PCL-Logo   PolyContextural Logic Web Site
 
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Keywords

Mindmap

Abstract

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Welcome to the official
PCL Website!

We organized the material on our server in a somewhat "polycontextural" way to make the navigation more transparent:
We want to provide navigational support for various possible approaches to Polycontexturality.
Therefore you can start with any of the four starting points of the following
sketch which will take you to distinct ways of approaching PCL.

If you prefer a more systematic approach you may continue with the
keywordlist, the Mindmap or the introduction below.

If you have any questions regarding our work or want to participate in the activities of the PCL group don't hesitate to contact us:

Have a look at our gallery


The big sketch:


Keywords:

antinomy, autology, autopoiesis, BCL, calculus of indications, combinatory logics, computational reflection, concurreny, deconstructivism, deviant logics, functional programming, grammatology, kenogrammatics, learning, morphogrammatics, multivalued logics, paraconsistency, paradoxy, PCL, P-combinator, PKL, polycontextural logics, polylogic, postmodernism, proemial relationship, radical constructivism, second order cybernetics, self, selfreference, semiology, semiotics, theory of conversations, transjunction, zerology.

To get familiar with the PCL terminology used on this site have a look at our glossary of PCL.


Mindmap

If your Browser supports Java you will see an animated Mindmap of the PCL keyword list below. You can drag the items with the mouse and thus change the appearance of the mindmap. Just enjoy this playful way of coming in "touch" with the PCL terminology.

Unfortunately your Browser doesn't support Java-Applets so you miss our animated mindmap of PCL related keywords.


Abstract:

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 transklassiche Logik. For a systematic overview on the articles provided on this website look here.

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 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.

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. 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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Last edited:
12/04/06
 
                   
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