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Gotthard Günther 
2000 Special


GÜNTHER - 2000

A contribution in three parts 
to the 100th aniversary of Gotthard Günther

Topic of Part 1:
"Erkennen und Wollen - Cognition and Volition"

by Eberhard von Goldammer

The philosopher and logician Gotthard Günther who was born in 1900 and who died in 1984 can be seen as one of the most distinguished thinkers of the 20th century comparable to Albert Einstein. This holds even if one considers that by scientific mainstream no great notice of Günther´s work has been taken yet. There are several possible reasons for this situation: 

1) as a German emigrant Günther lived in the USA and was working at the Biological Computer Laboratory (BCL) at the University of Illinois (Urbana); 

2) the far most parts of his work are written in German and were funded by US air force;

3) his work introduces a new and extended concept of logic which is related to Hegel´s dialectics, i.e. Günther´s work strongly reflects the ideas of the Occidental philosophical tradition. 

In his autobiography [1] he describes a situation giving a lecture at the University of Hamburg in 1955/56 on ´the philosophical consequences of cybernetics´ that more than fifty percent of the audience never heard something about ´cybernetics´, and the rest only had some very vague ideas about ´cybernetics´ as a field of engineering and mathematics without any contacts to human sciences and philosophy. This was the beginning and the end of Günther´s academic career in Germany. In 1960 Dr. John Ford (who was at that time at the George Washington University, Washington D.C.) arranged a meeting between Gotthard Günther and Warren S. McCulloch. As Günther himself quoted this was the beginning of a deep friendship [2] and an extremely fruitful cooperation at the Department of Electrical Engineering of the University of Illinois (Urbana, Ill.). The German philosopher became a professor of electrical engineering ! Although Günther´s work radiates some kind of American ´frontier's spirit´ it was not really admitted by the scientific community in the USA - maybe this is caused by natural language problems. Gordon Pask once made the following remark: "Although my German is very poor, I have the feeling that Günther´s articles which are written in English are more difficult to understand than the corresponding articles written in German". The non-reception of Günther´s work of the German academic circles was strongly influenced by Jürgen Habermas´ remarks on Günther´s article "Kritische Bemerkungen zur gegenwärtigen Wissenschaftstheorie - Aus Anlaß von Jürgen Habermas "Zur Logik der Sozialwissenschaften"" [3]. It is rumored that Habermas himself commented on this article with his name in the title, that one can ignore Günther´s work because the author (Günther) is paid by the US air force. Although this article was published more than 30 years ago it is still up to date. It is incredible that the German social scientists and the majority of their colleagues from the faculty of philosophy have successfully ignored Günther´s work [4] for more than fifty years. This certainly reflects something about the level of the German intellectual life after World War II, which we will not comment further. In order to get a short overview on Günther´s work, we have copied the contents of the "Beiträge zur Grundlegung einer operationsfähigen Dialektik" as well as the foreword of volume 2 of this series.

Günther has founded the basis of a formal theory which goes far beyond the Aristotelian logic and all its (mono-contextural) derivatives which have been developed mainly in the last century.[5] The basic idea of the concept of poly-contextural logic (pcl) is given by the introduction of new operators in order to mediate different logical domains (contextures) in a complex compound which allows to describe self-referential processes formally without the problem of generating antinomies and ambiguities. In other words, Günther introduced the concept of a non-Aristotelian logic.

What is a non-Aristotelian logic ?

The American philosopher Oliver L. Reiser has given the following answer [6]: "... any abandonment of the three laws of thought would constitute a non-Aristotelian logic". Reiser was well aware about the consequences of this radical statement, which means that not only the "law of the excluded middle" but also the "the law of identity" and "the law of contradiction" have to be questioned. He wrote: "If the laws of thought should fall, then the most profound modification in human intellectual life will occur, compared to which the Copernican and Einsteinian revolutions are but sham battles." Reiser already described one of the most interesting physiological aspect behind the Aristotelian logic, namely: "... the impossibility of simultaneous innervation of reciprocal neuro-muscular patterns. If the bodily process underlying the thought of ´A´ is in process, the bodily process underlying the thought of ´non-A´ cannot also be in process at the same time." In other words, a neuron which is stimulated within a certain process cannot execute the negation of this process at the same time.

On the other hand there are parallel simultaneously interacting processes in living systems which cannot be described separately or sequentially. One example is given by the processes of cognition and volition. In his the article "Cognition and Volition" Günther describes this very old intellectual problem from a more philosophical point of view. For more information on this particular problem it is referred to the literature ( cf. Ref. [7] ).

Now we have to ask for the meaning of a ´contexture´.

A contexture is a logical domain were all classical logical rules hold rigorously. The essential point or poly-contexturality results from the mediation by order and exchange relations between different (at least three) contextures. It is important to realize that the contextures do not exist in isolation, but are mediated with each other by new and non-classical logical operators, such as for example, the ´transjunction´, which allows the modeling of bifurcation from one logical domain into at least two parallel, simultaneously existing contextures. In summary, the poly-contextural logic represents an intrinsic parallel (multi-negational) calculus with different logical domains (contextures) closely interwoven with one another by means of new logical operators. In contrast, all non-polycontextural logical systems are mono-contextural. In other words, the Aristotelian logic and all its derivatives are mono-contextural concepts. It is impossible to describe living processes without antinomies and ambiguities in a mono-contextural logical concept. All the laws of physics belong to a mono-contextural concept, and even the models of neural nets are mono-contextural models. They never will teach us anything about cognition (cf. Ref. [7]).

Mono-contextural formal models are always hierarchically structured, i.e., they are organized ultrametrically [8]. Hierarchy constitutes itself intra-contextural, i.e. within a contexture. Hierarchical models reflect sub-ordination. On the other hand, heterarchy constitutes itself inter-contextural, i.e. by transitions between different contextures in poly-contextural formal models (heteros := the other, and archein := the rule). Heterarchically organized structures or processes belong to the category of autonomous systems. Heterarchical structured models reflect co-ordination.

Without going into details we only would like to mention that an inter-contextural transition - a transjunction - is a process where the ´law of the excluded middle´ is rejected within a contexture. The law of identity in its classical sense only can be used within a contexture. Despite of its importance for mathematical proofs ´the law of identity´ in its classical form

becomes useless for modeling living systems. It was Heraclitus who already realized in his famous principle "everything flows" that identity is a kind of "divided unity", an identity which contains the difference.

Within a poly-contextural scientific concept it is possible to model "identity" as a property distributed among several contextures which is of necessity for the development of any ´theory of the living´ or a ´theory of subjectivity´.

For more details on the poly-contextural theory, i.e., the relation between kenogrammatics, graphematics and poly-contextural logic is referred to the literature [9]. For the terminology see also  "Glossary of PCL" [10].

In part_1 of the series "Günther_2000" we present a complete version of "Cognition and Volition" in German as well as in English. In addition we present two conference contributions of Gotthard Günther: "Als Wille verhält der Geist sich praktisch" and "Bewußtsein als Informationsraffer". Then there is the introduction of volume 2 (Beiträge zur Grundlegung einer operationsfähigen Dialektik) and the contents of volume 1-3. The article of the philosopher Willy Hochkeppel "Negativsprache zur Erfassung der Welt ? - Der Philosoph Gotthard Günther wird achtzig Jahre alt" was published 1980 in ´DIE ZEIT´ and gives an excellent picture about the philosopher Gotthard Günther.

In part 2 of the series "Günther 2000" we will present more theoretical aspects of the poly-contextural theory. Part 2 will be presented in February´2000. In part 3 a contribution about the concept of "time" within a poly-contextural theory will be presented.


[1] Gotthard Günther, in: "Philosophie in Selbstdarstellung", Vol. II, Felix Meiner, Hamburg, 1975, p. 1-76. back to text

[2] Gotthard Günther, Number and Logos, für die MCCUlloch-Festschrift ~ 1975 back to text

[3] Gotthard Günther, "Kritische Bemerkungen zur gegenwärtigen Wissenschaftstheorie - Aus Anlaß von Jürgen Habermas ´Zur Logik der Sozialwissenschaften´", in: Soziale Welt Bd. 19, 1968, 328?341 - translated: "Critical remarks about the contemporary theory of sciences - on the occasion of Jürgen Habermas´ "To The Logic of Social Sciences"". 
([download] as PDF-file) zurück zum Text

[4] Gotthard Günther : - "Grundzüge einer neuene Theorie des Denkens in Hegels Logik", Felix Meiner, Hamburg, 1933/1973 - "Idee und Grundriß einer nicht-Aristotelischen Logik", Felix Meiner, Hamburg, 1959/1978 - "Beiträge zur Grundlegung einer operationsfähigen Dialiktik", Band 1-3, Felix Meiner, Hamburg, 1976/80 Einige Beiträge Gotthard Günther´s finden sich auch im Internet hier im vordenkler webforum und unter: http://www.thinkartlab.com/pkl//  zurück zum Text

[5] Such as: 
- the many-valued logics of Lukasiewicz : J. Lukasiewicz, in: Selected Logical Papers, North Holland, Amsterdam, 1970 , - the fuzzy logic: L.A. Zadeh, "A new approach systems analysis", in: Man and Computer (M.Marois, ed.), North Holland, Amsterdam 1974, p.55-94. 
- the quantum logic : C.F.von Weizsäcker, "Classical and Quantum Description", in: The Physics Conception of Nature, (J.Mehra, ed.), Reidel Publ., Dodrecht, 1973. 
- the modal- or temporal- logic concepts, 
- the combinatorical logic : H.B.Curry, R. Feys, "Combinatory Logic", North Holland, Amsterdam, 1969 
- the dialogue logic : P.Lorenzen, K.Lorenz, "Dialogische Logik", Darmstadt, 1978.
- the calculus of indication : G. Spencer-Brown, "The Laws of Form", Julian Press, N.Y.1972 
- the calculus for self-reference : F.J.Varela, "A Calculus for Self-Reference", Int.J.General System, Vol.2, 1975, p.5-24. 
An analysis of the different logical-concepts has been given by: R. Kaehr, "Neue Tendenzen in der KI-Forschung - metakritische Untersuchungen über den Stellenwert der Logik in der neuen Künstlichen-Intelligenz-Forsschung", Stiftung Warentest, Berlin, 1980 (A reprint will be given in: www.vordenker.de 
- from Feb.´2000) R. Kaehr, "Zur Logik der Second Order Cybernetics - Von den Laws_of_Form zur Logik der Reflexion" in: Kybernetik und Systemtheorie, Dresdner Symposium, 1991, p.129-154. ( see also : www.vordenker.de) zurück zum Text

[6] O.L. Reiser, "Non-Aristotelian logic" in: The Monist 45 (1935) p.103 zurück zum Text

[7] For further publications in this field see also: R. Kaehr and E.von Goldammer, "Poly-contextural modelling of heterarchies in brain functions", in: Models of Brain Functions, (R.M.J. Cotterill ed.) Cambridge Universty Press 1989, S. 483-497. (siehe auch : http://www.vordenker.de ) and R. Kaehr und E. von Goldammer, "Again, Computers and the Brain", Journal of Molecular Electronics 4, 1988, S. 31-37 ( see also in publication area of ICS ) zurück zum Text

[8] R.Rammal, G.Toulouse und M.A.Virasoro, "Ultrametricity for physicists", Rev.Mod.Phys.58 (1986) 765-788. P. Erde, "On the Ultrametric Structure or Semantic Memory: Scope and Limits", in: Cybernetic and Systems, (R.Trappel, ed.), Kluver Acad.Publ., 1988, p.329-336. zurück zum Text

[9] a) R. Kaehr, "Materialien zur Formalisierung der dialektischen Logik und der Morphogrammatik 1973-75." in: G. Günther "Idee und Grundriß einer nicht-Aristotelischen Logik.", 2. Aufl., Felix Meiner Verlag, Hamburg 1978, 117 S. b) R. Kaehr und T. Mahler, "Morphogrammatik - Eine Einführung in die Theorie der Form" in: http://www.thinkartlab.com/pkl// zurück zum Text

[10] Glossary of PCL: within vordenker webforum or under http://www.thinkartlab.com/pkl// zurück zum Text