by native speakers in their definitions led to very different kinds of structures (see Kronenfeld's 1980 analysis of Fanti for an early version, and the articles by Read and Lehman in Kronenfeld's 2001 edited collection as well as Gould's 2000 A New System for the Formal Analysis of Kinship, for sophisticated algebraic versions). These structures have the formal properties of algebraic structures and lend themselves to rigorous and informative graphic representations.

7.7 Open Models

We have so far developed two conceptions under which a symmetric, constructive semantics for quantification yields classical first-order logic. But our constructive fictionalism is not yet free-range. Neither conception reflects Cantor's idea that the essence of mathematics is its freedom; neither reflects Poincaré ' thought that existential assertions in mathematics require nothing more than consistency. To capture those notions, we need the concept of an open model, an model, analogous to a canonical model in modal logic, in which all possibilities — or, at least, all possibilities consistent with certain constraints — are realized.

Let W be a set of infinite cardinality k. The open model of cardinality k for W, OW=〈k≤,D⊩〉, is generated from k = {k : ∃U ⊆ W(|U| < k & D(k) = U)}, where k ≤ k’ ⇔ D(k) ⊆ D(k’). It is straightforward to show that OW is an inexhaustible weak net with the understudy properties — in short, a structuralist model. It follows that Th(OW) is a first-order theory.

Say that model k for L is reductively complete iff for all k ∈ K and every L’ such that L ⊆ L’ ⊆ L(k), k | L’ ∈ K. In reductively complete models, altering the quantificational clauses to ones considering only nodes extending the current one by the addition of a single object would make no difference, provided that for any sentence A of Lk and k ≤ ?’ ∈ k, k⊩A⇔k′⊩A.

We can use this fact to show (somewhat tediously) that if L contains no individual constants and O is an open model of cardinality k, Thh(O) is decidable. Moreover, Thh(O) is an ∀ ∃ theory, axiomatized by the set A(O) of axioms of the form ∀xi…xn∃yi…ymF(x→,y→), where n ≥ 0, m ≥ 1, F(x→,y→)is a consistent conjunction of basic formulas built from predicates of L and variables from among x1 … xn, y1 … ym, and in each conjunct there is at least one occurrence of one of the ys.

It is possible to generalize this result in two different directions. First, suppose that k is a reductively complete structuralist model: a reductively complete permutable weak net. Then Th is a first-order theory axiomatized by U(k), consisting of

all axioms of the form ∀x→(G(x→)→∃yG′(x→,y)), where for some c→,c,G(c→),G′(c→,c)are diagrams of some k,k’ ∈ K such that D(k’) extends D(k) by a single object, and

all axioms of the form ∀x→,y(G(x→)→∨iGi(x→,y)), where for some such c→,c,G(c→),G1(c→,c)…,Gn(c→,c)are diagrams of all the k’ ∈ K extending k by a single object. If K is not reductively complete, but has an analogous property with respect to finite extensions, then Th (K) is similarly axiomatizable, and will in fact be decidable iff A(K) is recursively enumerable.

Second, and more immediately relevant to mathematics, suppose that P is a decidable set of purely universal sentences of L — sentences, from a metaphysical point of view, carrying no ontological commitment. Then we can characterize the P-open model of cardinality k for W, OP,W=〈K≤,D,⊩〉, generated from K = {k : ∃U ∩ W(|U| < k & D(k) = U & the diagram of k is consistent with P)}, where k ≤ k’ ⇔ D(k) ⊆ D(k’). It is straightforward to show that OP,W is an inexhaustible weak net with the understudy properties. It follows that TK(OP,W) is a classical first-order theory.

Suppose, for example, that L consists of a single nonlogical two-place predicate < characterized as a strict linear order by the purely universal axioms ∀x,y(x<y→<y<x), z((x<y&y<z)→x<z), and ∀x,y(x<y∨y<x∨x=y). Among the theorems of the theory of the orems model of cardinality ℵ0 for N would be ∀x∃yx<y,∀x∃y y<x, and ∀x,y(x<y→∃z(x<z&z<y)). We thus get a theory of a dense linear order extending infinitely in both directions, even though every stage k in the structure has a finite domain.

If every mathematical theory could be analyzed as the theory of a P-open model of some cardinality, we could stop the account here, and have, perhaps, a version of modal structuralism that would capture a variety of fictionalist insights. Whether it would deserve to be called a version of fictionalism is unclear. Unlike other forms of structuralism, it does take seriously the thought that the structures in question are products of human creative activity governed by no constraints other than those applying to fiction. How many mathematical theories might be analyzed as theories of P-open models remains an open question.

It appears, however, that some mathematical theories are fictionalist in a stronger sense. They appear not to be analyzable as theories of P-open models. Peano arithmetic, for example, assumes the existence of zero as the sole natural number without a predecessor. Set theory assumes the existence of the null set and of an infinite set. Geometry, on Hilbert's axiomatization, assumes the existence of two points lying on a line, three points not lying on a line, and four points not lying in a plane. It is possible to account for some such theories in terms of Q-open models in which, among the axioms of Q, there are not only purely universal sentences but also (a) pure existentials (needed, for example, in the case of geometry) and (b) definitions of one or more constants (needed, for example, in the case of arithmetic). Suppose, for example, we define 0 by means of the formula ∀x(x=0→∃ySyx), where S is the successor relation, and stipulate that ∀x,y,z((S xy & S yz) → y = z) and ∀x,y,z((S yz & S xz) → x = y). The theory of the relevant open model then includes ∀x∃yyS xy and ∀x(x ≠ 0 → ∃yS yx). The induction schema corresponds to a pure universal in a second-order language, and so can perhaps in principle be included in the axiom set Q. For that reason, in fact, it is easier to analyze second-order arithmetic as the theory of a Q-open model than it is to analyze first-order arithmetic in similar fashion.

For the same reason, it is easier to attempt an analysis of second-order set theory. Whether set theory or geometry can be understood as the theory of a Q-open model is a large question I cannot discuss here in detail. The general strategy for set theory would be to use arithmetic or the theory of dense linear order to define an infinite set, thus justifying the axiom of infinity; to use Q to define unions, pair sets, and power sets, and to express a second-order abstraction axiom; and then to view axioms of sum sets, pair sets, and power sets as theorems.

However the details of this might go, the philosophical moral appears to be that certain mathematical theories, especially existential mathematical theories such as Peano arithmetic and set theory, if capable of being given a fictional interpretation, are fictional in two senses. They are fictional in the sense that they speak of objects constructible given the general criteria of construction governing fiction. They are also fictional in the sense that they require the postulation of an object — zero, in the case of the theory of natural numbers, or the null set, in the case of set theory — that accords with those criteria but the existence of which cannot be viewed as a logical truth. The semantic fictionalism I am outlining is irresistably fictionalist; it does not collapse into deductivism or reductionism.

An Interdisciplinary Imperative

The biographical perspective has also engendered new forms of interdisciplinary, psychosocial understanding of learning and learners. These new developments seek to transcend old style disputes between structuralist sociology and essentialist psychology in the literature of adult learning. Adult learning was conceived, on the one hand, as a largely internal psychological process, dependent on dispositions, inherent motivations, and objectively measurable intelligence. The social and historical could largely be excluded from the frame (Tennant, 1997). On the other hand, there was great resistance to such ideas, especially in more radical and oppositional theories of adult learning. In the British tradition, for instance, there was criticism of what was seen to be a mainly North American tendency to overly psychologize the human subject and learning processes, and to reduce sociocultural forms of oppression to matters of individual pathology (Tennant, 1997). On the other hand, more radical, structural perspectives on adult learning have lacked any convincing theory of how the sociocultural translates into diverse internal states and why some people, more so than others, in objectively similar situations, are able to transcend oppression and become life spacers.

There is a considerable momentum in the biographic research family to bridge the conceptual gap, as defined above. There are a number of psychosocial studies – often drawing on psychoanalytic ideas – which explore the interplay of inner and outer worlds, psyche, and society: of learning in families or in working contexts, for example (West, 2007; Weber, 2007). Psyche is perceived to be a product of our intersubjective experiences, which are shaped, in turn, by the structuring and discursive processes within a given society, such as of class, race, or gender. However, psyche is no longer reduced, as in an overly structuralist sociology, to a kind of epiphenomenal or determined status: the inner world has a dynamic and power all of its own. If culture and society shape even in the most intimate of spaces – through poverty or the gendered distribution of emotional labor – such processes are mediated through the intimate relationships in which we are embedded. They can encourage relative emotional openness or closedness to experience and others. If curiosity, desire, and wholehearted engagement with the world are repressed or profoundly inhibited, because of our most significant others, then learning, in a psychological sense, easily becomes something to be avoided rather than embraced.

Such processes have been mapped, biographically, in studies of young mothers in parenting projects, like Sure Start in the United Kingdom (similar to Head Start in the United States) (West, 2007). One project was designed to support young single mothers who lived on a run-down public housing estate, suffering badly from deindustrialization, demoralization, and poverty. The particular project provided the base for a university and a community arts collaboration to utilize the visual arts to stimulate creativity and build confidence among hard-pressed single young mothers. The project was located in a youth center and the disaffected young mothers were to be recruited through outreach. The arts, it was hoped, would boost participants' confidence, planning and parenting skills, as well as broaden horizons. The young mothers would be encouraged to progress toward structured educational achievement or into work.

One particular case study chronicles, in detail, how a young woman, Gina, could retreat defiantly to the edge of any group of learners. This was part of a pattern in a life riddled with abuse, hard drugs, and ridicule. Yet, providing a creative artistic space, in the context of the strong relationships that Gina forged with tutors and youth workers over time, gradually enabled her to take some risks. Her messy feelings about her pregnancy, for instance, were projected into a sculpture, made of chicken wire and plaster of Paris, which became a narrative of her pregnancy. She was able to work on the story artistically and, to an extent, transform her relationship to the experience and to her life more widely, through new narrative understanding. Her progress depended on the quality of interactions between people (the social context) and the extent to which she felt encouraged and able to play, imagine, think, and perceive herself differently, as a learner, mother, and person, and to relate to her toddler in new ways. There was as shift in her internal psychological drama, as new characters and symbolic objects, in the language of psychoanalysis, entered the stage. We are witnesses, in work of this kind, to how experience can stifle the desire to learn, and can psychologically close us down to new possibilities. However, new transitional spaces for learning and people coming alongside and tolerating our ambivalence – with sufficient self-knowledge, patience, and love, in a non-narcissistic sense – can reinvigorate creativity and the capacity to learn anew.

Other biographical researchers have used psychosocial ideas to explore learning processes from a gender perspective. Weber (2007), for example, focuses on gender and the learning processes of adult men training for work in the caring professions. Drawing on what she terms critical psychodynamic theory, she reveals learning in the workplace as a gendered battlefield where learning subjects' basic orientations can manifest themselves along gendered lines. These processes are partly theorized with reference to classic psychoanalytic insights into male struggles with intimacy. However, this is not to neglect culture, language, or material conditions. In this view, gender is inherent in social structures, stemming from historic divisions of labor, and is reproduced or changed within the scope of the accessible choices that people can make. Yet, in understanding reproduction and change processes, Weber observes that girls tend to identify with and separate from a model of their own gender while boys' paths to autonomy involve separation from a first intimacy. These patterns of early interaction are reinforced by language as symbolic representation, all of which serves to define what she calls gendered subjectivity. (Weber, building on the work of others, distinguishes gender subjectivity – the processes by which a person becomes a psychological subject – and gender identity, which refers to sexuality and cultural conceptions of gender.) Gendered subjectivity can find expression in what can be the differing responses of men and women to new kinds of training opportunities in which learning a capacity to care for others is required. Men, mirroring earlier patterns, tend to achieve this by experiencing and demonstrating degrees of autonomy first, whereas women tend to seek intimacy as a prerequisite of autonomy. Weber stresses that these distinctions are far from absolute, but there are patterns nonetheless. We are given glimpses, through such biographical research, of the defended as well as social subject at the heart of learning.

Conclusion

In the light of the discussion above, it may be useful to re-visit in what way this approach to the sociology of curriculum should be regarded as structuralist. The Durkheimian and linguistic influences are clearly apparent. There is however a deeper sense in which this approach can be distinguished from the empiricism of current approaches to both school effectiveness and textual cultural critique. In a way that could more properly be called realist (Manicas, 2006), Bernstein and those using his theory are engaged in a search for explanatory mechanisms (structures) for reading the world. With the theory of codes, and in a less elaborated form with the theory of knowledge structures, researchers are able to create a powerful and precise language for modeling pedagogic modalities and explaining their effects. This search for explanatory mechanisms is what distinguishes this approach to the sociology of curriculum, whether we call it structuralist or realist.

Paradigm Shifts in Second and Foreign Language Education

The major disciplines informing second and foreign language education have traditionally been linguistics and psychological theories of language acquisition. It follows that knowledge paradigm shifts in these disciplines also lead to corresponding shifts in knowledge and views on second and foreign language curricula and pedagogy. In designing any language curriculum (or curriculum in general), two central questions naturally arise: What should be included in the curriculum and how should the curriculum content be taught (e.g., in what sequence and with what kinds of teaching methods)?

Structural linguistics has long been the chief framework underlying the development of language curricula. Richards (2001) reviewed the historical background of vocabulary and grammar gradation/selection in developing language curriculums from the 1920s to the 1970s. The assumptions underlying early structuralist approaches to language syllabus design can be summarized as follows:

the basic units of a language curriculum are vocabulary and grammar;

learners everywhere have the same needs;

learners' needs are identified exclusively in terms of language needs;

the process of learning a language is largely determined by the textbook;

the classroom and the textbook provide the primary input to the language learning process; and,

the goal of the syllabus designer is to simplify and rationalize this input through selection and gradation (Richards, 2001: 15–16).

It can be seen that the basic assumptions of structural linguistics permeate the early approaches to language syllabus design. Mastering human language communication is seen as equivalent to mastering the structural units of the language system. The systematic, logical, sequencing and presentation of linguistic structural units become the central task for language syllabus designers. These assumptions had influenced the design of language syllabus and pedagogy until the 1970s, when functional linguistics became the strongest rival of traditional, structural linguistics.