Theoretical unification and sociological theory: An appreciation of the contributions of T.J. Fararo

1.

Thomas J. Fararo, my mentor and long time collaborator, was one of the pioneers of mathematical sociology. When he passed away in August 2020, he left an intellectual legacy to the field of mathematical sociology and a financial legacy to the ASA Section on Mathematical Sociology. Tom Fararo viewed mathematical sociology as first and foremost a theoretical activity, an activity whose driving concern should be the unification of disparate theories and theoretical frameworks, setting out these ideas in two books The Meaning of General Theoretical Sociology: Tradition and Formalization Fararo (1989) and Social Action Systems: Foundation and Synthesis in Sociological Theory (2001).

In August of 2022, the Section on Mathematical Sociology sponsored a panel on his work that I organized. The panelists were Professors Carter Butts, Willie Jasso, and Gianluca Manzo. I asked them to comment on the contributions of Tom Fararo to sociological theory through mathematical modeling and to assess the prospects for the achievement of his vision: the unification of disparate theories and frameworks in sociology. We agreed to memorialize the session with papers from each of the participants written in the spirit of and to honor Tom Fararo. The three contributions that follow this introductory note make good on that agreement. In the introductory note, I offer some biographical details regarding Tom’s life and then some comments about overarching themes in his work.

Professor Thomas J. Fararo was born in 1933 and spent almost his entire academic career at the University of Pittsburgh. His book published by Wiley in 1973 Mathematical Sociology: An Introduction to Fundamentals was one of the first three foundational books on mathematical sociology published in that era (Coleman in 1964 and Leik and Meeker 1975 were the other two). He viewed mathematical sociology as first and foremost a theoretical activity, an activity whose driving concern should be the unification of disparate theories and theoretical frameworks. He set out these ideas in two books The Meaning of General Theoretical Sociology: Tradition and Formalization (1989) and Social Action Systems: Foundation and Synthesis in Sociological Theory (2001).

As the timeline in Figure 1 displays, Tom did his undergraduate work at City College of New York, majoring in history and political science. He did his graduate work in sociology at Syracuse University and participated in empirical studies of community power structure, both under the mentorship of Linton Freeman. During the years at Syracuse, he developed interests in symbolic logic, finite mathematics, cybernetics, and general systems. In his dissertation, he applied Anatol Rapaport’s biased net theory mathematical model to study structural features of observed social networks. That work led to his first monograph in 1964, A Study of a Biased Friendship Network, coauthored with Morris Sunshine.

Figure 1. Timeline.

Appointed an Assistant Professor at Syracuse, he applied for and was awarded a three-year NIH postdoctoral fellowship for advanced studies in pure and applied mathematics at Stanford University from 1964 to 1967, to build his skills in mathematical model building. On the postdoc, he studied various branches of mathematics and published papers that used abstract algebra, absorbing Markov chain theory and nonlinear systems of differential equations to study status-related phenomena. He also

developed long-standing ties to the founding figures in expectations states theory at Stanford sociology, Joe Berger and Morris (Buzz) Zelditch, Jr.

In 1967, Tom joined the department at the University of Pittsburgh as an associate professor and then, in 1970, he was promoted to the rank of full professor. In 1998, the University honored him with the title Distinguished Service Professor of Sociology for his scholarly contributions. He retired in 2006. In between, he served as Director of Graduate Studies for several years in the 1970s and as departmental chair from 1980 to 1985. Over the years, he served on the editorial boards of leading journals, including The American Sociological Review, The American Journal of Sociology, Social Networks, Sociological Theory and Sociological Forum. In addition, for many years he was an Associate Editor of The Journal of Mathematical Sociology. In the 1990s, he was elected to the Sociological Research Association. In 1998 he was elected chair of ASA’s mathematical sociology section and in 2004 he received that section’s Distinguished Career Award.

Tom’s early authoritative text on mathematical sociology, Mathematical Sociology: An Introduction to Fundamentals, explored three main ideas of fundamental importance to the development not only of mathematical sociology but also of sociology and, more broadly, social science. The first idea is that a theory is most effective when it is mathematically expressed. The second argues for the rigorous mathematical modeling of a vast array of processes at all levels of analysis and at all levels of generality. The third encourages the cultivation of the tools necessary for successful mathematization of sociological theory. These three themes recur in all his work.

In his masterpiece, The Meaning of General Theoretical Sociology: Tradition and Formalization (1989), Tom provides a comprehensive examination of theoretical sociology, its roots and traditions, its methods, and its key substantive questions. He holds that theoretical sociology comprises a single research tradition, that what appear as conflicting theoretical traditions are “intersecting and communicating subtraditions” of the single tradition (p. 342). The key substantive questions concern the “emergence, maintenance, comparison, and transformation of social structures” (p. 62). To study these basic questions, Tom proposes a “process worldview” whose key idea is “recursive generativity:” “The interactive nexus of human organisms generates transformations in both the individual humans as such and the advancing nexus they constitute” (pp. 47–53, italics in the original). The process worldview leads naturally to a set of methods whose centerpiece is a nonlinear dynamical social systems framework. The system comprises (a) dynamical variables that define its states and its possible trajectories through time and (b) parametric variables that capture the relatively fixed conditions under which the system labors. Within this framework, the aim is to formulate mechanisms that generate changes of state from which the possible trajectories are derived and then prove four types of theorems. The first two are the existence and stability of equilibrium states, states of the system in which the mechanisms postulated to produce change are balanced, and the conditions for which depend on the parametric variables defining the system. The second two questions involve the relationship between parametric and dynamical variables: the comparative statics problem, how stable equilibrium states vary with variation in values of the parametric variables; and the structural stability or structural change problem, how dynamic outcomes vary if parametric conditions change. In the context of dynamical social systems, these are the four fundamental problems of social structure at the heart of scientific sociology: (a) the existence and forms of social structure, (b) the stability of social structures, (c) the comparative statics of social structures, and (d) the change of social structures (p. 109).

Finally, work on these basic questions was to be conducted in “the spirit of unification.” By this phrase, Tom meant activity that had cognitive component and a behavioral component. The first referred to “a cognitive value commitment not only to the production of integrative episodes [over theoretical structures] but also to the promotion of intellectual conditions that encourage both the production and understanding of such integrative efforts” (Fararo, 2001, p. 281). That is, scholars were enjoined to look for and produce theoretical integrations whenever possible and to appreciate and applaud such efforts of others. The behavioral component highlighted “another type of embodiment of the spirit of unification: more frequent interaction and genuine intellectual communication among members of distinct research groups … [so] that with sufficient attention to the requisite cultural and social conditions, comprehensive integration efforts may play a more important role in the future of theoretical sociology” (Fararo & Skvoretz, 1993, 450). The commandment for mathematical sociology is clear: Communicate across research group boundaries to succeed at the vital task of theoretical integration.

The authors of the following papers, Professors Carter Butts, Willie Jasso, and Gianluca Manzo adhere to this commandment. Professor Butts is well known for his contributions to statistical methodology for network analysis. Professor Jasso has left her mark on the study of inequality and the field of demography, specifically migration studies. Professor Manzo is a leader in the analytical sociology tradition, deploying agent based models to address diverse substantive questions. Their contributions to this volume to celebrate the life and work of Professor Fararo are varied. Professor Butts picks up the thread of biased net theory and modeling. He proposes a new means by which such models can be estimated and illustrates the method with an application to a friendship network, quite appropriately, since Tom’s contributions to the estimation problem were also made in the context of data on friendship network (Fararo & Sunshine, 1964). Professor Jasso documents through her own work on the theory of justice, the very Faraoian themes of integrative theoretical episodes in the quest for theoretical unification. Furthermore, she reveals how much her own work was directly influenced by communication with Tom over the years. Professor Manzo turns detective in an exploration of the intellectual history of the analytical sociology movement. He finds evidence that Fararo’s work, particularly, its insistence on generative mechanisms, should be recognized as foundational to the analytical sociology project.

To close I offer the following personal statement from the preface of Tom’s dissertation (Fararo, 1963: iiif). He wrote “I am not really interested in data. I am interested in theory, and data are useful to me because they shed light on the theory. … I want my translation of private drive [learn about net theory] to public knowledge to culminate in statements about the only thing that survives after all the data are washed down the shores of time: the recurrent process encapsulated into a theory. I am not really interested in today, but tomorrow. I am forced to operate with today’s data, but I want my results to apply to the future: for a community of [scholars] unborn who will inherit from us what transcends the local situation of today. And this is science.” In 1963, I and the contributors to this special issue were unborn as scholars in sociology (and some of us unborn period) and thus the future inheritors of the fruits of Tom’s commitment to science and to mathematical sociology. We among many others have benefitted greatly indeed.

Disclosure statement

No potential conflict of interest was reported by the author(s).