Paradoxes arise when the conditions for the Possibility of an Operation are at the same time the conditions for its impossibility.
One of the most well-known examples of a paradox was given by Epimenides in the (slightly revised) statement: “this sentence is false.” It is impossible to decide if the statement is true or false because the conditions of its falseness are simultaneously also the conditions for its truth (and vice versa): if the sentence is taken to be true, then it simultaneously contradicts what it expresses (the sentence is then false). If, however, the statement is taken to be untrue, we are forced to agree with its content (the sentence is then true).
The paradox is not, therefore, of the form: “A = not A,” which represents a contradictory but not a paradoxical statement. It is rather of the form: “A because not A,” whereby the conditions of the statement are at the same time the conditions of its negation.
For an observer, the undecidability lies in the fact that it is impossible to indicate one value without also indicating the other: the observer begins to oscillate between the two sides and it becomes impossible to continue the observation.
Paradoxes arise when observers making distinctions question the unity of the distinction they are currently applying [→Operation/Observation]. Every distinction is inherently paradoxical because both sides of it are always present simultaneously: one as the indicated side, the other as the intended, implied side to which the indication refers.
One example of this duality in every observation is the fundamental distinction between system and environment [→System/Environment]. Each system can only construct its identity as a system when it is able to distinguish itself from an environment, i.e., only when it negates that which it is not.
The environment, however, can only be distinguished on the basis of internal operations, as the operation of negation can only be produced as a system-specific operation. The system must therefore observe the distinction between itself and its environment as a product of itself. This is paradoxical because the system must distinguish itself from an environment that does not belong to it, whilst simultaneously observing that this environment is nothing but an internal product of its own operations. This occurs whenever a self-referential system capable of observation—and therefore capable of negation—observes itself [→Self-Reference].
This self-observation becomes particularly problematic for today’s society when it is undertaken in functional systems. One such case is the reflection of subsystems in modern society.
In the case of science, the distinction of the scientific code can be applied to itself, landing it in Epimenides’ paradox: the distinction true/untrue observes itself with the paradoxical result that the possibility for further observations is blocked in the way described above.
This problem arises in all functionally differentiated subsystems. The legal system, which operates on the basis of the distinction between who is juridically right and who is wrong, finds itself confronted with a paradoxical situation when it questions whether it has the right to determine who is right and who is not. The question cannot be answered, since any answer (e.g., social contract, original act of violence that is justified by the actions that follow it) inevitably affects both sides of the distinction so that the problem becomes unsolvable.
Similar examples can be given for all codes belonging to the subsystems and the →symbolically generalized media: when the observation is directed at the same binary schematization that the observation itself employs, the system must indicate the unity of the distinction that it is currently using—with paradoxical consequences.
Every self-referential system capable of negation is therefore unable to establish exclusively self-observations, since self-observation can never be complete. In order to be complete, it should also be able to observe the distinction that it uses, and that is not possible [→Operation/Observation].
Paradoxes are a problem for the observer, but not necessarily for the operations of the observing system. That science operates paradoxically is a problem only for the observer of the system (which can be science itself).
Separate operations and observations
In this sense, paradoxes serve to separate operations and observations. They allow the occurrence of operations but block observations. Operations run blind without the ability to observe themselves: in order to observe an operation, a second operation is required that can observe the paradoxical constitution of the first, but also runs blind itself.
The distinction it uses is a blind spot
Every observation can raise the question of how a system observes or how an operation is produced, but it cannot ask the question of itself: for every observation, the distinction it uses is a blind spot. In this way, paradoxes do not block the autopoiesis of the system, but represent a problem for its possibilities of observation.
In terms of structural aspects, every distinction exists only in the simultaneity of its two sides. In terms of operational aspects, the distinction can only be actualized as indication of one side (and not the other). For this reason, every system must unfold the paradox at the structural level; it must de-paradoxicalize itself in such a way that observations are not blocked.
This can happen when conditions are introduced that make the circularity of self-reference asymmetrical and avoid short-circuiting the references within the distinction used [→Asymmetrization].
These conditions can take on many different forms depending on the type of system and the form of differentiation in society as a whole [→Differentiation of Society]. In functionally differentiated subsystems, the de-paradoxicalizing function can be fulfilled by the way in which the system takes the relation between the two values of its code into account. Operations orient themselves to the binary schematization of the code in that they regard it as a self-contradictory difference and not as a unity.
Thus, in the →scientific system an observation is true or untrue and one value excludes the other; the decision is facilitated by particular →programs, which in the case of the scientific system are theories and methods. These make the system capable of operation by determining the allocation criteria of the values, whilst only scientific reflection deals with the problem of the paradoxical constitution of scientific truth and the necessity of introducing specific asymmetries.
The asymmetries, for their part, assume the form of contingency formulae, which allow the system’s coherent description of itself without oscillating between the values of its own distinctions, unable to decide between them.
Whichever form the asymmetrization takes, it always allows the system to find anchor points for its operations. From this view point, paradoxes appear to fulfill a function of irritating observers, who, when confronted with a paradox and seeing themselves forced to make an impossible decision, either give up because their observation is blocked, or become creative by finding some Form of asymmetrization.
The recent tendency within different disciplines (e.g., cybernetics, systems theory, art, logic) to seek out paradoxes instead of avoiding them is probably undertaken with the goal of irritating observers (i.e., ourselves) searching for new forms of structuring their own operations. [G.C.] – (Unlocking Luhmann, p 167– 170)
Tautology and Paradox in the Self-Descriptions of Modern Society (1988); Sthenography (1990); The Paradox of Form (1999).