PARADIGMS AND MODELS

The terms "paradigm" and "model" have enjoyed considerable popularity in sociology, in part because the terms have a range of meanings. In everyday language, model has two senses: (1) a replica of an object being modeled, for example, a "model of a building," and (2) an exemplar to be emulated, as in "role model." "Paradigm" is somewhat more esoteric in everyday usage, but has become quite important in academic disciplines including sociology, largely due to Thomas S. Kuhn's 1962 book, The Structure of Scientific Revolutions.

The original meaning of paradigm overlaps that of "model" in the sense of exemplar. The term comes from the study of grammar where a paradigm provides a model of, for example, the way to conjugate all the regular verbs of a particular type (I love, you love, he or she loves, etc.). Its appearance in sociology predates Kuhn, but since Kuhn, it has become a much grander idea. Merton used the device of analytical paradigms for presenting codified materials, by which he means a technique for exposing the "complete array of assumptions, concepts and basic propositions employed in a sociological analysis" (1949, p. 13). Parsons treated "paradigm" in a similar way when he presented paradigms for social interaction and social change and emphasized that these are distinct from theories (1951, p. 485).

It is quite clear, however, that Kuhn's work has brought "paradigm" from relative obscurity to a central place in the discourses of the humanities, the social sciences, and the history and philosophy of science. Kuhn's paradigm and his model of change in science are highly controversial; yet, they have had considerable influence in these academic fields. Some of the effects Kuhn intended; many effects, however, were unintended, causing Kuhn to disavow explicitly some of the interpretations of his work (Kuhn 1970, 1974). Crews (1986) comments that a loose reading of Kuhn's book—which he calls the most frequently cited academic book of modern times—even justifies the rejection of science as empirical.

WORKING DEFINITIONS

A useful definition of model draws on Kaplan:

Any system A is a model of a system B if the elements and relationships of A aid in the understanding of B without regard to any direct or indirect causal connection between A and B. (1964, p. 263)

For example, one could use ideas about political change (system A)—stable government, crisis, revolution, new government attains stability—to model change in science (system B). Models range from informal analogies or metaphors (e.g., society as an organism) to highly formal equation systems.

A model contains elements that have (or are given) properties—that is, are characterized by descriptive terms, and connections among some or all of these elements. One could construct a physical model of a social network using balls with holes in them and rods that fit into the holes. The rods would connect some but not all of the balls; the balls (elements of the model) would represent individuals in the network and the rods (connections) would link those individuals who communicate with one another.

The critical property of a model is an isomorphism with its object, the thing being modeled. Strictly speaking, isomorphism is a one-to-one correspondence between the elements and relationships in the model and the elements and relationships in its object. Needless to say, strict isomorphism is not satisfied by many metaphors and analogies even though these can aid understanding; the lack of strict isomorphism, however, should serve as a caution in taking analogies too literally. Similar caution applies to models in general since it is all too easy to reify the model, that is, confuse the model with its object. Models do not capture all the properties of their objects, so that even with strict isomorphism, a model inevitably omits significant aspects of the object. As long as those concerned with a model recognize this limitation, they can employ the model fruitfully and unproblematically.

A loose usage of "model" treats it as synonymous with "theory" or as theory expressed in mathematical symbols. While it is possible to have a model of a theory, the working definition given above rules out synonymous usage because a model of x must resemble x in terms of pattern or structure, whereas a theory about x, that predicts or explains x, need not, and generally does not, resemble x. In short, theories of x do not have to be isomorphic with x; models do.

In formulating a working definition of paradigm, it would seem reasonable to follow Kuhn since he is largely responsible for the contemporary significance of the idea. This presents serious difficulties, however, for as Laudan observes, "Kuhn's notion of paradigm has been shown to be systematically ambiguous . . . and thus difficult to characterize accurately" (1977, p. 73). While constructing a definition of "paradigm" is a formidable task, it is an essential one because the paradigm is critical to an understanding of Kuhn, and Kuhn's work plays an important role in many of the current controversies in sociology. Some of the ambiguity disappears if one distinguishes between what a paradigm is and what a paradigm does; still, it would be presumptuous to believe that one could fully capture Kuhn's concept with all its nuances. The following working definition has the more modest goal of representing many of his key ideas:

A paradigm is a significant scientific achievement recognized by a particular community of scientists that provides a model from which springs a coherent tradition of scientific research and also a general way of looking at the world.

The principal functions of a paradigm include: (1) determining what kinds of problems are appropriate objects of study, (2) specifying appropriate ways to study these problems, and (3) delimiting the types of theories and explanations that are acceptable. For example, one could consider Durkheim's Suicide ([1897] 1951) as a paradigm for many sociologists that provides a model for research and a way to look at phenomena. For Durkheimians, Suicide is an exemplar that specifies ways to look for and at social facts, and that limits explanations of given social facts to other social facts, rather than, for example, explaining social facts with psychological ideas like motives.

It is important to distinguish "paradigm" from "theory." While a well-developed paradigm may contain a number of specific theories, a paradigm is "metatheoretical." A theory makes statements about the world, whereas a paradigm involves statements about the nature of acceptable theory, the appropriate entities to investigate, and the correct approaches to these investigations. As an exemplar, a paradigm serves as a normative standard; hence, it is a special type of model, a model of what the given scientific community considers to be exemplary work.

KUHN'S MODEL OF SCIENTIFIC CHANGE

Kuhn developed a model of change in science built around his concept of paradigm. The model employs several concepts related to "paradigm" that extend its meaning: normal science, anomaly, crisis, revolution, paradigm shift, and incommensurability. Brief explications of these ideas follow. (Page references below are to Kuhn 1970.)

Normal Science. When a paradigm gains acceptance in a scientific community, it is largely in terms of a promise of success if researchers in the community follow the exemplar. "Normal science consists in the actualization of that promise, an actualization achieved by extending the knowledge of those facts that the paradigm displays as particularly revealing, by increasing the extent of the match between those facts and the paradigm's predictions, and by further articulation of the paradigm itself" (p. 24). To Kuhn, normal science involves "mopping-up operations [that] engage most scientists throughout their careers" (p. 24), and is primarily devoted to puzzle solving: "Perhaps, the most striking feature of the normal research problems . . . is how little they aim to produce major novelties, conceptual or phenomenal" (p. 35).

Anomaly. The term anomaly refers to "the recognition that nature has somehow violated the paradigm-induced expectations that govern normal science" (p. 52).

Crisis. A crisis, a period of "pronounced professional insecurity" (p. 68–69), occurs when enough anomalies accumulate so that scientists question the appropriateness of the paradigm.

Revolution. Kuhn takes scientific revolutions to be "those non-cumulative developmental episodes in which an older paradigm is replaced in whole or in part by an incompatible new one" (p. 92).

Paradigm shift. Kuhn argues that scientists with a new paradigm do not merely have new interpretations for what they observe, but rather "see" things differently. This difference in perception, or paradigm shift, is in a sense similar to the Gestalt switch studied by psychologists, in which the same figure can yield a right-hand face or a left-hand face depending on how it is viewed.

Incommensurability. During crisis periods, rival paradigms coexist and advocates of rival paradigms cannot understand one another because they have different ways of seeing the world, different standards for appraisal, and different objectives for their scientific community; that is, there is incommensurability. Consequently, paradigm conflicts are not resolvable by appeal to a set of shared criteria.

These concepts allow a sketch of Kuhn's model:

Paradigm I → Normal Science → Anomalies → Crisis → Revolution → Paradigm II

When the members of a scientific community accept a paradigm, that acceptance generates a set of shared commitments to objectives, methods for achieving those objectives and criteria for appraising theories and research. These commitments are the foundation for a period of normal science, since what to study, how to study it, and what constitutes adequate explanations are not problematic. During normal science, the community regards the paradigm itself as unalterable and immune to challenge. Scientists work to solve the puzzles that the paradigm presents and for which the paradigm guarantees solutions; in this process of puzzle solving, refutations for theories contained in the paradigm arise and empirical studies come up with unexpected findings. The more serious refutations and the more surprising findings come to be regarded as anomalies, and as these anomalies accumulate, scientists are at a loss as to how to deal with them. In the crisis period, rival paradigms arise, but because paradigms are incommensurable, scientists adhering to rivals have no common basis for choosing among the competitors. Paradigm II wins out because some scientists undergo the conversion experience of a paradigm shift where they see the world in a new way, because the adherents of Paradigm II are especially persuasive, or because the adherents of Paradigm I die off.

Kuhn's model questions ideas of cumulation and progress in science. While normal science is cumulative, revolutions do not preserve all, or even the most important, achievements of previous paradigms. "There are losses as well as gains in scientific revolutions" (p. 167). Furthermore, the incommensurablity thesis argues that Paradigm II does not win out because it is better or more progressive; the lack of shared standards precludes definitive judgments.

CRITIQUE

Kuhn's work has raised important questions for scholars in the history, philosophy, and sociology of science and has generated a large literature in these areas. Interestingly enough, it has also had broad appeal to intellectuals outside of these specialized fields. Although Kuhn presented his basic model in 1962, his ideas continue to command attention and engender controversy, both within relevant technical fields and in broader academic circles. His work seems to have had less impact in the natural sciences, although it attacks the conventional views of many natural scientists.

Kuhn's emphasis on scientific communities and on noncognitive factors in the development of science clearly appeals to sociologists, especially sociologists of science—for instance, those who study social networks among scientists or the effects of reward systems. His model provides an antidote to the mythology of cumulative, linear growth of knowledge, the view that characterizes science as building one discovery on another and, with each increment, coming closer to total truth about nature. Nearly forty years after his initial publication, it is difficult to appreciate how dominant such mythology was when Kuhn challenged it.

If prior views overemphasized cognitive and rational factors and held to a naive and simplistic view of progress in science, many post-Kuhnians underemphasize the cognitive and the rational or overemphasize the social and the political; moreover, some totally deny the possibility of scientific progress. For many, Kuhn provides the license to remove science from its pedestal, to deny that science has any distinctive character or special claim on society's attention or support, and to demand that social sciences cease their attempts to be scientific. Close examination of a few of Kuhn's key ideas indicates how Kuhn came to be used in ways he, himself, disavowed.

The first problem is the ambiguity of the term "paradigm." Masterman (1970), a sympathetic critic, has pointed to twenty-one different senses of "paradigm" in the 1962 book, and Kuhn has added to the problem with later modifications of his ideas (1970, 1974). Laudan notes, "Since 1962 most of Kuhn's philosophical writings have been devoted to clearing up some of the ambiguities and confusions generated [by the 1962 book] . . . to such an extent that . . . [m]ore than one commentator has accused the later Kuhn of taking back much of what made his message interesting and provocative in the first place" (1984, pp. 67–68).

The metaphorical language in Kuhn's model poses a second serious problem. As Laudan puts it:

Notoriously, he speaks of the acceptance of a new paradigm as a "conversion experience," conjuring up a picture of the scientific revolutionary as a born-again Christian, long on zeal and short on argument. At other times he likens paradigm change to an "irreversible Gestalt-shift." . . . Such language does not encourage one to imagine that paradigm change is exactly the result of a careful and deliberate weighing-up of the respective strengths of rival contenders. (1984, p. 70)

Although Laudan believes that problems of misinterpretation can be "rectified by cleaning up some of the vocabulary," and although Kuhn has assumed some responsibility for the misunderstandings due to his own rhetoric (1970, pp. 259–260), it should be noted that Kuhn's ambiguity and his vivid metaphors are important reasons for much of the enthusiastic embracing of his model. The possibility of reading into the meaning of "paradigm" and "paradigm shift" enables the model to serve a variety of agendas.

Kuhn's incommensurability thesis is both the most frequently criticized and the most frequently misused element of his model. It has provided ammunition for a radical subjectivism that denies all standards (Scheffler 1967). In attacking those who use Kuhn to justify any sweeping paradigm of their own, Crews writes, "By incommensurability Kuhn never meant that competing theories are incomparable but only that the choice between them cannot be entirely consigned to the verdict of theory-neutral rules and data" (1986, p. 39; emphasis added). Since Kuhn never clearly specified how rules and evidence entered into paradigm change and since he understated the degree to which different scientific communities can share rules and objectives, it is not surprising that this thesis became a rallying point for attacks on scientific rationality.

Another major criticism—and one that goes to the heart of Kuhn's model—involves the indivisible character of paradigms. Paradigm shift is an all-or-nothing process; a paradigm is accepted or rejected as a whole. Treating the parts of a paradigm as inseparable almost requires the transition from one paradigm to another to be a conversion experience; moreover, such a holistic view does not provide an accurate picture of how large-scale changes of scientific allegiance occur (Laudan 1984, pp. 71–72).

Many of these criticisms are widely held. Nevertheless, Kuhn's model remains important to many disciplines including sociology. Some scholars remain adherents to the basic features of the model; others believe they must respond to the model's challenges to contemporary philosophy and methodology of science.

USE OF "PARADIGM" IN SOCIOLOGY

While several leading British sociologists of science who focus on the sociology of knowledge reflect the intellectual mood of Kuhnian analysis (Collins 1983), the main applications of "paradigm" have occurred in either descriptive or normative efforts in the sociology of sociology.

Analysts have employed versions of Kuhn's concept to classify sociological activities as belonging to one or another paradigm; for example, Ritzer (1975) distinguishes three paradigms for the field at large: social facts, social definition, and social behavior. Bottomore (1975) identifies four paradigms of macrosociology: structural-functionalist, evolutionist, phenomenologist, and structuralist. Other sociologists discriminate varying numbers of paradigms from as few as two to as many as eight for a single subfield. Some writers classify theories into different paradigms; others categorize research strategies; still others codify more general philosophical orientations. In addition to disputing the number of paradigms, sociologists also disagree about whether paradigm applies to the field in general or only to subfields and whether there are any paradigms at all in sociology, that is, whether the field is preparadigmatic.

A few studies have applied Kuhn to examine historical development of a paradigm. Colclough and Horan (1983), for example, use content analysis of status attainment studies to illustrate Kuhn's model. Their analysis finds evidence for a stage of normal science and a stage in which anomalies arise, and they suggest the onset of a crisis for status attainment research.

Sociologists who use Kuhn focus on different properties of paradigms and debate the utility of their approaches or their faithfulness to Kuhn (cf. Ritzer 1975, 1981a, 1981b; Eckberg and Hill 1979; Hill and Eckberg 1981; Harvey 1982). Compounding the confusion are the many interpreters who read their own meanings into Kuhn. One critic argues:

[F]or the most part the use of the term paradigm in sociology fails to reflect the analytic elements of Kuhn's concept . . . Arbitrary pigeon-holing schemes of varying degrees of sophistication, are constructed and theories of, ideas about, and approaches to, sociology are dropped in. The result is a personalized schematic device that . . . plays little part in providing . . . any explanation or understanding of the growth of knowledge. The labeling of such pigeon-holes as paradigms legitimizes the scheme and implies an authority it does not possess. (Harvey 1982, p. 86)

The disarray led Bell to ask "Does the term "paradigm" carry too many possible meanings for rigorous thinking? Has it become quasi-mystical? Is it time to review its many usages and to consider discarding it in favor of more precise terms that convey to others more accurately what we mean to say?" (1990, p. 17) Bell went on to answer yes to all three questions.

MODELS IN SOCIOLOGY

The first basic distinction necessary to characterize the use of models in sociology is among substantive, measurement, and statistical models. The substantive modeler's objective is to model a specific theory, phenomenon, or process in order to learn (or teach) something about the specific object of the model. For example, Pfeffer and Salancik (1978) use a theory of interpersonal power and dependence (Emerson 1962) to model interorganizational relations, or Gamson (1969) creates an elaborate game that simulates the operation of key features of a society. In both examples, the model focuses on a particular problem—to learn about organizational relations in the first, or to teach students about major aspects of society in the second.

The objective of a measurement model is to create and justify a measuring instrument that has a wide range of applicability. One measurement area to which sociologists were early contributors is attitude measurement; sociologists were among the first to develop models for scaling attitudes. These scaling models provide the rationale for assigning numbers to represent different expressions of the attitude. For example, Bogardus (1925), in a classic work, created a measure of social distance on the analogy of physical distance, in which allowing a member of some ethnic group into your family represented less social distance than only allowing that person to live in your neighborhood. Guttman (1950) developed one of the most frequently used attitude scaling models, which defines and justifies procedures for ordering a set of attitude questions.

Statistical models are the basis for the systematic quantitative analysis of sociological data, and most empirical research in the field employs one or more statistical models. These models are general tools, broadly applicable to diverse problems; the nature of the subject matter that the data reflect is largely irrelevant to the model as long as the data have certain properties (e.g., as long as they are drawn randomly from some population). A large number of different statistical models appear in the sociological literature. Some are simple, for example, using the analogy of coin tossing to evaluate the likelihood that a given event occurred by chance; others are highly complex, using systems of equations to represent the structure of relationships in a set of variables. Models for multivariate analysis have become extremely important to sociology, including, for example, structural equation models, also known as path or causal models (Bielby and Hauser 1977), and log-linear models (Goodman 1984).

In recent years, models have become a central feature of the sociological literature. Researchers have constructed verbal, mathematical, and computer models to deal with a range of substantive phenomena and measurement issues. The application of statistical models to sociological data has increased dramatically in both the diversity of models employed and their mathematical sophistication. The most significant developments, however, have occurred in the creation, elaboration, and testing of formalized models of substantive phenomena, that is, models involving mathematics or logic.

In the early years of model building, substantive sociologists did not regard formal models as central to their concerns. Many mainline researchers were dubious about the utility of formal models in advancing knowledge about a substantive problem and often considered model construction as primarily an intellectual exercise, stimulating to the creator but of little relevance to anyone else. Articles presenting models appeared mainly in esoteric journals read by small audiences of the initiated.

A striking feature of recent sociological work is the emergence of formal models as a central feature of several research traditions. Papers presenting formal models, extensions of these models, critiques of them, and empirical studies testing the models have appeared regularly in journals such as the American Sociological Review. While specialized journals such as the Journal of Mathematical Sociology still publish many articles dealing with substantive models, the fact that general sociological journals also publish reports dealing with formal models indicates that formal modeling has become much more integrated with substantive research in several problem areas of the discipline.

Recent research involving formal models has dealt with a diversity of substantive problems, employed a variety of mathematical tools, and used many different types of data to evaluate the empirical predictions of the models. Sociologists have constructed models for collective behavior (Heckathorn 1996; Kim and Bearman 1997), demographic processes (Yamaguchi and Ferguson 1995), exchange processes (Lawler and Yoon 1996; Yamaguchi 1996; Molm 1997; Burke 1997), geographic mobility (Herting et al. 1997), organization ecology (Gábor et al. 1994; Hannan et al. 1995) performance expectations and power-prestige orders (Troyer and Younts 1997; Berger et al. 1998), and social differentiation-inequality (Rickson and Palange 1994; Nielsen 1995; Orbell et al. 1996; Mark 1998). What has changed from the past is that highly developed models in each of these lines of research have become part of the core of theory building rather than merely interesting adjuncts.

FUNCTIONS OF MODELS

A model, first of all, is an abstract representation of what the modeler regards as important aspects of the object being modeled. It involves assumptions, explicit or tacit, about that object, its elements, and the relationships among these elements. The definition given above requires that modeling lead to increased understanding; examining the relationships assumed in the model and ascertaining those that fit the object well, those that fit the object somewhat, and those that do not fit at all serves this most important function. In other words, scrutinizing ways the model resembles the object and ways it does not can uncover previously unrecognized features of the object. Formal models, as noted earlier, employ logical or mathematical tools to derive conclusions from the model's assumptions, and researchers then test whether these conclusions represent hitherto unknown properties of the object. A model, in general, provides the means to ask new questions about the phenomenon it represents and thus functions to generate new ideas.

A model provides a vehicle for communication. Since a model is more abstract than its object and since it omits many properties of the object, it is easier for writer and audience to share understanding of the model than of the object. Caution, however, is necessary, particularly when the model is a vague analogy (e.g., society as a living organism). The possibility of reading into analogies and metaphors can defeat shared understanding when the audience focuses on aspects that are unintended. A model may display the complexities of the object. Attempting to represent the ties among members of a social group, for example, may require the elaboration of a simple model that represents only the presence or absence of a relationship to one that distinguishes types of relationships—attraction, task interdependence, relative status, and so on. Even if a model inadequately represents its object, it can enhance the understanding of that object by exposing issues that need to be addressed. One important class of models—those known as "baseline models"—are developed in order to study how the object deviates from the model's minimal representation. Investigating discrepancies between a baseline representation and the object can direct the construction of a more complex model (Cohen 1963).

The last general function to be noted is that a model can serve to relate what appear to be different phenomena. An abstract model can apply to a variety of different objects, thus calling attention to their common aspects; sometimes, particularly with metaphors and analogies, the features of one phenomenon serve as the model for another. Using drama as a model for everyday interaction calls attention to some common elements (e.g., what it means to play a role).

Berger and colleagues (1980) present a typology of models based upon more specific functions. Although their concern is mathematical models, their typology has more general application; they distinguish: (1) explicational models, (2) representational models, and (3) theoretical construct models. Explicational models are those for which the primary goal is to explicate or render precise one or more concepts. Many social network models are explicational models in that they provide an explication of the concept of social structure (Marsden and Lin 1982). While all models are representational, in this typology the term refers to those models that attempt to represent a particular observed social phenomenon. The majority of models developed in sociology are representational in this sense as long as one has some latitude in interpreting "observed," in many cases, the object of the model is a generalization from observed phenomena. Coleman (1964, 1973) has formulated a number of representational models dealing with social change and with collective action.

Theoretical construct models are those which formalize an explanatory theory. In sociology, these models have focused on a variety of substantive topics as the following examples illustrate: Fararo and Skvoretz (1989) have devised a model drawing on social structural theories of Blau (1977) and Granovetter (1973); Hannan and Freeman (1989) have constructed models of organizational birth and death processes based on bioecological theories; Berger and colleagues (1977) have formulated a model of status characteristic theory (Berger et al. 1966, 1972).

Sociological models are models in a sense that is close to the everyday meaning of model as a replica or representation. It is even reasonable to think of many of them in the other everyday sense, as exemplars, since we can point to sociological research traditions devoted to their development and test. Only with the benefit of more hindsight than is presently available, however, will it be possible to judge whether any of these models are paradigmatic.

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