Morphograms
The morphogram is a term from the " polycontextural logic " of the philosopher and logician Gotthard Günther .
introduction
The classical logic treats statements systems, which may not contain any obvious contradictions, respectively. Furthermore, classical logic does not allow self-references ( circular conclusions ).
The polycontextural logic allows logical subsystems (so-called contextures ), which each meet the requirements of classical logic, to be linked with one another (hence: poly contextural ), even if the resulting overall system does not meet these requirements. To achieve this, methods are required that are outside of classical logic. The morphogram provides them. Self-references are also possible outside of the individual contextures.
One of the main areas of application for polycontextural logic and morphogrammatics is biology, and in particular the description and modeling of natural neural networks that work, but do not always comply with the laws of classical logic.
presentation
Morphogrammatics is about being able to represent the reflection on others and at the same time on oneself ( self-referentiality ) formally without contradictions. If a subject directs his thinking not only towards other things (towards his objects ), but also towards himself, then it is at the same time subject and object. But this cannot be represented in a two-valued (Aristotelian) logic, where something can only be either “subject” or “object” (S | O). The encounter the Morphogrammatik by being the sites on the logical sites do not (eg.) Values "true" | "false" starts, but only points form (Greek morphé ) from which can be found only where identical or . unequal values must appear. These values can then be more than 2 - e.g. B. "subject", "object" and "denial of this alternative" (S, O, V). Therefore morphogrammatics belongs to the theories of multi-valued logic , but goes beyond these, since it carries out value abstraction. This enables it to link several contextures (see also: Theory of polycontexturality ); all other multi-valued logics only ever belong to a single contexture. ( Gotthard Günther explained the idea of polycontexturality in his essay Life as Polycontexturality .)
After Günther's death, this approach was u. a. continued by Rudolf Kaehr (1942–2016) in his work on semiotics .
Steffen Heise presented a critical analysis of morphograms and their embedding in naive set theory. On the one hand, he makes the z. Some of the cryptic hints of Günther and his epigones are understandable and at the same time proves that Günther's formal ambitions - developing a dialectical logic - are not fulfilled by morphograms and the formalisms based on them (kenograms), since morphograms can be fully expressed in naive set theory.
More about Gotthard Günther's approach
The conception of polycontextural logic (multi-valued, multi-digit, multi-location logic) requires a special pre-logical theory for the formal description of the extra-logical distribution and communication of logical contexts (relationships) , for which Gotthard Günther introduced the name "morphogrammatics".
Morphogrammatics is a theory of reshaping and linking sublogical operations, which Gotthard Günther proved to be the deep structure of classical propositional calculus. It describes the prelogical architecture of logical systems in general. Günther used morphogrammatics in particular to establish his logical conceptions of "place value logic" and "polycontextural logic".
The polycontextural logic designed by Gotthard Günther postulates a form conception that goes beyond the structural realm of classical formal systems and that should make it possible to depict complex dialectical and self-referential systems in a non-reductionist manner.
Günther's approach is based on the thesis that with the transcendental dialectic of German idealism a new conception of logical form was discovered, which stands beyond the Aristotelian conception of form, but is just as accessible to a philosophical and mathematical analysis.
In his extensive work he designs a self-referential architecture to depict his trans-classical conception of form. The basic idea for the realization of such an architecture in the polycontextural logic is to represent it as a mechanism for the mediation of distributed logics in a complex system network . Self-referentiality should be mapped in the overall complex of logically independent, but extra-logically linked, formal systems - contextures - non-reductionistically and free of antinomies .
"Morphogrammatics [describes] a structural layer in which the difference between subjectivity and objectivity is first established and therefore cannot yet be assumed there"
This prelogical character of the morphogrammatics is supposed to enable the formally contradicting representation of the mediation of several logics in a polycontextural network which violates the axiomatics of logics.
See also
Individual evidence
- ↑ Steffen Heise: Analysis of the morphogram. In: Contributions to the Klagenfurt technology discussion, issue 50; ISSN 1028-2734. Bammè, Arno; Baumgartner, Peter; Berger, Wilhelm; Kotzmann, Ernst. 1993, accessed April 10, 2019 .