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Günther Philosophy Web

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
(19001984, USAmerican 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
selfreferential systems  a cybernetic theory of subjectivity
as an interplay of cognition and volition [2].
Polycontextural
logic is a manysystems 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
twovalued system of logic when viewed in isolation. However, a
coexistence  a heterarchy  of such locations can only be
described by a nonclassical 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 nichtAristotelischen Logik. Die Idee und ihre
philosophischen Voraussetzungen, 2.Auflage, Hamburg, Verlag
Felix Meiner, 1978
[2] Günther, G.: Beiträge zur Grundlegung
einer operationsfähigen Dialektik. Bd.13, Hamburg, Verlag Felix
Meiner, 19761980
[3] Kaehr, R.: Materialien zur Formalisierung
der dialektischen Logik und der Morphogrammatik 19731975. 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
