Sociologists frequently invoke the concept of form when analyzing organizations, collective action, art, music, culture and other phenomena. Nonetheless, the form concept has not received careful theoretical analysis, either generally or in specific context. Using the tools of formal logic, set theory, and algebra, we propose a language for defining social forms that is suAEciently general to incorporate feature-based, position-based, and boundary-based approaches to defining forms. We focus on organizational forms although we intend for our conceptualization to be general. We define forms as a type of socially coded identity. We de_ne identity in terms of social codes that specify the properties that an entity can legitimately possess. These codes can be enforced by insiders or outsiders. We claim that one knows that a social code exists when one observes that departures from the codes after periods of conformity cause a devaluation of the entity by relevant insiders and/or outsiders. This construction allows us to de_ne a population as the set of entities with a common minimal external identity in a bounded system in period. The minimal property ensures that we localize to the most speci_c socially enforced identities. The reliance on identities instead of forms allows us to de_ne populations that never achieve form status and to extend population de_nitions back to the period of early legitimation. Research design implications follow.

This article develops a formal theory of the structural aspects of organizational change. It concentrates on changes in an organization's architecture, depicted as a code system. It models the common process whereby an initial architectural change prompts other changes in the organization, generating a cascade of changes that represents the full reorganization. The main argument ties centrality of the organizational unit initiating a change to the total time that the organization spends reorganizing and to the associated opportunity costs. The central theorem holds that the expected deleterious effect of a change in architecture on the mortality hazard increases with viscosity and the intricacy of the organizational design.

Although the concept of niche has been extremely useful in sociological theory and research, some aspects of the concept have not been clearly developed. This article advances a theoretical reconstruction of the concept of niche, with special application to organizations. The proposed formal model unifies several active lines of sociological theory. It also extends the notion of the niche from the realm of behaviors to apply to the rules coding social identities and organizational forms. The reconstruction gives deeper insight into the niche of an organizational population as well as individual organizations. Finally, the model analyzes the (thus far) tacit assumption that niches are convex, examines the implications of convexity for commonly used measures of niche width, and provides a general sociological argument for the predominance of convex niches.

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