Abstract.
Until late 19th century scientist almost always assumed that the world could be described as a rule-based and hence deterministic system or as a set of such systems. The assumption is maintained in many 20th century theories although it has also been doubted because of the breakthrough of statistical theories in thermodynamics (Boltzmann and Gibbs) and other fields, unsolved questions in quantum mechanics as well as several theories forwarded within the social sciences. Until recently it has furthermore been assumed that a rule-based and deterministic system was also predictable if only the rules were known, but this assumption has now been undermined by modern chaos-theory describing rule-based and deterministic, but unpredictable systems, while catastrophe-theory delivers a set of types describing various kinds of instability and conditions for the stability of a given system.
Hence a main trait in the theoretical development in the 20th century science can be described as a basic modification and limitation of some of the fundamental and strong assumptions forwarded in the previous epochs of modern science. Ironically, the very same process has been a process in which the human capacity to intervene in nature has expanded dramatically and mainly by the help of the very same theories, and not least because they allow nature to be described and made manipulable on a lower level and a more fine-grained scale.
While the overall theoretical consistency between the various theories has gone, the reach of human intervention in nature has increased based on quite new dimensions whether in the area of physics (e.g.: energy technologies, chemical technologies, nanotechnologies etc.) of biology (genetic manipulation) or in the area of psychology, sociology and culture (artificial simulations of mental processes, new means of communication, implying changes in the social infrastructure and cultural behaviour etc.).
While some of these changes and new conditions can be reflected from within the conceptual framework of rule-based systems, albeit more complex than formerly recognised, others seems to give rise to the question whether there are »systems« and relations between different systems in the world which are not rule-based?
For instance, it seems to be obvious that the notion of instability represents a major conceptual break with former theories of rule-based systems, as the stability of the latter is an axiomatically given property implied in the very notion of rule-based systems, while instability can only be the result of external influence which should be explained as the result of another rule-based system. While there are no difficulties implied concerning the stability of rule-based systems, the notion of instable states of a system raises the question how there can be a system at all if there is no invariant stabilising principles?
This is the first question which I will address. And I shall do so by taking two examples of such systems as my point of departure. The first example will be the computer and the second will be ordinary language. In both cases I will argue that the stability of these systems (which are both defined by the existence/presence of human intentions) are provided by the help of - differently organised - redundancy functions which both allows the maintenance of systems in unstable macro-states, suspension of previous rules, underdetermination and overdetermination and generation/emergence/creation of new rules more or less independent of previous rules by the help of optional recursions to the permanently accessible underlying levels as for instance the level of binary representation in computers.
Since the notion of redundancy is both controversial as such and often avoided, the concept is discussed (as defined in Claude Shannon's mathematical theory of information and in the semiotic framework of J. J. Greimas) and leading to a more general definition in which the redundancy functions serve to overcome noisy conditions, but at the cost of rule-based stability, determination, and predictability.
A second question will be how the notion of rule-generating systems relates to the notion of anticipatory systems and it will be argued that rule-generating systems shares some features with anticipatory systems and that the former from a certain viewpoint can be seen as a subclass of the latter, although anticipative features are not necessarily a part of the definition of rule-generating systems. On the other hand, it will be discussed whether anticipatory systems which are not rule-generating systems can exist and it will be argued that the capacity to anticipate is strongly limited if it is not part of a rule-generating system. Therefore, it is concluded that the most powerful anticipatory systems need to be rule-generating systems.