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POLYCONTEXTURAL LOGIC,
A BRIEF OVERVIEW

by Rudolf Kaehr

 

The following lines give a very brief overview of some of the central ideas of Polycontexturality. It is not meant as an indroduction to Polycontexturality. For introductions on PCL see the articles "Introducing and Modeling Polycontextural Logics" or Technologische Zivilisation und transklassische Logik.

The idea of an extension of classical logic to cover simultaneously active ontological locations was introduced by Gotthard Günther (1900-1984, US-American thinker, born in Germany, colleague of Heinz von Foerster at the BCL, Urbana, Illinois). The idea of Polycontextural Logic originates from Günther's studies of the work of Hegel, Schelling and the foundation of cybernetics [1] in cooperation with Warren St. McCulloch. His aim was to develop a philosophical theory and a mathematics of dialectics and of self-referential systems - a cybernetic theory of subjectivity as an interplay of cognition and volition [2].

Polycontextural logic is a many-systems logic, a dissemination of logic, in which the classical logic systems (called contextures) are enabled to interplay with each other, resulting in a complexity which is structurally different from the sum of its components [3,4]. Although introduced historically as an interpretation of many valued logic, polycontextural logic does not fall into the category of fuzzy or continuous logic or other deviant logical systems. Polycontextural logic offers new formal concepts such as multinegational and transjunctional operations.

The world has infinitely many logical places (or locations); each location is representable by a two-valued system of logic when viewed in isolation. However, a coexistence - a heterarchy - of such locations can only be described by a non-classical relationship in a polycontextural logical system. We shall call this relation the proemial relationship which is the term used by Günther. "Proemial" means "to preface" and the relationship "prefaces" the difference between relator and relatum of any relationship as such. Thus the proemial relationship provides a foundation of logic and mathematics on a deeper level as an abstract potential from which the classic relations and operations emerge. The proemial relationship rules the mechanism of distribution and mediation of formal systems (logics and arithmetics), as developed by the theory of polycontexturality.

Referenzen

[1] Günther, G.: Idee und Grundriß einer nicht-Aristotelischen Logik. Die Idee und ihre philosophischen Voraussetzungen, 2.Auflage, Hamburg, Verlag Felix Meiner, 1978
[2] Günther, G.: Beiträge zur Grundlegung einer operationsfähigen Dialektik. Bd.1-3, Hamburg, Verlag Felix Meiner, 1976-1980
[3] Kaehr, R.: Materialien zur Formalisierung der dialektischen Logik und der Morphogrammatik 1973-1975. In: Ref.2, Anhang
[4] Kaehr, R.: Das graphematische Problem einer Formalisierung der transklassichen Logik, In: Beyer, W.R. (Ed.): Die Logik des Wissens und das Problem der Erziehung, Hamburg, Felix Meiner Verlag, 1981