It is a →Meaning-constituting system. Its operations and final elements are →Communications. There is not just one social system, but many. Through self-catalysis, social systems emerge from the problem of →double contingency, which is processed through communication.
The concept of a social system is related to general systems theory, which formulates the essentials of the description of each system. There are three analytic levels that allow the differentiation of social systems from other types of system, and the determination of connections between the different types.
The first level is the conceptualization of general systems theory. The paradigm shift in general systems theory has important consequences for a theory of social systems. This shift is from the system as a whole, made up of parts, to the distinction between system and environment, where the system is autopoietic and operationally closed [→Autopoiesis]. A system exists only if it can reproduce its operations through its operations, i.e. in the network of these operations. The autopoietic process of self-reproduction determines the operational closure of systems.
This general definition, however, does not suffice for the analysis of social systems. In order to observe social systems, we must first differentiate them from other types of system (living and psychic) and avoid any mixing of analytic levels. Above all, we may not assume that what is identical at one level is also identical at other levels.
At the second level in the schema, we find concepts that indicate the specificity of social systems and distinguish them from other types of system. Here, the central concepts are meaning and communication. The concept of meaning distinguishes social and psychic systems from living system such as cells, organisms and brains. Social and psychic systems are meaning-constituting systems. The specificity of social systems as autopoietic and meaning-constituting systems is that their operation is communication. They generate communication through communication, in a network of communications that is based on the medium of meaning. This distinguishes social systems from psychic systems based on the operation of thinking; thinking cannot be included in social systems through communication.
The formulations at the first two levels lead to an analysis of social systems that, contrary to sociological tradition, no longer takes the problem of stability as a starting point. Instead, the problem of social systems is the continuation of autopoiesis in relation to the environment. The initial problem of double contingency transforms into the question of how communications without duration (that disappear as soon as they emerge) can be continuously produced and connected to one another.
At the third level, three types of social system can be differentiated: →interactions, →organizations and →society. We can neither reduce one type into another, nor use models that presuppose the primacy of any one type. The theory of social systems explains the social reality with recourse to the three types, their autonomy and their interdependencies. For this reason, we can no longer speak, as Talcott Parsons did, of a theory of the social system in the singular, but must speak instead of social systems in the plural. [C.B.] – (Unlocking Luhmann, p 221–222)
Social Systems (1995); The Autopoiesis of Social Systems (1986); Insistence on Systems Theory (1983).
LUHMANN, Niklas, 1983. Insistence on Systems Theory: Perspectives from Germany—An Essay*. Social Forces. 1 Juni 1983. Bd. 61, Nr. 4, S. 987–998. doi 
A social system is an autopoietic, self-referential system [→Autopoiesis; →Self-Reference] that is constituted as differentiated from its environment [→System/Environment].
It is a →Meaning-constituting system. Its operations and final elements are →Communications. There is not just one social system, but many. Through self-catalysis, social systems emerge from the problem of →double contingency, which is processed through communication.
The concept of a social system is related to general systems theory, which formulates the essentials of the description of each system. There are three analytic levels that allow the differentiation of social systems from other types of system, and the determination of connections between the different types.
3 analytic levels
The first level is the conceptualization of general systems theory. The paradigm shift in general systems theory has important consequences for a theory of social systems. This shift is from the system as a whole, made up of parts, to the distinction between system and environment, where the system is autopoietic and operationally closed [→Autopoiesis]. A system exists only if it can reproduce its operations through its operations, i.e. in the network of these operations. The autopoietic process of self-reproduction determines the operational closure of systems.
This general definition, however, does not suffice for the analysis of social systems. In order to observe social systems, we must first differentiate them from other types of system (living and psychic) and avoid any mixing of analytic levels. Above all, we may not assume that what is identical at one level is also identical at other levels.
At the second level in the schema, we find concepts that indicate the specificity of social systems and distinguish them from other types of system. Here, the central concepts are meaning and communication. The concept of meaning distinguishes social and psychic systems from living system such as cells, organisms and brains. Social and psychic systems are meaning-constituting systems. The specificity of social systems as autopoietic and meaning-constituting systems is that their operation is communication. They generate communication through communication, in a network of communications that is based on the medium of meaning. This distinguishes social systems from psychic systems based on the operation of thinking; thinking cannot be included in social systems through communication.
The formulations at the first two levels lead to an analysis of social systems that, contrary to sociological tradition, no longer takes the problem of stability as a starting point. Instead, the problem of social systems is the continuation of autopoiesis in relation to the environment. The initial problem of double contingency transforms into the question of how communications without duration (that disappear as soon as they emerge) can be continuously produced and connected to one another.
At the third level, three types of social system can be differentiated: →interactions, →organizations and →society. We can neither reduce one type into another, nor use models that presuppose the primacy of any one type. The theory of social systems explains the social reality with recourse to the three types, their autonomy and their interdependencies. For this reason, we can no longer speak, as Talcott Parsons did, of a theory of the social system in the singular, but must speak instead of social systems in the plural. [C.B.] – (Unlocking Luhmann, p 221–222)
Social Systems (1995); The Autopoiesis of Social Systems (1986); Insistence on Systems Theory (1983).
LUHMANN, Niklas, 1983. Insistence on Systems Theory: Perspectives from Germany—An Essay*. Social Forces. 1 Juni 1983. Bd. 61, Nr. 4, S. 987–998. doi