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.
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