4.2.  World-Model II: One Logic/Many Worlds

Plagiarism in world-model II demands for some distinctions, which are not easily be codified in Western culture and law. The problems of law in post-modern societies, which are playing in world-model II, can be undestood as the problems of a transition of the strict private/public dichotomy to a complex and interactional chiasm of the terms.

"My argument starts with the obvious observation that the public/private distinction is an oversimplified account of contemporary society. More controversially, my argument continues that any idea of a fusion of the public and private spheres is equally inadequate. As an alternative conceptualisation, I propose that the public/private divide should be replaced by polycontexturality.

The claim is this: Contemporary social practices can no longer be analysed by a single binary distinction; the fragmentation of society into a multitude of social sectors requires a multitude of perspectives of self-description. Consequently, the simple distinction of state/society which translates into law as public law vs. private law needs to be substituted by a multiplicity of social perspectives which are simultaneously reflected in the law.” (Teubner)

If everybody has his/her “model of the world”, then comparison of inventions demands for a many-to-one procedure of translation. That is, if two taxonomies (term trees) share the same knots (terms) there is no guarantee that their meaning is the same. As the diagram shows, the origin of the taxonomies might be different, hence, the meaning of a term, which is defined by the position of the term in a tree, will be different.

http://www.thinkartlab.com/CCR/2007/03/chinese-centralism.html

Interactions between different term-trees, as they are needed for translations, are involving some new operators not known in logic-based theories. One such operator is mentioned by Luhmann as tranjunction.Transjunctions had been introduced by Gotthard Gunther in his famous paper “Cybernetic ontology and transjunctional operators” (§ 3: Logic with Transjunctions). Further formalizations are proposed at PolyLogics, (§ C.1.6)

In polycontextural systems, transjunctions are logical operators, which are beyond (trans) junctions, like conjunctions and disjunctions, this mainly because they are rejecting the logical values offered by the logic in which they are positioned. Junctions, in contrary, are always accepting the offered values. Hence, in a polycontextural interpretation, transjunction are bridging different logical contextures (systems). Junctions are behaving by definition intra-contexturally, transjunctions are interacting between contextures, hence transcontexturally.

Also this is known since the early 60s, it would be naive to think that it had any influence on a theory of transdisciplinarity.

What we can read, again and again, is the mantra “modern society is a polycentric (pluri-centric) system”. This seems to be the great message of the second-order system theorists.

"Modern society is a polycentric, polycontextural system. (...) Consequently there must be transjunctional operations, which make it possible to go from one contexturality into another, still marking which differentiation is accepted or rejected for specific operations.” (Luhmann 1996).

Interestingly, the terms “pluri-" or “polycentic” are mostly, see: Luhmann, Teubner, Baecker, Fuchs, Qvortrup, etc., followed by the term “polycontextural” as if this term would demonstrate the “non plus ultra"-state of their theory.
Their is no surprise, that not only no logical formulas are in the game but that the complex terminology of Gunther’s theory of polycontexturality is reduced to 1 or 2 terms: polycontextural and transjunction. Terms, like intra-, inter-, trans-, dis-, elementary/compound, etc. are not part of the references.

The possible IP theft involved in such a writing production is quite harmless. Not much would be changed in their texts if the term “polycontextural” would be replaced at all its occurrences by the much more appropriate terms “polycentric” or ”.pluri-centric”. Thus, it is more reasonable, especially in the case of Luhmann, to think of a friendly carriage case. in his citations (Zettelkasten), Luhmann is carrying the torch of “polycontexturality” through some hostile times of German academia.

Nevertheless, the consequences from polycentrism for international law systems are dramatic. Gunther Teubner gives a big picture of the destiny of law in a post-modern society in his: The king's many bodies: The self-deconstruction of Law's hierarchy.

“Law's constructed identities change chameleon-like with the change of observation posts, each of which has an equally valid claim to truth. There is no stable predefined identity to the legal system but rather a multiplicity of conflicting identities that are constructed in different contexts of observation. Law is the same and it is not the same. So what's the difference between constructing and deconstructing legal systems?” (Teubner)

4.2.1.  Limitations of the idea polycentrism

Lars Qvortrup, following Luhmann, has sketched the situation of postmodernism in his “The Hypercomplex Society"'

"Polycentrism characterizes a society that cannot observe itself or its environment from a single observational position-or, rather, from within a single observational perspective or “optics”-but has to employ a large number of positions of observation, each using its own individual observational code to manage its own social complexity. This implies that no universal point of observation can be found. Furthermore, this means that a large portion of these observations are observations of observations: of others’ observations and of the observer’s own observation."

Without a “universal point of observation” communication between the different position has to be mediated, otherwise we would be forced to subsume, again, the multitude of positions under the umbrella of a unique and ultimate meta-position. In other words, a multitude of observational positions is involved with the interpretation of an unique objectivity. This is demanding for a many-to-one codification of the observed reality.

Because of this many-to-one constitution of world-model II, reality has to be constructed and reality-constructions are entering self-referential situations. The self-referentiality of reality-constructions are becoming more and more meta-theoretical self-descriptions of the reality-construction language. The description language is re-entering into its own description. This is producing paradoxes and hence, provoques a clear affront to the rationality of world-model I.

Codification in world-model I is highly developed and well based in the classic scientific paradigm. The rationality of world-model I has its final conceptual and operational codification in logic, formal  and programming languages. Formalisms and metaphors for world-model I might be universal algebra; for world-model II it might be universal co-algebra and modal logics but this connection is not yet realized by postmodernist thinkers.

From a second-order cybernetic point of view, objectivity is a construction of an observer. The form of the construction is understood as a fix-point of a recursive formula. A recursion is a step-by-step iteration of the formula-scheme, including the results from the lower levels into the higher levels of the step-wise development. Independent of the complexity of the recursive function, the step-wise development of the iteration belongs to the paradigm of ‘forwards'-iterability. This is obvious, because the recursive function is solution-oriented, hence aimed to reach a final goal. The idea of a simultaneous ‘backwards'-oriented movement, in parallel to the ‘forwards'-movement  of the ‘same’ movement is strictly absurd in world-model II. Polysemy occurs in world-model II as disseminated, only.

A compromise was offered with the idea of a polycontextural number theory. This theory is constructed as a dissemination, i.e., distribution and mediation, of the classic systems of natural numbers over different loci in a kenomic grid. Such disseminated, different and autonomous natural number systems, might then run  their numbers forwards and backwards seperatedly and simultaneously. But this happens not for a genuine operation as such, i.e., ’ inside’ an arithmetical system, but only for the interpretation of different simultaneous operations, which remain distributed and separated over different loci. Such a restriction in the process of simultaneity and sameness of the differentness of an operation in itself will be removed in world-model IV.

Despite the big pictures of post-modernism drawn by Luhmann and his followers, there is still nothing comparable to the operational formalisms of world-model I for the world-model II. The operative terms are taken by Luhmann are selectively  from Gotthard Gunther’ s theory of polycontexturality and Henz von Foerster’ s recursive observer theory, but without any attempt to further formalization. Hence, a theory of mediation, necessarily for an understanding of the interaction of the different observational positions, is still lacking. This, obviously, are bad news for the realization of global control and surveillance desires and phantasms. But for a functioning free society, too.

Epistemology: The same is different.

Fazit: The case needs mediation.