### Negative Ecology of Sign Systems

Die Ressourcen des Denkens

Das Denken vollzieht sich im Medium des Zeichengebrauchs. Die Semiotik als formalisierte Theorie des rationalen Zeichengebrauchs kennt nur die abstrakte Verknüpfung (Konkatenation/Substitution) von vorgegebenen Zeichen eines (beliebigen, endlichen oder unendlichen) Zeichenrepertoires, das allerdings formal auf zwei Elemente (Atomzeichen und Leerzeichen) reduziert werden kann. Das Zeichen als Zeichengestalt trägt sich im Denken aufgrund der Trägerfunktion der Materialität des Zeichenereignisses. Die Differenz von Zeichengestalt und Zeichenvorkommnis kommt in der Semiotik selbst nicht zur Darstellung; sie ist ihre verdeckte Voraussetzung.

Die Zeichengestalt verbraucht sich nicht im Gebrauch ihres Ereignisses. Der Modus der Wiederholung des Zeichens ist abstrakt und gründet sich auf der Abwesenheit des Subjekts und der Annahme der Unendlichkeit der Ressourcen (Raum, Zeit, Materie).

[...]

Der Alphabetismus findet in seiner letztlichen Digitalität und Linearität multimedial zu sich selbst und zu seinem Abschluß in der Objektivation seiner vermeintlichen Vernetzung. Die Graphematik be-wegt den Übergang der Inskription zur Ermöglichung einer nach-schriftlichen und trans-terrestrischen Epoche des Welt-Spiels.

Kaehr, Proömik und Disseminatorik, 1995

Translation

Thinking is realizing itself in the medium of the use of signs. Semiotics as the formalized theory of rational use of signs knows only the abstract linkage (concatenation/substitution) of given signs (finite or infinite) of a sign repertoire, which however can be formally reduced to two elements (atomic sign and blank) only.

In thinking, the sign as sign type carries itself due to the carry function of the materiality of the event of sign tokens. The difference of sign type and sign token (occurrence) itself is not reflected in semiotics; it is its covered condition.

The sign type does not use (consume) itself in the use of its event. The mode of iterability of the signs is abstract and based on the absence of subjectivity and the assumption of the infinity of resources (space, time, matter).

About sign systems

Elementary signs

„Elementary signs are signs that we shall consider as not having parts. The content of this concept depends upon the conventions that are assumed. [..] In simultanous consideration of any two elementary signs, we determine whether they are the same or different. These concepts are also conditional."

Abstraction of identification

"The possibility of determining when two elementary signs are the same permits us, applying an abstraction of identification, to speak of two identical elementary signs or of one and the same elementary sign. On this basis, we introduce the concept of an abstract elementary sign, that is, of an elementary sign, considered up to identity.

Concrete elementary signs will be considered as representatives of the corresponding abstract elementary signs. Two concrete elementary signs represent one and the same abstract elementary sign if and only if they are identical."

Abstract alphabets

"Lists of elementary signs are called alphabets. We shall call two alphabets equal if every elementary sign appearing in the first alphabet is identical with a certain elementary sign appearing in the second alphabet, and conversely. Alphabets considered up to equality will be called abstract alphabets."

Potential realizability

"Another abstraction, (...), is abstraction of potential realizability. This consists in departing from real limits of our constructive possibilities and beginning to discuss arbitrarily long abstract words as if they were constructible. Their realizability is potential: their representatives could be practically realized if we had at our disposal sufficient time, space, and materials." A. A. Markov

Ideality of Notational Systems

The abstractness of sign systems and their independence of real world conditions like space and matter, are brought one step further by Alfred Goguen’s definition of institutions and signatures for programming languages.

To speak about alphabetism in formal systems, with its atomicity, linearity, iterability, and ideality is not forgetting the conceptual move from alphabets as sign repertoires to the more abstract, category theoretic concept of signatures of institutions.

"Institutions accomplish this formalization by passing from "vocabularies" to signatures, which are abstract objects, and from "translations among vocabularies" to abstract mappings between objects, called signature morphisms;

then the parameterization of sentences by signatures is given by as assignment of a set Sen(S) of sentences to each signature S, and a translation Sen(f) from Sen(S) to Sen(S') for each signature morphism f: S –-> S', while the parameterization of models by signatures is given by an assignment of a class Mod(S) of models for each signature S, and a translation Mod(S') –-> Mod(S) for each f: S –-> S'.

[...]

Satisfaction is then a parameterized relation |=S between Mod(S) and Sen(S), such that the following satisfaction condition holds, for any signature morphism f: S –-> S', any S-model M, and any S'-sentence e: M |=S f(e) iff f(M) |=S' e

This condition expresses the invariance of truth under change of notation."

http://www.cs.ucsd.edu/users/goguen/projs/inst.html

Signatures are even better realizing alphabetism than sign repertoires because they are emphasizing the abstractness of alphabetical signs, that is, the ideality of signs, and sign systems, in contrast to the concrete occurrence of signs, independent of the content of the sign repertoire, i.e., the concrete notational material. Sign systems are not only characterized by atomicity, linearity, iterability, but also by ideality. Ideality is the medium of the realization of signs.

Uniqueness of Semiotics

Despite the fact that semiotics, like institutions, have many realizations, they are conceived as being conceptually unique. There is, in principle, one and only one semiotics. As there is, in principle, one and only one (universal) logic. There may be many different semiotic or logical systems realizing special purposes.

In the conceptual graph, uniqueness (oneness) is marked as 1. The trichotomy of semiotics is ruled by the order relations between alphabet (signature), rules (morphisms) and semiotics (institution) based on 1.

The oneness of semiotics has its foundation in mono-contexturality as opposed to poly-contexturality.

Negative Ecology

Today, we have to consider the destructiveness of sign systems. Technology, as realized in computing, is based on a sign-economy which is denying the limitations of its resources. By the application to real-world problems of understanding, organizing and computation, the abstractness of sign systems has become, after its deliberating function to human society, more and more an ecologically exploitative and destructive power. This might be a historical situation and might not to be the final paradigm of scriptural work. New notational systems, beyond alphabetism and not based on uniqueness, have to be invented.

Das Denken vollzieht sich im Medium des Zeichengebrauchs. Die Semiotik als formalisierte Theorie des rationalen Zeichengebrauchs kennt nur die abstrakte Verknüpfung (Konkatenation/Substitution) von vorgegebenen Zeichen eines (beliebigen, endlichen oder unendlichen) Zeichenrepertoires, das allerdings formal auf zwei Elemente (Atomzeichen und Leerzeichen) reduziert werden kann. Das Zeichen als Zeichengestalt trägt sich im Denken aufgrund der Trägerfunktion der Materialität des Zeichenereignisses. Die Differenz von Zeichengestalt und Zeichenvorkommnis kommt in der Semiotik selbst nicht zur Darstellung; sie ist ihre verdeckte Voraussetzung.

Die Zeichengestalt verbraucht sich nicht im Gebrauch ihres Ereignisses. Der Modus der Wiederholung des Zeichens ist abstrakt und gründet sich auf der Abwesenheit des Subjekts und der Annahme der Unendlichkeit der Ressourcen (Raum, Zeit, Materie).

[...]

Der Alphabetismus findet in seiner letztlichen Digitalität und Linearität multimedial zu sich selbst und zu seinem Abschluß in der Objektivation seiner vermeintlichen Vernetzung. Die Graphematik be-wegt den Übergang der Inskription zur Ermöglichung einer nach-schriftlichen und trans-terrestrischen Epoche des Welt-Spiels.

Kaehr, Proömik und Disseminatorik, 1995

Translation

Thinking is realizing itself in the medium of the use of signs. Semiotics as the formalized theory of rational use of signs knows only the abstract linkage (concatenation/substitution) of given signs (finite or infinite) of a sign repertoire, which however can be formally reduced to two elements (atomic sign and blank) only.

In thinking, the sign as sign type carries itself due to the carry function of the materiality of the event of sign tokens. The difference of sign type and sign token (occurrence) itself is not reflected in semiotics; it is its covered condition.

The sign type does not use (consume) itself in the use of its event. The mode of iterability of the signs is abstract and based on the absence of subjectivity and the assumption of the infinity of resources (space, time, matter).

About sign systems

Elementary signs

„Elementary signs are signs that we shall consider as not having parts. The content of this concept depends upon the conventions that are assumed. [..] In simultanous consideration of any two elementary signs, we determine whether they are the same or different. These concepts are also conditional."

Abstraction of identification

"The possibility of determining when two elementary signs are the same permits us, applying an abstraction of identification, to speak of two identical elementary signs or of one and the same elementary sign. On this basis, we introduce the concept of an abstract elementary sign, that is, of an elementary sign, considered up to identity.

Concrete elementary signs will be considered as representatives of the corresponding abstract elementary signs. Two concrete elementary signs represent one and the same abstract elementary sign if and only if they are identical."

Abstract alphabets

"Lists of elementary signs are called alphabets. We shall call two alphabets equal if every elementary sign appearing in the first alphabet is identical with a certain elementary sign appearing in the second alphabet, and conversely. Alphabets considered up to equality will be called abstract alphabets."

Potential realizability

"Another abstraction, (...), is abstraction of potential realizability. This consists in departing from real limits of our constructive possibilities and beginning to discuss arbitrarily long abstract words as if they were constructible. Their realizability is potential: their representatives could be practically realized if we had at our disposal sufficient time, space, and materials." A. A. Markov

Ideality of Notational Systems

The abstractness of sign systems and their independence of real world conditions like space and matter, are brought one step further by Alfred Goguen’s definition of institutions and signatures for programming languages.

To speak about alphabetism in formal systems, with its atomicity, linearity, iterability, and ideality is not forgetting the conceptual move from alphabets as sign repertoires to the more abstract, category theoretic concept of signatures of institutions.

"Institutions accomplish this formalization by passing from "vocabularies" to signatures, which are abstract objects, and from "translations among vocabularies" to abstract mappings between objects, called signature morphisms;

then the parameterization of sentences by signatures is given by as assignment of a set Sen(S) of sentences to each signature S, and a translation Sen(f) from Sen(S) to Sen(S') for each signature morphism f: S –-> S', while the parameterization of models by signatures is given by an assignment of a class Mod(S) of models for each signature S, and a translation Mod(S') –-> Mod(S) for each f: S –-> S'.

[...]

Satisfaction is then a parameterized relation |=S between Mod(S) and Sen(S), such that the following satisfaction condition holds, for any signature morphism f: S –-> S', any S-model M, and any S'-sentence e: M |=S f(e) iff f(M) |=S' e

This condition expresses the invariance of truth under change of notation."

http://www.cs.ucsd.edu/users/goguen/projs/inst.html

Signatures are even better realizing alphabetism than sign repertoires because they are emphasizing the abstractness of alphabetical signs, that is, the ideality of signs, and sign systems, in contrast to the concrete occurrence of signs, independent of the content of the sign repertoire, i.e., the concrete notational material. Sign systems are not only characterized by atomicity, linearity, iterability, but also by ideality. Ideality is the medium of the realization of signs.

Uniqueness of Semiotics

Despite the fact that semiotics, like institutions, have many realizations, they are conceived as being conceptually unique. There is, in principle, one and only one semiotics. As there is, in principle, one and only one (universal) logic. There may be many different semiotic or logical systems realizing special purposes.

In the conceptual graph, uniqueness (oneness) is marked as 1. The trichotomy of semiotics is ruled by the order relations between alphabet (signature), rules (morphisms) and semiotics (institution) based on 1.

The oneness of semiotics has its foundation in mono-contexturality as opposed to poly-contexturality.

Negative Ecology

Today, we have to consider the destructiveness of sign systems. Technology, as realized in computing, is based on a sign-economy which is denying the limitations of its resources. By the application to real-world problems of understanding, organizing and computation, the abstractness of sign systems has become, after its deliberating function to human society, more and more an ecologically exploitative and destructive power. This might be a historical situation and might not to be the final paradigm of scriptural work. New notational systems, beyond alphabetism and not based on uniqueness, have to be invented.

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