Polycontexturality theory

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The polycontexturality theory expands the classical mathematical logic so that context dependence / subjectivity and paradoxes can be formally described.

introduction

The polycontexturality theory or the theory of polycontexturality was introduced to science by the philosopher and logician Gotthard Günther in the 1970s . This theory is a direct further development of Günther's place value logic , which emerged from his attempts to develop a multi-valued ontological system of place value logic. The theory of polycontexturality encompasses both the polycontextural logic, the morpho- and kenogrammatics as well as the semi-classical place value logic first developed by Günther, which he called the "ontological place value system" in 1974, around the concept of place value logic, which he first introduced in 1958 clearly differentiated from its use in non-logical contexts (such as by the sociologists of the Frankfurt School ). A detailed description of the historical development of Günther's works as well as their substantive and conceptual differentiation can be found in the essay Exercise in Another Reading by Rudolf Kaehr and Joseph Ditterich.

"Value added" with Günther and Łukasiewicz

If one describes the propositional calculus with the help of the two values ​​1 and 0, which as usual with the terms "true (T)" - "false (F)" or "designated" - "not designated" for 1 resp. 0 can be interpreted, then the values ​​additionally introduced by Łukasiewicz lie between 0 and 1, i.e. within the logical domain under consideration and one speaks of a multi-valued logic . This is sketched in Fig. 1b, Fig. 1a shows the simple case of a logical domain with only 2 values ​​(zero and one). From these approaches, one arrives at the probabilistic logic conceptions as well as the very popular fuzzy logic . In principle, any number of values ​​between 0 and 1 can be introduced.

Fig. 1a Fig. 1b
1 ------------- 0 1 ----- 1/2 ----- 0

In contrast, Günther's theory of polycontexturality is based on two-valued logic (which could also be extended to multi-valued logics), but links several such - spatially distributed - logic systems at certain points. This makes it possible for Günther to formally describe context dependency / subjectivity. Paradoxes (e.g. representation of self-reference) can also be formally described with this, since one is no longer bound to a single context; Self-reference / paradoxes therefore do not have to end in logical circles (serialized / timed), but can be represented "from above" / "at a glance" / "pictorial" / "parallel" instead of just serialized.

See also

literature

  • Gotthard Günther: Idea and outline of a non-Aristotelian logic (PDF; 1.0 MB) , 3rd edition. Meiner, Hamburg, 1991
  • Gotthard Günther: Contributions to the foundation of an operational dialectic , Volume 1 to Volume 3, Meiner, Hamburg, 1976–1980
  • Kurt Klagenfurt: Technological civilization and transclassical logic - An introduction to Gotthard Günther's philosophy of technology , Suhrkamp taschenbuch, 1995
  • Rudolf Kaehr: Materials for the formalization of dialectical logic and morphogrammatics 1973-1975 , in: G. Günther, Idea and ground plan of a non-Aristotelian logic , Felix Meiner Verlag, Hamburg, 2nd edition 1978, appendix.
  • Engelbert Kronthaler: Fundamentals of a mathematics of qualities , Peter Lang Verlag, Frankfurt a. M., 1986
  • Rudolf Kaehr & Thomas Mahler: Morphogrammatics - An introduction to the theory of form (PDF; 1.2 MB) , 293 S., 1993, report of the research project: Theory of complex biological systems - Autopoiesis and polycontexturality: formalization, operationalization and modeling (competition Life Sciences, Volkswagen Foundation)
  • Rudolf Kaehr u. a .: Polycontextural logic - on conception, formalization and validation (PDF; 109 kB)
  • Rudolf Kaehr: Dissemination
  • Rudolf Kaehr: Sketch of a web of computing spaces in a thinking void (PDF; 1.5 MB)
  • Rudolf Kaehr: Derrida's Machines
  • Petra Sütterlin: Dimensions of Thought - Trivalent Logic, explained on the basis of Gotthard Günther

References

  1. ^ Gotthard Günther: Das Janusgesicht der Dialektik , in: Hegel Jahrbuch (ed. WR Beyer), Pahl-Rugenstein Verlag, Cologne 1979, p. 98-117
  2. ↑ Gotthard Günther: The Aristotelian Logic of Being and the Non-Aristotelian Logic of Reflection , Journal for Philosophical Research, 12, 1958, p. 360–407 In 1, Das Janusgesicht der Dialektik Günther writes on page 97: The author wrote in 1958 with an article in the Ztschr. philos. research introduced the term "place value" into the theory of formal (multi-valued) logic. Since then, this term has been used so often in non-logical contexts (especially by the Frankfurt School) that it is no longer used here. From now on the author says "location value" to avoid misunderstandings.
  3. ↑ Rudolf Kaehr & Joseph Ditterich: Practicing a different reading: Diagram of a reconstruction of Günther's theory of negative languages , Philosophical Yearbook, 86th year, 1979, pp. 385–408, http://www.vordenker.de/ggphilosophy/ kaehr_einuebung.pdf