Theoretical Sociology in the 20th Century

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Theoretical Sociology in the 20th = Century

Thomas J. Fararo
University of Pittsburgh
tjf2+@pitt.edu

Prepared for a Festschrift in = Honor of Linton=20 C. Freeman
Vancouver, B.C., April 16, 2000=20 [Revised: April 21, 2000]=20

ABSTRACT: This chapter discusses theoretical sociology in=20 historical perspective: From the classic tradition to postclassical = efforts of=20 synthesis that culminated in multiple paradigms, to the situation today = in which=20 theorists are more and more constructing formal models as essential = components=20 of their methodology. The classical phase is treated very briefly and = the=20 discussion of the postclassical phase is limited to two major theorists, = Parsons=20 and Homans, in terms of their common focus on the Durkheimian problem of = social=20 integration. The bulk of the chapter deals with developments in recent=20 theoretical sociology. I describe models of structure and of process = before=20 defining two types of models that combine a structural focus with = process=20 analysis. Finally, I set out a general perspective on theoretical model = building=20 and conclude with a discussion of standards in the assessment of such = work.=20

Prelude

This paper is written in honor of the person who had the greatest = influence=20 in shaping my professional career, Linton C. Freeman. It was Lin who = hired me as=20 a research assistant back in 1960 at Syracuse University, for a project = dealing=20 with community power structure that he and others were about to = undertake. I had=20 been a student in an integrated social science program, mainly studying = the=20 history of social thought. Earlier and even then, however, I was reading = the=20 literature of the philosophy of science and this prepared me to become = very=20 enthusiastic about the process of building knowledge. I transferred to = the=20 Department of Sociology to pursue a Ph.D. under Lin's direction and to = continue=20 to work with him and others on research projects.

Lin's own strong commitment to basic science was communicated in = every=20 context of our interaction and further strengthened the more abstract = lessons I=20 was learning through my reading. It was he who brought me into every = phase of=20 the community power structure project from conceptual discussion to = interviewing=20 to data analysis to writing of research reports and an article for = publication=20 in ASR. It was socialization to basic science that, even today, few = students=20 acquire in such depth.

Among other things, when I became aware of a then recent paper by = Rapoport=20 and Horvath (1961) dealing with a new way to analyze large sociograms, I = followed Lin's advice and embarked on learning enough about it to apply = it to=20 our data as my Ph.D. thesis project.

After earning the doctorate, through Lin's influence, I was appointed = to the=20 faculty of the department and assigned to very congenial courses, one or = two of=20 which dealt with formalization problems. These courses allowed me to = communicate=20 my ideas about the philosophy of science and to teach formal logic and=20 axiomatics as well as finite mathematical model building in sociology = (e.g.,=20 finite Markov chains). I felt inadequately prepared in classical = (non-finite)=20 mathematics and applied for and obtained a three-year postdoctoral = fellowship=20 for the study of pure and applied mathematics at Stanford University. = Then, in=20 1967, through Lin's influence I was offered a position at the University = of=20 Pittsburgh where Lin and I resumed our contact for several years. I = remained=20 there for the remainder of my career, while Lin moved on. Here now, in = the=20 twilight of a career that would have been quite different without my = connection=20 to him, I am pleased to present some ideas about sociological theory = that=20 developed over the years.

Overview

This paper discusses theoretical sociology in historical perspective: = from=20 the classic tradition to postclassical efforts of synthesis that = culminated in=20 multiple paradigms to the situation today in which theorists are more = and more=20 constructing formal models as essential components of their methodology. =

The tradition of sociological theory as a whole exhibits a mixture of = three=20 types of sociological interests that I call theoretical sociology,=20 world-historical sociology and normative-critical sociology. I discuss = this=20 mixture in the classical phase and then the remainder of the paper has=20 theoretical sociology as its focus. This focus represents the sort of = basic=20 science interest that Lin communicated to me about forty years ago and = to which=20 I remained committed over the years.

I limit my treatment of the postclassical phase to two theorists, = Parsons and=20 Homans, each discussed in terms of a shift in theory construction = strategy as=20 well as in terms of their common focus on the Durkheimian problem of = social=20 integration.

In analyzing the recent phase of theoretical sociology, I first = discuss the=20 situation of multiple theoretical perspectives and then draw attention = to what I=20 call mutations and new combinations. I emphasize that the role of models = has=20 become a major part of the tradition of theoretical sociology, = describing models=20 of structure and of process before defining two types of models that = combine a=20 structural focus with process analysis. Finally, I set out a general = perspective=20 on theoretical model building and conclude with a discussion of = standards in the=20 assessment of such work.

Phases and Components of Sociological = Theory

Three Phases. In the late 19th and early 20th = centuries, a=20 handful of scholars who by and large worked independently, elaborated=20 conceptions of sociology as a science. Probably the most enduring = contributions=20 were produced by Weber, Durkheim, and Simmel, and, mainly for his = influence on=20 later theorists, Pareto. In addition, Comte and Spencer were important = 19th=20 century precursors. Finally, although neither George Herbert Mead nor = Karl Marx=20 ever elaborated a conception of sociology, their writings have been = incorporated=20 into the tradition. These various writings are commonly referred to as=20 "classical sociological theory" and comprise the first phase of the=20 tradition.

The second phase, which I will call "postclassical," began with = integrative=20 efforts directed toward building a common theoretical framework for = sociology.=20 Influential writers with this ambition included Talcott Parsons and = George=20 Homans, among others. But a unifying framework did not emerge and an era = of=20 proliferation of perspectives took hold under the conception of = sociology as a=20 multiple-paradigm science.

In the recent third phase of sociological theory, the multiple = paradigms or=20 perspectives continue -- with mutations and new combinations -- = alongside=20 renewed efforts to consolidate theoretical ideas. Examples of = commitments to the=20 growth of scientific theories in sociology compete with postmodernist = and other=20 viewpoints that rest upon a repudiation of the entire idea of sociology = as a=20 science.

Three Components. In addition to this phase = description, it=20 is useful to interpret the corpus of writings over these phases as = comprised of=20 three components, reflecting different intellectual interests. In a = simplified=20 model, I suggest just three such components pervade the = entire=20 tradition of sociological theory. (See Figure 1.)

Figure 1. Three Components of = Sociological=20 Theory in the 20th Century

One is the elaboration of ideas relating to the construction of = generalized=20 frameworks of sociological thought. I treat this aspect of classical = theory as=20 the first phase of theoretical sociology, the first of the three = component sets=20 of interests.

A second component relates to an intellectual interest in = world-historical=20 social and cultural forces in the creation of the modern world. Today, = this type=20 of world-historical interest has shifted from modernization to = globalization and=20 postmodernity. One reason for distinguishing this focus from general = theoretical=20 sociology is that it enables a distinction between the importance of a = general=20 theoretical problem and the importance of the empirical instance studied = in=20 terms of that problem. Thus, the evaluation of theoretical model can = occur with=20 respect to empirical instances that have little importance outside this=20 scientific context.

Finally, a third component of the tradition of sociological theory = involves=20 critical normative ideas. It entails evaluation of social phenomena = rather than=20 their explanation or historical interpretation. For instance, from Hegel = and=20 Marx to Habermas, critical theory emphasizes the task of critique of = society and=20 culture in the interests of human emancipation from what it treats as = coercive=20 structures of production and consumption. Feminist theory also has a = primacy of=20 interest in social critique. Although such theories draw upon general=20 theoretical sociology, as does the world-historical orientation, they = foster a=20 primacy of ideology that detracts from the pursuit of an interest in = basic=20 scientific knowledge of social life. Nevertheless, the three components = tend to=20 be interrelated in the literature of sociological theory. As a result, = any body=20 of theory -- or even a single work -- can be regarded as a kind of = weighted=20 combination of the three components. I will illustrate this point in my=20 discussion of the classical phase of sociological theory.

The Classical Phase

For brevity, I select just five classical theorists and present a = compact and=20 brief listing of some of the key ideas of each of them: Mead, Weber, = Simmel,=20 Durkheim and Pareto, organized in terms of the three components. The = format=20 serves to illustrate the three types of intellectual interests that = permeate the=20 tradition of sociological theory. Each theorist's main foundational = contribution=20 to theoretical sociology is also highlighted at the outset of the = listing of=20 sample elements of the three components in that theorist's work.=20

Weber: Social action as a foundation concept=20
- Theoretical sociology. For = sociological=20 purposes, social life consists of complexes of social action that = can be=20 studied by the explicit use of analytic procedures involving = idealization.=20
- World-historical sociology. The = history of=20 the West is one of increasing rationalization trend and its = consequences.=20
- Normative-critical sociology. = Modern=20 rational capitalism is an iron cage.
Mead: Social behavioral foundations of human action=20 systems=20
- Theoretical sociology. Mind, self, = symbols, and institutions are co-emergent in natural evolution. The = starting=20 point for social psychology is the social act as an organized social = activity in which actors take each other's attitudes.=20
- World-historical sociology. Human = history=20 is evolution on a smaller time-scale in which variant institutional=20 solutions arise in relation to common social problems.=20
- Normative-critical sociology. The = basic=20 problem of human society is how to have orderly change and the best = answer=20 to this, so far, is to organize society along democratic lines. =
Simmel: Interaction concept as essential for = sociology=20
- Theoretical sociology. Society is=20 interaction among individuals. The subject matter of formal = sociology=20 consists of forms of interaction, a kind of geometry of the social = world.=20
- World-historical sociology. The = history of=20 the West is one of increasing social and cultural complexity.=20
- Theoretical Normative-critical = sociology.=20 Because culture becomes so complex, the modern individual is in = danger of=20 alienation with a subjective self that is not truly cultivated. =
Durkheim: Integration as a fundamental problem=20
- Theoretical sociology. Neural = networks are=20 to psychic facts as social networks are to social facts. The domain = of=20 sociology consists of social facts that require a distinctive = sociological=20 explanation. Emergent social integration is a key problem of = sociology.=20
- World-historical sociology. The = history of=20 the West is one of increasing social differentiation and its = consequences,=20 such as increasing individuation.=20
- Normative-critical sociology. = Modern=20 societies are not in a healthy state because their moral regulation = has not=20 yet caught up with changes in social relationships, especially in = the=20 economy.
Pareto: System concept as a key tool for = theorizing=20
- Theoretical sociology. Scientific = theory=20 is analytical, which means abstract and, in basic science, involving = the=20 construction of idealized models.=20
- World-historical sociology. = History is a=20 story of interdependent economic, political and cultural cycles.=20
- Normative-critical sociology. = Human=20 non-scientific belief systems, whether religious or secular, are all = ideologies subject to detached critique (the standards for which are = broadly=20 humanistic).
In what follows, my discussion of the postclassical and recent = phases of=20 sociological theory will be limited to theoretical sociology. Figure 2 = outlines the phases of theoretical sociology, showing the foci of = discussion=20 in this chapter.

Figure 2. Three Phases of = Theoretical=20 Sociology in the 20th Century

Postclassical Theoretical Sociology

Although there are various streams of developments in theoretical = sociology=20 that can be traced to the influence of the classical theorists, in this = paper I=20 focus on two theorists with a common background and a common aspiration, = namely=20 Talcott Parsons and George Homans. Both were at Harvard in the 1930s = when the=20 idea of creating a general theoretical sociology was discussed in the = famous=20 Pareto seminar. The keynote for Parsons and Homans was the creation of = an=20 analytical sociological theory that was based upon the classical phase = of=20 sociology and on related empirical research not only in sociology but = also in=20 related fields, particularly anthropology. In each instance, we can = partition=20 the resulting career of theoretical work into two phases marked by a = shift in=20 theory construction strategy.

Parsons: The First Phase. Theoretical sociology was = a=20 central but not exclusive concern of Talcott Parsons and his first major = work,=20 The Structure of Social Action (1937), played a major role = in=20 subsequent developments. He analyzed the writings of the economic = theorist=20 Marshall as well as those of Pareto, Durkheim and Weber. His objective = was to=20 show that these writers had expanded the scope of analytical social = theory=20 beyond the traditions from which they emerged, with their more limited=20 perspectives.

Any analytical theory, Parsons argued, treats only selected aspects = of a=20 complex reality, formulating two kinds of conceptual schemes. One such = scheme=20 specifies a general structural account of the type of empirical system = of=20 interest. It key concepts refer to parts and relations among them. The = other=20 type of conceptual scheme presupposes some sort of structural analysis = and goes=20 on to specify an analytical system, a set of variables and relationships = among=20 them. His convergence argument, he noted, pertained only to structural=20 analysis.

Following Weber and Pareto, Parsons initiates his analysis in terms = of an=20 action frame of reference. He treats social entities such as groups as = systems=20 of social actions. Hence, structural analysis, at this level, will focus = on=20 relations among types of acts so as to describe "the structure of social = action"=20 as a prelude to an analytical theory of such social action systems.

Parsons' basic structural concept is the means-end chain. Each such = chain=20 represents a series of interconnected actions, a kind of path through an = action=20 space. This suggests representing means-end chains by paths in a finite = directed=20 graph. An edge, denoted (m, e), corresponds to an action in which = certain means=20 m are employed toward some end e. Two such edges, (m1, e1) and (m2, e2) = are=20 adjacent when the end point of the first is the means point of the next: = e1 =3D=20 m2. Paths intersect because some means are employed toward the same end = and some=20 ends are means in various further actions.

The structure of this system of social action has three sectors. = Think of the=20 graph in a vertical orientation, the lines point upward. At the bottom = are=20 points with no edges directed to them: they are only means, never ends. = They=20 comprise what Parsons calls the ultimate means sector of the structure = of social=20 action. Similarly, at the top are points such that no edge is directed = from=20 them: they are only ends, never means. They comprise what Parsons calls = the=20 ultimate ends sector of the structure. All other points have edges = entering and=20 leaving them: they are both means and ends. They comprise what Parsons = calls the=20 intermediate sector of the structure. Looking downward, in which ends = control=20 the selection of means, we have a hierarchy of normative control from = the=20 ultimate end sector to the intermediate sector to the ultimate means = sector of=20 the social action system. Moreover, the various ultimate ends (some of = which are=20 diffuse values) are not independent. Connections among them constitute = the=20 emergent property of value-integration, as in the existence of value = systems.=20 When such values are not only connected but are shared among actors, = they are=20 said to exhibit the property of common value-integration.

Parsons argues that the classical phase of sociological theory = converged on=20 the thesis that the emergent property of common value-integration is = essential=20 for social order. His "sociologistic theorem" says that a necessary = condition=20 for social equilibrium (social order) is the existence of a common value = system.=20 He argues that economic and political theories have focused on the = intermediate=20 sector in which actions are means to immediate but not ultimate ends. = Some such=20 ultimate ends are not even empirical. In such cases, Parsons classifies = the=20 corresponding actions as nonrational because there is no scientific way = of=20 saying that the means are inappropriate, in intrinsic or causal terms, = to the=20 attainment of such ends. The actions may be appropriate in some symbolic = sense,=20 as in ritual action. Thus, Parsons' conceptual scheme links the = existence of=20 social order to the nonrational aspect of action systems via the = sociologistic=20 theorem. Moreover, in defining sociological theory as only one of the = analytical=20 sciences of action, Parsons associates it with the emergent common=20 value-integration property and the sociologistic theorem.

Parsons: The Second Phase. In his next major work, = The=20 Social System (1951), Parsons elaborates on the psychological = foundations=20 for this idea, stating what he calls =93the fundamental dynamic theorem = of=20 sociology," drawing upon ideas from Freud that support Pareto's focus on = nonrational elements in social system dynamics. The theorem states that = the=20 stability of social equilibrium requires the institutionalization of a = value=20 system that is also sufficiently internalized in the personalities of=20 members.

Between the first and the second books, Parsons had changed his = theory=20 construction strategy. In the first work, the entire elaborate = discussion of the=20 means-end structure of social action systems was regarded as a = preliminary to=20 the task of constructing an analytical theory. With the conception of = the scope=20 of theoretical sociology as focussed on the emergent property of common=20 value-integration, the analytical variables that were needed would be = value=20 pattern variables -- variables whose combinations could be used to = characterize=20 the dynamics of social action. These led to his famous "pattern variable = scheme"=20 involving such value polarities as universalism versus particularism and = affectivity versus affective neutrality. Combinations of selections from = these=20 value alternatives define value patterns that are definitions of the = directions=20 of action to be expected in social relationships. For instance, in a=20 doctor-patient relationship, the value pattern that defines the = relationship=20 includes universalism and affective neutrality, among other value = elements. In=20 dynamic terms, such value patterns would function as "control = parameters" that=20 enable and constrain actions in the hierarchy of normative control.

However, at some point, Parsons became convinced that a = simplification of the=20 theory task would be required. This took the form of forgoing a true = dynamic=20 analysis with derived equilibria in favor of a focus on a social system = as a=20 "going concern." For each social relational nexus satisfying this = condition, the=20 corresponding value pattern is treated as a pattern tending to be = maintained=20 despite disturbances. Thus the problematic feature for theory was to = describe=20 the mechanisms that tended to counteract disturbances and thereby to = help=20 maintain the pattern. The theory becomes structural-functional with its = focus on=20 mechanisms of socialization and social control.

In turn, the elaboration of this structural-functional type of = theorizing=20 eventually led to two related classifications, one of social structural = parts=20 and one of social functional subsystems. The four types of social = structural=20 parts are values, norms, collectivities and roles. For instance, in = American=20 society, there is a diffuse value of freedom with its implementation in = diverse=20 norms, such as the normative conception of a free press. In turn, this = norm is=20 embodied in numerous collectivities, such as news organizations, that=20 disseminate ideas through the specialized activities of people acting in = such=20 roles as editor, reporter and the like.

To define and analyze functional systems, Parsons applies a general=20 conceptual scheme for functional analysis. The starting point is that = any system=20 of action is said to have four key functional problems: (latent) pattern = maintenance (L), integration (I), goal-attainment (G) and adaptation to = the=20 environment (A).

As applied to what we might call a societal action system, the four = types of=20 functional problems are specified, respectively, in the reverse order, = in two=20 steps. In the first step, this action system is modeled as a system with = four=20 types of interdependent functional subsystems: cultural systems (L), = social=20 systems (I), personality systems (G) and behavioral systems that adapt = to the=20 biophysical environment (A). What is normally called "the society" is = the most=20 inclusive social system in this analysis of the societal action system, = so that=20 its environment consists of cultural systems as well as the personality = and=20 behavioral systems of its members. Then the analysis of a society, in = this=20 sense, proceeds by four-function analysis once again. In AGIL order, the = society=20 as an integrative system of action (I) has four functional problems: = economic=20 (collective adaptation to the action and biophysical environments, IA),=20 political (collective goal attainment, IG), social integrative (II), and = fiduciary (maintenance of the cultural traditions, IL). Corresponding to = these=20 four problems are four interdependent functional subsystems of the = societal=20 action system: economy, polity, societal community and fiduciary = system.

Linking the two conceptual schemes for structure and function, for = instance,=20 yields political values, political norms, political collectivities and = political=20 roles as the structural components involved in the polity. These units=20 interpenetrate with the components of all the other systems because the = same=20 people who act in political roles (e.g., voter) perform actions in other = roles=20 (e.g.. consumer). Thus, functional connectivity characterizes the = partial=20 differentiated structures (assuming here a modern differentiated = society).

In this conceptual scheme, in principle, each analytical theory of = action has=20 a scope that corresponds to one or more functional subsystems. The = analytical=20 focus of theoretical sociology, in this four-function perspective, is = the=20 integrative subsystem of any social action system. This is a "system of=20 solidarities" to use the nice terminology of Baum (1975). The focus is = on the=20 problematic integration of a social system. In the limit, the system may = consist=20 of a single collectivity without subcollectivities. In another = direction, it may=20 consist of a huge number of intersecting subcollectivities but not = itself form a=20 single collectivity. Finally, it may be both "many" and "one," in the = sense that=20 it is both a single collectivity and has plural subcollectivities within = it. For=20 instance, at the societal level, the term "nation" points to a single = solidary=20 system, a collectivity, but the nation will be comprised of intersecting = subcollectivities. In short, as in Durkheim, the fundamental theoretical = problem=20 of sociology is social integration at any level of social life, the = "double I"=20 (II) problem in Parsons's four-function scheme.

In general, Parsons seems to have an image of a tree of analytical = theories,=20 each scope-defined:=20

Cultural theory (L)=20
Social theory (I)=20
- Fiduciary theory (IL)=20
- Solidarity theory (II)=20
- Political theory (IG)=20
- Economic theory (IA)
Personality theory (G)=20
Behavioral theory (A)

The analytical view of theoretical sociology as focussed on the = problem of=20 social integration or solidarity (II) leads to a specification of a = fundamental=20 problem: What holds society together? It has been framed as the problem = of=20 order. From Hobbes to Parsons to Dahrendorf (1959) and into recent = theory, the=20 problem has a long history in social theory. For instance, Dahrendorf = criticized=20 Parsons' approach to the problem, revising Marx's coercion-based = approach to=20 make power relations central. Subsequently, Collins (1975) attempted a = synthesis=20 of Durkheimian theory with this Dahrendorf-type of conflict theory. = Actually,=20 Dahrendorf makes legitimacy a fundamental feature of his treatment of = power=20 relations, thereby invoking values and norms and taking the sting out of = his=20 critique of Parsons' treatment of the problem.

However, criticism of Parsons' theory came not only from those who = favored a=20 conflict theory perspective but also from theorists adopting other = perspectives.=20 Prominent among these was George Homans. His early work initiated = another mode=20 of generalized synthesis in theoretical sociology that led to a second = phase=20 that itself drew considerable critical reaction.

Homans: the First Phase. In the first of his two = major=20 theoretical works, The Human Group (1950), Homans argued = that the=20 creation of theoretical sociology should begin with a scope restriction = to small=20 groups, defined as those in which each member could interact with every = other=20 during the time the group meets. In framing a general theoretical = problem,=20 Homans asked: What makes customs customary? In other words, how do we = account=20 for order? The problem is framed at the elementary level of interaction = and=20 pertains to the emergence, maintenance or change of systems of social=20 relationships among persons. Order in the form of social integration is=20 explained through an emergent "internal system," given external = conditions.=20 Social bonds among members and shared norms are generated by mechanisms = that are=20 described in terms of specific hypothesized linkages among analytical = elements=20 pertaining to activities, sentiments, and interaction. For instance, the = more=20 frequently people interact with each other, the more similar their = sentiments,=20 normative ideas and activities become. Far more clearly than in Parsons' = work, a=20 system of variables and their relationships is specified so as to = undertake the=20 verbal equivalent of the sorts of steps that are taken in the = mathematical=20 analysis of a dynamical system model.

Moreover, Homans synthesizes classical ideas within his theoretical=20 framework. For example, in treating social control, the Durkheimian idea = of the=20 ritual effects of punishment is embedded in the discussion of the = stability=20 analysis of equilibrium states. In addition, he delimits the scope of = two=20 seemingly opposing theories of ritual -- those of Malinowski and=20 Radcliffe-Brown, respectively -- before reconciling them, i.e., = integrating=20 them. In short, Homans' social system theory is in the Durkheimian = tradition,=20 although critical of functionalist arguments that do not specify = mechanisms that=20 account for the emergence and stability of equilibrium states.

If Homans' analytical hypotheses or laws describe group dynamics and = the=20 build-up (or dissolution) of a group, what explains the laws? In = searching for=20 this more fundamental level of theorizing, Homans invoked a conceptual = scheme=20 from behavioral psychology in the next phase of his theoretical work = (Homans=20 1961, 1974). Interaction is an exchange involving material and = non-material=20 goods, and social approval is a fundamental category of social = reward.

Homans: the Second Phase. Just as Parsons had = changed theory=20 construction strategy between his first and second major works, so did = Homans.=20 From a theory as modeled on a system of differential equations, he moved = to=20 theory as a system of propositions forming a deductive system. The = behavioral=20 principles have the function of covering laws in logical arguments that = explain=20 regularities in social life, including the results of experimental = social=20 psychology as well as field studies of the sort analyzed in the earlier=20 work.

We can interpret the basic logic of this approach as reduction in the = sense=20 of explanation of social life from a non-social foundation. This is = somewhat=20 analogous to the explanation of molecular levels of existence from a = purely=20 atomic basis. Critics might ask: What if atoms only could have the = postulated=20 properties they have if these properties emerge out of molecular = relations? Then=20 this sort of organic relationship makes reduction nonsense. Similarly, = if=20 individuals are socialized beings, how can their interaction explain = social=20 order? You are simply presupposing what is supposed to be explained.

But there is a response to this criticism. In Homans' behavioral = theory, the=20 fundamental unit is not the person but the behavioral act. The person as = a=20 complex socialized entity is not the subject matter of interest to = Homans,=20 although such a system -- corresponding to Parsons' personality system = -- is=20 within the scope of the behavioral theory. In other words, Homans has a = tree of=20 theory with a basic behavioral or action theory at its root and with a = number of=20 branches. Given his commitment to analytical theory, he pursues just one = branch,=20 namely the one that deals with the problem of the integration of the = actions of=20 plural persons to form a dynamic social system with emergent patterns of = order.

In this interpretation, Homans can agree with the classical = sociological=20 theorist Charles Cooley who argued that individual and society are = "twin-born,"=20 in that the person is socially constructed in social interaction and = that a=20 society is a system of interaction. In practice, then, Homans took mind, = self=20 and symbols -- three important elements from the Cooley-Mead standpoint = -- as=20 givens in the pursuit of a pure theoretical sociology that would = formulate and=20 explain group processes.

In taking this approach, Homans accompanied his work with a polemical = argument. He took aim at Durkheim, who had argued that what explanation = means=20 for sociological theory is a causal account that remains at the level of = social=20 facts. For instance, to explain varying rates of deviance in groups, = Durkheimian=20 theory would point to varying levels of solidarity: the greater the = solidarity=20 of the group, the lower the rate of deviance from its norms. (See Figure = 3.)

Figure 3. Durkheimian Social = Generativity=20 via Homans and Coleman

What Homans argued was that such a proposition, if it is true, could = be=20 derived logically from a behavioral foundation. For instance, in a = highly=20 solidary group, members experience or can anticipate high costs in lost = social=20 approval for deviation from group norms, while in a less solidary group, = such=20 costs are lower. Solidarity or cohesion is "micro-translated," to use = Collins'=20 (1981) term, in such an explanation. Then the behavioral mechanisms are = able to=20 explain why varying rates of solidarity lead to varying rates of = deviance. In=20 this way, Durkheimian explanation is cause-effect explanation while = behavioral=20 explanation can be seen as providing the mechanism that, logically = speaking, is=20 invoked through covering laws drawn from behavioral psychology. = Combining the=20 two, we have what I have called "Durkheimian social generativity" = (Fararo 1989a:=20 Ch. 2).

The Recent Phase of Theoretical = Sociology

I will treat the recent phase of theoretical sociology in two steps. = In the=20 first, preliminary step, I discuss the current state of the field in = terms of=20 the existence of multiple theoretical perspectives inherited from the=20 postclassical phase but undergoing a process that I describe as = producing=20 mutations and new combinations. In the second, more extensive step, I = turn to=20 the growing use of formal models in theoretical sociology.

Theoretical Perspectives. During the postclassical = phase of=20 theoretical sociology and amidst its proliferation of perspectives, a = book=20 appeared that shaped the way many sociologists reflected upon theory in = their=20 discipline. Thomas Kuhn=92s The Structure of Scientific Revolutions = ([1962], 1970)=20 argued that a normal science is characterized by a shared paradigm but = that=20 there are also revolutionary episodes in the history of science = involving=20 paradigm shifts.

In application of the paradigm concept to sociology, commentators=20 characterized the field as one with multiple paradigms, usually called=20 theoretical perspectives. By the late 1970s, most texts reflected this=20 consensus, featuring separate chapters on functionalism (Parsons), = conflict=20 theory (both critical theory and the Dahrendorf tradition), exchange = theory=20 (Homans), symbolic interactionism (Blumer), structuralism (French and = American=20 versions), and phenomenology (social constructionism and = ethnomethodology).

To make the picture even more diverse, two other developments = occurred.=20 Feminists launched a wide-ranging critique of sociological theory and = helped to=20 make the study of gender a key research topic. Postmodernist = sociologists=20 attacked the project of sociological theory as a continuation of the=20 Enlightenment=92s grand narrative with scientific pretensions that could = not=20 succeed. Critics respond by attacking the cognitive relativism of this=20 approach.

Some commentators argue that there is no possibility of placing these = paradigms under a common intellectual framework, thereby seeing the = discipline=20 as permanently fractured and at war with itself. Others regard the = situation as=20 a positive one, emphasizing the importance of diverse viewpoints that = could be=20 brought to bear on any particular feature of social life. Still others = recognize=20 the diversity but argue for integrative theorizing, as we shall see = below.

The most prominent mid-century efforts in theoretical sociology that = aimed=20 toward generality and synthesis -- the ideas of Parsons and Homans = described=20 earlier and a strong integrative effort by Blau (1964) - have failed on = the=20 criterion of acceptance as the paradigm of general theoretical = sociology. Yet=20 the spirit of what they tried to accomplish is not gone. We can call it = "the=20 spirit of unification," meaning a value-commitment to generalizing = synthesis=20 efforts in episodes of consolidating components of distinct theoretical = systems=20 (Fararo 1989b). Robert Merton emphasized this idea in his often-cited = paper "On=20 Sociological Theories of the Middle Range" (included in ([1949] 1968). A = middle=20 range theory employs a general conceptual scheme with analytical = elements, but=20 it is scope-restricted to some abstractly specified class of empirical = systems,=20 e.g., thermodynamic systems. It explains intuitively very different = empirical=20 systems using the same analytical elements and laws that do not exhaust = the=20 content of the empirical system. In short, a middle-range theory is an=20 analytical theory. Its scope is limited in the sense of dealing only = with=20 certain analytical elements, not in the sense of dealing only with a = class of=20 concrete entities as classified in folk culture.

Recent Developments. A value-commitment to the = construction=20 of limited-scope but abstract theories coupled with a recursive process = of=20 integration of such theories may well be a plausible path for the = advance of=20 theoretical sociology. At present, this approach is most strongly=20 institutionalized in the field of research known as group processes, in = which=20 theorists elaborate and integrate their theories over time in connection = with=20 the construction of experimental situations that provide opportunities = for=20 testing the implications of theories. Long-term theoretical research = programs,=20 spanning decades, have characterized some of this work. For instance,=20 expectation states theory and exchange network theory are two such = programs=20 among others (see Berger and Zelditch 1993). These programs are a kind = of=20 mutation out of the earlier small group research of the 1950s and early = 1960s,=20 many of them influenced by the work of Homans.

Other recent developments indicate other mutations in the paradigms = and the=20 emergence of new paradigms. Three such developments may be noted:=20 neofunctionalism, social network analysis, and rational choice = theory.

Neofunctionalism is a mutation of Parsons' theory. It departs from = his=20 four-function paradigm in a number of ways that reflect the influence of = external critiques. For instance, Alexander (1985) tries to incorporate = ideas=20 from various perspectives, including conflict theory and symbolic=20 interactionism. Much of neofunctionalist writing is focussed on = historical and=20 normative interests. The revised functionalist framework is employed to=20 interpret historical situations, e.g., in terms of a baseline social=20 differentiation trend (Alexander and Colomy 1990).

One of the new paradigms is social network analysis. Although social = system=20 theorists such as Parsons and Homans employed the network concept as a = metaphor,=20 they did not employ formal tools. By contrast, the social network = paradigm=20 incorporates a strong mathematical and statistical foundation in a = program of=20 cumulative research on the properties of social networks. In the = following=20 section of this paper, when I discuss structural models, I will pick up = on this=20 discussion of social network analysis.

Rational choice theory has departed from the behavioral psychological = foundation that Homans advocated, often favoring a more mathematically = tractable=20 rational choice approach. Coleman (1990) presented his foundations of = social=20 theory as directed to resolving the micro-macro transition problem that = Blau's=20 (1964) earlier effort had defined. On the one hand, he endorsed Parsons' = action=20 framework with its concept of purposive action and repudiated the = transition to=20 structural-functional analysis. On the other hand, he endorsed Homans'=20 methodological individualism and repudiated the transition to reduction = in terms=20 of behavioral principles.

In Coleman's theory, macro-level systemic givens constrain and enable = micro-level situations of actors. Making rational choices based on their = internal preferences and the situational constraints, actors then = collectively=20 shape macro-level outcomes. This is not equivalent to Homans' reduction = program.=20 Among other things, it is a trade-off of behavioral realism for the = deductive=20 fertility that optimization arguments enable. Homans is much more = attuned to the=20 task of the scientific theorist: to explain empirical findings. = Coleman's=20 theory, in part, is more in the classical tradition of sociological = theory as a=20 whole in that it blends general theoretical, world-historical and = normative=20 interests.

A key contribution of sociological rational choice theorists has been = their=20 sharp theoretical focus on variants of the basic problem of order or=20 integration, treating solidarity, coordination, cooperation, and trust. = At the=20 same time, the synthesis of the Durkheimian theory of solidarity with = conflict=20 theory undertaken by Collins provides a different middle-range = perspective on=20 the problem of social integration. I have pointed out the centrality of = this=20 problem in the tradition of theoretical sociology. Now, with such = explicit=20 theories treating it, the problem may well constitute an important locus = of=20 episodes involving theoretical unification. In addition, some of this = work=20 illustrates the use of mathematical models in relation to sociological = theory=20 (Doreian and Fararo 1998). Model building can fulfill a variety of = goals,=20 including the clarification of concepts, the representation of = processes, and=20 the specification of theoretical constructs that explain a variety of = phenomena=20 (Berger et al 1962). Such formal model-building developments are of = growing=20 importance in recent theoretical sociology, a topic to which I turn at = this=20 point.

Formal Models in Theoretical = Sociology

A model is an abstract entity that functions as a representation of = some=20 system in the world that is of sociological interest. My aim now is to = discuss a=20 variety of types of models that theoretical sociologists have employed = in the=20 analysis of social structures and social processes. Thereafter I will = treat the=20 philosophy and methodology of model building in more general terms. It = should be=20 noted that the term "model" is used in sociology in diverse ways. Very = often it=20 refers to statistical models employed in the analysis of data. This = usage is=20 excluded from this discussion, which is focused on models and model = building in=20 relation to sociological concepts and theories. Also excluded is the = diffuse=20 idea of a general model of society as a kind of social organism.

In the present context, a model is a formal object functioning as a=20 representation of some structure or process of sociological interest. A = type of=20 model is constructed, generally, as an implementation of a = representation=20 principle (Fararo 1989a: Ch. 1), a claim that a certain category of = phenomena=20 can be modeled in some specified way. In what follows, some important=20 representation principles associated with the concept of social = structure are=20 described, and then the discussion turns to models of social = processes.

Models of Social Structure

Sociologists have employed at least four different types of models in = the=20 analysis of structure in social life. We may regard these as four = representation=20 principles under the headings: structure as network; structure as = distribution;=20 structure as grammar, and structure as game. One aspect of recent = theoretical=20 sociology is the use of combinations of these models in developing = theories.=20 Thus, the four types of models form a set of interrelated conceptual = elements=20 (see Figure 4).

Figure 4. Four Interrelated = Representations=20 of Structure in Social Life

Structure as Network. The metaphor of a social = system as a=20 network, widely employed informally in sociology, was transformed into a = mode of=20 model building and analysis through a convergence of ideas and = techniques from=20 several traditions. One such source was sociometry (Moreno 1934), = involving the=20 analysis of network diagrams indicating relationships among people in a = small=20 population. A second source was balance theory, which deals with = configurations=20 of positive and negative sentiments. The theory was absorbed into social = network=20 analysis via the formalization of the configurations of sentiments in = terms of=20 signed graph theory (Harary, Cartwright an Norman 1965). A third source = was the=20 analysis of structures of kinship, especially after the publication of = an=20 influential monograph by White (1963). Sociometric models, = balance-theoretic=20 models, models of kinship structure, as well as numerous other = model-building=20 efforts -- such as those treating social diffusion and small worlds -- = converged=20 by the late 1970s and the term "social network paradigm" was used to = describe=20 this whole area of model building (Leinhardt 1977). Over time, it became = common=20 for measured properties of networks -- for instance, centrality (Freeman = 1977,=20 1979) -- to be employed in the formulation and testing of empirical = hypotheses=20 about the behavior of actors. By the end of the 20th century, social = network=20 analysis had become a mode of structural analysis with an extensive = battery of=20 formal techniques at its disposal (Scott 1991; Wasserman and Faust, = 1994). The=20 close connection between formal representation, concept formation, and=20 application makes it a domain of social science that strongly exhibits = what=20 Freeman (1984) has described as "turning a profit from mathematics."

Structure as Distribution. However, social network = analysis=20 has been regarded by most macrosociologists as not the sort of model = required=20 for the description of macrostructure. Sociologists often speak, in the = latter=20 context, of such entities as "occupational structure" or "income = structure."=20 These terms refer to distributions. Blau (1977) proposed a systematic = theory in=20 which the key analytical properties of such distributions, in relation = to rates=20 of intergroup relations, provide one type of answer to the Durkheimian = problem=20 of the nature of the integration of a large complex social system. Blau = employed=20 the concepts of heterogeneity, inequality, and consolidation as such key = parameters and formulated theorems relating them to the extent of = intergroup=20 relations, e.g., rates of intermarriage.

A definite model that would represent such a macrostructure was not a = part of=20 this theory, but subsequently Skvoretz and myself formulated a = mathematical=20 treatment (see especially Skvoretz 1983). It drew upon developments in = the=20 application of the theory of random and biased nets (Rapoport and = Horvath 1963;=20 Fararo and Sunshine 1964). Thus, structure as distribution is linked to=20 structure as network. All the key parameters of Blau=92s theory are = formally=20 linked to key parameters of the biased net model - in particular, the = contact=20 density, the connectivity of the network and, in a later development, = the=20 strength of weak ties. (A summary of the formalization is presented in = Fararo=20 (1989a: Ch. 4).) This development, which we call formal macrostructural = theory,=20 was undertaken in "the spirit of unification" in theoretical sociology = (Fararo=20 1989b).

Structure as Grammar. A third type of model of = structure=20 emerges out of the language analogy or metaphor employed in one wing of=20 structuralist thought based upon the work of Saussure (1966 [1915]) and = Chomsky=20 (1957). This form of structuralism has been a perspective based on the = idea that=20 in some sense, that social and cultural systems should be treated with a = language-like model (Levi-Strauss 1963 [1958]). One implication of this = idea is=20 abstraction from time: the system exists as an infinite totality to be = analyzed=20 by algebraic or other formal tools.

Another strand of such work has been more process oriented, employing = the=20 idea that a set of finite recursively applied rules generates a system = of=20 symbolically mediated interactions comprising a domain of = institutionalized=20 social action (Fararo and Skvoretz 1984). The formalism is drawn from = cognitive=20 psychology (Newell and Simon 1972). The resulting model can be studied = from two=20 points of view. On the one hand, the finite rule basis and the = institution stand=20 to each as grammar and language: the analysis is in the spirit of = structuralism=20 (Skvoretz and Fararo 1980). On the other hand, the finite rule basis can = be used=20 to analyze a system of symbolic interaction as it is generated locally = and in=20 real time (Skvoretz and Fararo 1996b). This type of model is one among a = variety=20 of those that draw upon techniques from artificial intelligence and = cognitive=20 science (Bainbridge et al 1994).

I pointed out earlier how structure as distribution was integrated = with=20 structure as network in formal macrostructural theory. A similar effort, = not=20 discussed here (see Fararo and Skvoretz 1986), links structure as = grammar with=20 structure as network, drawing upon an abstract algebra of = interpenetration=20 framed in network terms to formally represent hierarchical levels of=20 institutional structure (Fararo and Doreian 1984).

Structure as Game. A fourth representation of = structure=20 employs game theory. A play of a game is analogous to an utterance in a=20 language, wherein the rules of the game play the role of the grammar. = Given such=20 rules, a tree of possible sequential plays of the game is implied, = called the=20 game in extensive form. However, as distinct from grammatical analysis, = the=20 focus in game-theoretic analysis is on strategic interaction, so that a = model of=20 rational choice usually supplements the game model. The aim of the=20 game-theoretic model-builder is to derive the consequences of rational = choices=20 on the part of each player, often with a view of showing how outcomes = involve=20 "perverse effects" (Boudon 1982). Thus, the game model is an alternative = to the=20 grammatical model that emphasizes emergent order at the level of the = tacit or=20 implicit rules governing institutionalized social action. The game = model, by=20 contrast, emphasizes the way in which the structure, as represented by = the game,=20 produces predictable but often-paradoxical effects from the conjunction = of=20 rational choices.

It turns out that structure as game has been linked to structure as = network.=20 A good example is the use of game-theoretic ideas to arrive at = theoretical=20 predictions of outcomes of network exchange experiments (Bienenstock and = Bonacich 1992). This type of theory actually combines structure as game = and=20 structure as network with structure as distribution because the outcome = of any=20 exchange process in a network is a distribution of resources among the = players.=20 The theory shows how and why this distribution depends upon the shape of = the=20 network. Another example of the linkage of game and network = representations=20 occurs in some of the work of Peter Abell (1989).

Process Models

The postclassical theoretical sociologists Parsons and Homans (among = others)=20 were committed to the project of bringing dynamic analysis into = sociological=20 theory. No clearer example of this exists than in Homans=92 treatment of = the=20 social system in The Human Group (1992 [1950]). So clearly = did=20 Homans try to model his discursive analysis of group phenomena on the = set-up and=20 analysis of a system of differential equations that shortly after this = book=20 appeared it was formalized as such by Herbert Simon (1952), including an = early=20 treatment of nonlinear dynamics with multiple equilibria.

Coleman (1964), responsive to the needs of survey research with its = discrete=20 data summarized as proportions, developed a family of dynamic models = that are=20 stochastic processes in continuous-time. Each individual makes = transitions from=20 one discrete state to another - for instance, shifting candidates during = an=20 election campaign - and the group makes transitions among states = representing=20 the number of individuals in each of the discrete individual states = (e.g., the=20 number of people favoring a particular candidate at a particular time.) = This=20 Coleman methodology extends to the social network context in which each=20 individual=92s transition is influenced by a composite flow of influence = from=20 other individuals to whom the person is connected in some social = relationship.=20

The most general way of thinking about processes is in terms of the = concept=20 of a behavior manifold (see Figure 5, upper part). This consists of a = parameter=20 space together with a state space, both multidimensional. Given a time = domain=20 and a generator, the parameterized process is the tracing out of = trajectory in=20 state space. For any given value of the parameter, apart from transient = states,=20 there may be various types of attractors (generalized forms of = equilibrium) as=20 well as repellors (unstable equilibria). For instance, the nonlinear=20 Simon-Homans model, under some conditions yields a configuration of two=20 attractor states separated by a repellor. Thus, when an initial state is = close=20 to the repellor it departs from it toward one or the other attractor. = The whole=20 subject of nonlinear systems is framed in terms of such generated = configurations=20 in state space that vary with parametric conditions. Special cases of = the=20 general dynamical system include topics catastrophes and chaos as well = as=20 classical linear system dynamics where equilibrium, if it exists, is = unique. For=20 an extended discussion, see Fararo (1989a: Ch.2).

Figure 5. Process and Social=20 Structure

Models Combining Structure and = Process

Of particular interest in sociology are two types of process models = that=20 relate to the concept of social structure. (See Figure 5, lower part.) = In one=20 type, a network or some other model object represents the structure, and = other=20 phenomena, say X, are taken as defining the state space. The aim is to = show how=20 the outcome of a postulated process with respect to X varies with = parameters=20 descriptive of the social structure. In the other type of model, the = structure=20 is treated as emergent. An interaction process model involving = "E-states" may=20 serve to illustrate (Skvoretz and Fararo 1996). The process involves the = over-time construction of stable relationships among pairs of actors = until=20 equilibrium, when the postulated rules lead to social reproduction of = the=20 relational pattern. The process is the trip through a state space of = possible=20 forms of the emergent local social structure. Which trip is taken, in = terms of=20 which network states are visited, depends upon the initial state, the=20 parameters, and the specific realization of the stochastic process=20 representation of the generator.

General Considerations

I conclude this paper with a presentation of a conception of how to = think=20 about models in relationship to the knowledge process as involving = theories,=20 data and the relationship between them. The following discussion relates = to=20 Figure 6.=20

Figure 6. Theoretical Model = Building=20

Framework, Problem and Model. Sociologists, like = other=20 social scientists, use the term "theory" to cover both general = frameworks and=20 more specific formulations that address particular problems. This double = usage=20 can be articulated to the model concept. Namely, we think of a = scientific theory=20 as having two levels, a framework level and a model level. The two are = linked by=20 theoretical problems that are addressed by constructing a model within = the=20 framework.

Suppose that T is a general theoretical framework, comprised of = general=20 concepts and principles. Often a formal theoretical framework will = contain what=20 I will call a "template," meaning a general form of a model that needs = to be=20 "filled-in" with more definite terms. For instance, the Newtonian = framework=20 contains the famous F =3D ma formula that provides a template for = mechanical=20 models.

Associated with the T-framework will be various problems, for = instance,=20 phenomena calling for an explanation, a "T-problem." The theorist will = invoke=20 the T-framework to address a T-problem in terms of theoretical methods = to=20 generate a theoretical model appropriate to the problem, call it a = T-model.

In addition, investigators will employ empirical methods to generate = data=20 appropriate to the problem. In particular cases, this is followed by = such=20 procedures as parameter estimation and calculations of empirical = predictions.=20 The comparison of the latter with properties of the body of data may = show=20 discrepancies that, in turn, may lead to revisions of the theoretical = model, to=20 questioning the quality or relevance of the data, to a reformulation of = the=20 problem, or a revision of the general framework itself. Even the = worldview is=20 not immune from rethinking, although this would be a last resort to = resolve some=20 intolerable inconsistencies not only between data and models but also = between=20 different frameworks within a research tradition.

In the event of a favorable assessment of the theoretical model, a = natural=20 step would be extension of the scope of the theoretical model through = removal of=20 analytical restrictions that were introduced to facilitate a first = theoretical=20 approach to the problem.

This sketch works best when the framework entails formal model = building. Let=20 me illustrate with a sociological example. In the recent phase of = theoretical=20 sociology, Coleman (1990) constructed a framework with both a = metatheoretical=20 template and a theory template. The former consists of an already famous = "boat"=20 diagram in which -- in one interpretation -- a given macro initial = condition M0=20 produces an outcome macro-state M1 via three linkages. First, there is a = linkage=20 from macro M0 to micro m0, interpretable as an actor with socially = induced=20 preferences in a situation with opportunities and constraints. Second, = there is=20 a link from m0 to m1, an act by that actor, postulated, as a first=20 approximation, to be a rational choice. Then, third, some mechanism = combines the=20 acts of the various actors to generate the macro outcome to be = explained, a link=20 from m1 to M1. This metatheoretical template serves to orient theorists = to=20 construct models that explain macrosociological causal relations by = postulation=20 of theoretical models that incorporate the three types of links.

Coleman's theory template is a generalization of the logical = structure of=20 general equilibrium theory in economics, compactly represented in two = matrices.=20 First, there is a matrix in which there is a distribution of rights of = control=20 of a set of resources among a set of actors. Second, there is a matrix = of the=20 distribution of each actor's interests over the same resources, where = the=20 interests are parameters in a Cobb-Douglas utility function. The = template then=20 invokes an exchange process to carry the state of the control matrix = from its=20 initial state to an equilibrium state. In this process, each actor's = utility=20 function is maximized subject to constraints. Thus, to create a = theoretical=20 model based on this framework means to specify the actors, the = resources, and=20 the initial control relations and interests. Thus, in Coleman's = structure of=20 theory, the exchange theory template satisfies the metatheory template = and in=20 turn exchange models created within the framework are designed to = satisfy the=20 theory template. For instance, one theoretical problem that Coleman = poses is:=20 How do norms emerge? The theoretical model he proposes employs the = theory=20 template to address this problem. Coleman includes conditions necessary = for "the=20 demand for a norm" to arise and also conditions necessary for effective=20 enforcement of the emergent norm.

A somewhat different and briefer example may be given in terms of the = use of=20 the construct "E-state," mentioned earlier. E-state structuralism is a=20 theoretical method, functioning as the basis for model of network = dynamics in=20 which actors hold evolving expectation states with respect to each = other, as in=20 a small group discussion setting (Skvoretz and Fararo 1996). In this = instance,=20 the framework is the core of expectation states theory itself with its = principle=20 that relational expectation states arise out of social behavior and then = come to=20 form stable bases for the control of such behavior as indicated by = differential=20 rates of participation in group discussion. Given the problem of = describing such=20 an interactive process in detail, the E-state structuralist method, as = combined=20 with several other ideas, yields a model that makes detailed = predictions.=20 Preliminary tests of the model were undertaken but it was clear that far = more=20 detailed interaction data were required. In turn, this led to further = empirical=20 inquiry to generate this more appropriate body of data to permit more = refined=20 tests of the predictions yielded by the dynamic model. This example, = then,=20 illustrates some of the dynamic aspects of the interplay of two modes of = implementation of a theoretical framework, one involving theoretical = methods=20 that aid in the construction of theoretical models and the other = involving=20 empirical methods that aid in the collection of appropriate data.

Although these ideas about theoretical frameworks, theoretical = problems and=20 theoretical models were devised with formal theories in mind, they also = enable=20 us to interpret the logical structure of theoretical work that is not = formal.=20 For instance, let T be a structural-functionalist theoretical framework. = One=20 T-problem is to explain the universality of stratification, which is = understood=20 within the T-framework to refer to rewards, especially prestige, = assigned to=20 positions in a social system. The famous Davis-Moore theory of = stratification=20 can be interpreted as a T-model proposing a theoretical solution of this = problem. Employing some ideas about motivation, what the authors do is=20 equivalent to proving a theorem about the T-model: If a social system, a = system=20 of interrelated positions, is stable, then that system is stratified. = Hence,=20 stratification is a necessary condition for social order.

To derive empirically testable claims that can be compared with = appropriate=20 data, a formalized functional approach would be helpful. For instance,=20 Stinchcombe (1968) represents functional arguments in terms of a = negative=20 feedback or homeostatic system. The problem of appropriate data for the=20 empirical assessment of such functional models is addressed by Faia = (1986).

Representation, Idealization and Approximation. The=20 connection between sociological frameworks and formal model-building = will become=20 much closer as theoretical sociologists become more explicitly oriented = to three=20 basic aspects of theoretical model-building, namely representation, = idealization=20 and approximation (Fararo 1989a: Ch.1). Representation is the core idea = of model=20 building and, therefore, in the context of constructing effective = theoretical=20 frameworks in sociology an essential aspect of theory development. = Berger et al=20 (1962) set out an important statement of the linkage between theoretical = goals=20 and model building. In their terms, there are three basic goals that = motivate=20 the construction of a model: to explicate a concept of a theory, to = represent a=20 recurrent process, or to formalize a theory in terms of some theoretical = construct.

The role of idealization in sociology was recognized by the classical = sociologist Max Weber, who used the term "ideal type" for "model." A = model is=20 based upon an act of abstraction. Only selected aspects of a concrete = reality=20 are represented. Even key features of reality may be omitted in this = process in=20 order to study a "pure" case. For instance, economic theorists define = and study=20 general equilibrium models of perfectly competitive economies. As of the = late=20 20th century, however, this important role of idealization has not yet = found its=20 way into most theoretical work in sociology. An exception occurred in = the work=20 of Coleman (1990) in his adoption of the economic approach, formulating = the=20 concept of a "perfect social system" and employing a general equilibrium = theory.

The role of approximation is closely related to the logical = derivation of=20 properties of a theoretical model. For instance, a complex mathematical=20 expression may be approximated by a simpler one that enables deductions = that=20 would not otherwise be obtained.

Standards in Theoretical Model Building. Implied in = this=20 entire discussion of formal models in theoretical sociology is some = conception=20 of cognitive standards for the construction and assessment of models. = Lave and=20 March (1975: Ch. 3) have produced a lucid discussion of such standards. = Two=20 groups of standards they explicate under the headings of truth and = beauty,=20 respectively.

I will discuss one of the standards of truth. There is general = agreement=20 among philosophers of science that a model is not really a theoretical = model=20 unless it can be shown to be wrong in relation to the world. This is = what Lave=20 and March call "the importance of being wrong." The comparison operation = mentioned earlier bears upon this aspect of model building. The standard = may be=20 called "truth," but idealization and approximation have to be taken into = account. The more precise the prediction made by a model the more likely = it is=20 to be untrue in the strict sense. The real point is that the development = of our=20 collective grasp of the world in respect to the problems we pose is = under=20 empirical control as well as informed by conceptual schemes and = theories.=20 Another important point is that the generality of a framework enables=20 alternative models to be constructed. In addition, it may be that a = given=20 problem can be re-framed so as to enable a quite different framework to = be=20 employed in the construction of an alternative model. In principle, this = could=20 lead to critical experiments to compare and judge two models.

Beauty is the other evaluative category. Fertility and surprise are = two of=20 the standards of beauty in model building. A poor model, in respect to=20 fertility, is one that has no logical consequences we consider worthy of = noting.=20 A good model is fertile in the deductive sense and it is an even better = model if=20 some of the consequences are surprising, not at all obvious in the = setting-up of=20 the model.

A second aspect of beauty is simplicity. Complexity in models is to = be sought=20 at the level of derived consequences, not at the level of postulates. In = a=20 process model, a few simple rules of transition can lead to enormous = complexity=20 in the concatenation of these rules over time and in regard to distinct = actors=20 in a system. Model builders usually urge that their readers wait and see = what=20 the results are before abandoning a model because a specific assumption = seems=20 too idealized or even "wrong," as if it were an empirical = generalization.

Let me add two ideas about standards in model building. Both relate = to what=20 seems to be required to have an explanatory model. On the one hand, from = a=20 formal point of view what seems essential is some kind of mechanism or = rule-set=20 that generates the phenomenon to be explained. A postulated process = literally=20 shows how the phenomenon arises, deducing it from premises or computing = it in a=20 simulation of the postulated process. On the other hand, and this is = perhaps=20 more controversial, from an interpretive point of view what seems = important is=20 that this generativity should be based upon premises that refer to=20 understandable human action. Simplicity of postulates about the actions = of=20 agents, with complexity of generated systemic outcomes: that is the = standard=20 that sums up these two ideas.

Realization of this standard is now in progress in theory-driven = simulation=20 studies, often grouped under the rubric of computational sociology = (Hummon and=20 Fararo 1995). Simulation methods enable process models to be constructed = that=20 are based on nonlinear parallel processing by a diverse set of actors in = a=20 dynamic network. The consequences of the process rules are generated in = "runs"=20 of the computational model rather than logically derived. However, there = is=20 still a place for the analytically simpler types of models that enable = the=20 derivation of crisp theorems. Theoretical sociologists are among those = on the=20 frontier of these new computational developments even as older formal = methods=20 continue to be important.

Summary

The tradition of sociological theory exhibits a mixture of three = types of=20 intellectual interests that I have called theoretical sociology,=20 world-historical sociology and normative-critical sociology. This was=20 illustrated in the classical phase of the tradition, where we see the = beginnings=20 of theoretical sociology as well as a focus on world-historical trends = and their=20 normative assessment. I discussed the postclassical phase of theoretical = sociology by reference to the common aim of generalized synthesis found = in the=20 successive works of Parsons and Homans. Between their earlier and later = phases=20 of theorizing, each shifted theory construction strategy while = maintaining=20 continuity of sociological ideas, Parsons to his four-function paradigm = and=20 Homans to his program of behavioral reduction.

In the most recent phase of theoretical sociology, I have emphasized = that=20 formal models have become a major part of the tradition. I have tried to = highlight major developments in terms of models of structure and of = process. I=20 also discussed two types of models that combine a structural focus with = process=20 analysis. Finally, in the context of treating a number of general = considerations=20 about formal models in sociology, I described a general perspective on=20 theoretical model building in relation to theoretical frameworks.

In sum, this paper has provided an historical perspective on = theoretical=20 sociology from the classic tradition to postclassical efforts of = synthesis that=20 culminated in multiple paradigms to the situation today in which new=20 developments -- that are productive -- more and more rely upon formal = models as=20 essential components of their methodology.

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_____ and Paul Colomy. 1990. Editors. Differentiation Theory = and Social=20 Change: Comparative and Historical Perspectives. New York: = Columbia=20 University Press.

Bainbridge, William, and Edward Brent, Kathleen Carley, David Heise, = Michael=20 Macy, Barry Markovsky and John Skvoretz. 1994. "Artificial Social = Intelligence."=20 Annual Review of Sociology 20: 407-436.

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