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Niels Ole Finnemann: Thought, Sign and Machine, Chapter 7 © 1999 by Niels Ole Finnemann.
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7. The semantics of notation forms

7.1 The expression substance and the semantic potential of informational notation

Shannon's theory left a certain terminological confusion behind it. The concept of information merges with the concepts of noise and signal. This is because Shannon measured these phenomena with the same yardstick, which relates solely to the temporal dimension of the physical form. The confusion, however, is understandable because the theory concerns signal systems in which noise signals with the same physical form as the intended signals occur frequently. The interpretation of the theory must therefore take its point of departure in the fact that there are no physical criteria for distinguishing between the symbolic notation form (whether this is called information, signal, notation or symbol) on the one hand, and the concept 'noise' in the same physical form, on the other. This distinction is of a semantic nature and can only be made through an interpretation which assumes an interpreter capable of deciding whether a given physical form should be understood as an intended symbolic notation or not.

As all physical forms which can be used as symbolic expression units can also occur without being symbolic expression units, this is a question of presenting the problem in terms of a general noise theory valid for all symbolic expression forms. In other words, a symbolic component is included in the definition of any symbolic expression form.

The question now is, whether the semantic procedure through which a signal is distinguished as a signal, i.e. as a valid member of a message, always has the same character no matter which notation system and no matter what the semantic exploitation of the notation system. Is an /a/ which occurs in a written message, for example, defined in the same way as a /+/ or an /a/ which occur in a mathematical expression?

If this is the case, this special semantic operation can reasonably be regarded as a general precondition for all symbol formation and this level can be omitted from the description of differences between symbol systems.

If, on the other hand, we can distinguish between different forms of semantic separation of notation elements it becomes necessary to include the semantics of notation forms in the description of the languages which use notation systems.

The following two chapters contain my arguments for the second of these two possibilities, as it will be demonstrated that informational notation is a new, independent notation system, which by virtue of its definition possesses a peculiar set of semantic potentialities which both separate themselves from the semantic potentialities of common language and formal languages.

In writing at this point of linguistic, formal and informational semantics (or semantic regimes) the term semantics is used in a more general sense than is usual within linguistics, where it is used of a special discipline, the study of linguistic meaning structures, as distinct from other linguistic disciplines. What I mean by a semantic regime in the following is a set of (implicit or explicit) codes which we use to produce or read a given symbolic expression, no matter whether we are capable of providing a consistent description of these codes or not. Over and above this, the concept of semantics will also be used in a number of more limited senses, as a distinction is made between semantic levels within the individual semantic regimes: those of the notation forms, those of the syntactic structures and those of the content forms. This differentiation in the use of the term specifies that the meaning dimension indicated by the term is valid at all these levels and has therefore an unlimited, but not unstructured character.

It will be shown in the following that the difference between the semantic potentialities of common language, formal languages and informational representation is rooted in two relationships, partly the relationship between expression substance and expression form and partly the relationship between notation, syntax and the general semantic regime.[1]

A short outline of the content of this thesis as it applies to informational notation follows.

The significance of the expression substance for semantic potential is first and foremost connected with the demand for mechanical execution, as this demand 1) releases the notation system from a function which is essential - and common - to both formal and linguistic notation systems, namely to serve as a means for human sensory recognition and 2) determines that a limited number of notation units, each of which is semantically empty, are used.

In both these respects, I claim that the semantic potential of the expression form is directly related to the properties of the expression substance, as these properties allow a number of previously unknown possible expressions, including new possibilities and types of relationship between expression forms and content forms. The postulate, in other words, is that that the expression substance provides the expression form with a semantic potential it would not have in an expression substance with other properties.[2] The most far-reaching new possible variation is included in the demand that rules must be represented in exactly the same form - and therefore with exactly the same possibilities for variation and editability - as all other forms of data.

The potential for semantic variation, which is rooted in the relationship between expression substance and expression form, provides not only the possibility of the mechanical execution of a delimited class of formal, closed semantic operations (the properties of the universal calculating machine), it is also the precondition for what will be described (in chapters 8 and 9) as the ]multisemantic potential of informational notation, as informational notation, unlike linguistic and formally defined notation systems, can be subjected to a multiplicity of semantic regimes, including both linguistic and formal, but also pictorial regimes. While linguistic and formal notation systems are characterized as mono-semantic with a fixed - but mutually different - bond between the notation system and the semantic regime, informational notation is characterized by multisemantic potential. A more precise description of the concept, multisemantic potential, is given in chapter 9. It should, however, be noted in advance that the concept 'multisemantic' differs from the concept 'polysemy', which describes the circumstance that an expression can have several interpretations within a given semantic regime. Both linguistic, formal and informational expression forms can thus be polysemic - each in its own way - but only the informational expression has multisemantic potential.

7.2 The expression substance and the sign function

The first problem in carrying out a comparative analysis of different symbolic expression systems concerns the terminological starting point where, there is a general choice between semiotic and formal symbol theories. As the formal symbol theories assume full equivalence between expression form and content form, they do not provide the necessary concepts for describing the differences between formal and linguistic expressions. They lack - as was shown by the description of Simon's symbol theory (section 5.9) and Shannon's description of informational notation (chapter 6) - in particular the concepts for describing the possibilities of semantic variation in the relationship between expression and content forms.[3]

I will therefore take my point of departure in semiotic concepts. As the semiotic understanding of signs was developed, on historical grounds, with the emphasis on the description of spoken and/or written common language, there is also a risk here of turning a given symbolic language (in this case the spoken/written language) into a norm for describing other symbolic languages. This risk, however, can be averted because the semiotic point of departure has been chosen as a means for a comparative analysis of the differences between informational, formal and linguistic expressions.

The choice of the semiotic approach thus implies no postulate that it is possible to fit the description of the informational and formal symbolic languages into the sign function which characterizes common languages. On the contrary, the choice has been made for the purpose of describing the sign theoretical differences between these languages.

It will be evident from the following that the linguistic sign description is inadequate with regard to an important point in the present connection, as it will become necessary to include the expression substance in the understanding of the sign function.

The fact that it is necessary to take this step - in spite of the conceptual problems consequent on it, because the sign function is defined in modern linguistic theory as a relationship between expression form and content form (independent of expression and content substances) - is first and foremost due to the semantic potential inherent in the relationship between expression substance and expression form in the informational notation system.

As a consequence of this there are two possibilities. One is that the expression substance has a semantically significant meaning for the informational sign function, but not for the linguistic function. The second is that the relationship between expression substance and expression form can also be included in the linguistic sign function.

The first possibility appears most attractive because it allows a greater degree of correspondence to and exploitation of existing linguistic theories. But it is the second possibility which gained the upper hand, because a comparison of informational and linguistic notation will have a different result depending on whether the starting point is spoken or written language.

The crux of the matter here is whether it can be claimed that the difference between the expression substance of spoken and written language can create a basis for a distinction between the semantic potentialities of spoken and written language. If this is the case, the relationship of the expression form to the expression substance must also be included in the linguistic sign concepts.

Although this question has general sign theoretical implications, it can be decided through a more limited analysis of the expression forms of spoken and written language.

There is no demand for a complete description of the general implications, all that is demanded is proof that the different expression substances of spoken and written language determine that there is no complete semantic compatibility between the two, that - in spite of a large semantic intersection of sets - they each have a semantic marginal zone connected to the dissimilarity of the expression substances.

The normal argument for the external and arbitrary (semantically irrelevant) relationship of the expression substance to the linguistic expression form builds upon the observation that the phonetic sound, or the physical form of the grapheme, provides no information on the linguistic utilization which, on the contrary, is assumed to be based on an "internal" linguistic system of sound patterns (Saussure) or relationships between figurae (Hjelmslev) that are of a psychological (or in Hjelmslev's terminology, "immanent" linguistic) and not physical nature. This point of view makes it possible to explain how the same language can be manifested in different expression substances. This last view will also be maintained here, as the analysis of Shannon's information concept confirmed that it is not possible to provide purely physical criteria for the decision as to whether a given physical form is a valid member of an expression.

None of these arguments, however, provides any reason to conclude - with Hjelmslev - that linguistic or other symbolic expression forms are independent of the properties of the expression substance. Although a language may use many different expression substances, it obviously cannot use them all. But language cannot exist without substance either, and there is nothing to prevent different expression substances from creating different restrictions - and possibilities - for its symbolic use. The relationship between substance and form cannot, in other words, create a basis for an axiomatic delimitation between the non-linguistic and the linguistic, but must be made the object of investigation.

The point of departure here (in section 7.3) will be taken in Umberto Eco's theoretical delimitation of the sign theory towards its "lower threshold" - attached to his distinction between "signals" and "signs" - as Eco at the same time attempts to describe a sign concept which is not only valid for (or formed around) the linguistic sign function.

This attempt leads Eco to a dissolution of the concept of a well-delimited language system which is outside (as a precondition of) the sign function. He therefore defines the sign function independently of the expression form connected with a multiplicity of possible codings, while the language system, the structure, becomes a conceptual entity, we "pretend" exists, just as the sign function itself is defined as a purely mental correlation of mutually different - mental - code procedures.

If the sign function is connected with - and manifested through - different codings, the transition between these code procedures cannot be explained at the level of the code procedures. The way the problem presents itself therefore gives rise - as a corollary to the noise theoretical conclusions extracted from Shannon's information theory - to the assumption that the formation of the code procedure occurs through a semantic exploitation of the forms inherited by the expression substance.

It is hardly possible to describe the complete repertoire of possibilities for the semantic exploitation of expression substance forms, possible signals, but, as we saw in chapter 6, any identification of a signal will depend on a concatenation in which a physical form is linked to a symbolic legitimacy, even in the cases where the physical signal manifests itself without any determinable content.

Where Eco attempted to determine the general sign function by defining it independently of expression substance and expression form, it is claimed here that it is necessary to include the relationship to the expression substance in the understanding of any sign relationship and that it is possible to describe central differences between different sign functions as differences which are rooted in different ways of coding expression substance forms.

The central point here is that the two criteria included in any definition of signals or physical notation forms are mutually dependent, but at the same time comprise two independently variable axes. It is possible to carry out the definition on the "physical" axis independently of the definition on the semantic axis. It is therefore also possible to connect the two axes in different ways.

The ambiguity explains, for example, the fact that we can recognize a multiplicity of different physical forms (variations of the substance form) as one and the same letter, as the recognition can both rely on the knowledge of the symbolic expression form and the expression's meaning. This also explains how it is possible to establish a notation system which - released from the demand for recognition - can be based primarily on an unambiguous definition of the physical form of the expression substance - with the modifications which follow from the problem of noise theory.

It will be evident from the analysis (chapter 7 and sections 8.1 - 8.3) that in certain respects informational notation is more closely related to alphabetical notation than to formal notation (the first two use a limited number of notation units and the individual notation units have no independent meaning). Whereas written language notation, however, allows variation on both the physical and semantic axes, informational notation allows only variation on the semantic, while formal notation only allows variation on the physical axis (as a given notation unit is defined on the basis of a semantic - fixed or variable - value of its own).

The definitions of physical form and semantic legitimacy therefore become connected in three different ways, of which only the latter brings about an unambiguous relationship between the expression form and its content, while the two others allow the same physical form to manifest itself with changing functions and values. These two, however, are also mutually distinguished. Informational notation is based on an unambiguous relationship between the form of the expression substance and the expression form, while written language notation not only generally allows a variation in the physical substantiation of the individual expression form, but also exploits certain substance variations - such as italicization - for semantic purposes.

What is lacking therefore is a concept which describes the semantic variation possibilities which are connected with the various forms of relationship between expression substance, expression form and content form.

In the following this relationship will be referred to with the concept 'redundancy structure'. Section 7.5 contains a theoretical definition of the redundancy concept, while the relevance of the concept for a description of linguistic expression forms is discussed with the starting point in a critical analysis of Hjelmslev's concept of figurae in section 7.6.

With this analysis as a starting point, the significance of the redundancy function for linguistic sign formation is discussed in section 7.7. Unlike Hjelmslev, I claim that the different expression substances in spoken and written language create a basis for two partially different forms of redundancy structure, which again determine differences in semantic potential. Further to this, I argue that redundancy structures should be understood as a precondition for the stabilization of linguistic rule structures, as this enables an explanation of the possibility of rule weakening, rule deviation and rule suspension and of co-existence between mutually overlapping, but not clearly delimited rule structures relative to the intended meanings expressed in the sign function. As different forms of redundancy can at the same time be semantically significant, it is correspondingly necessary - dissimilarly to ordinary linguistic assumptions - to include the redundancy function in the sign concept.

Section 7.8 includes a summary of the comparative analysis of the different semantic potentialities which are connected with the use of notation systems in common languages (written and spoken) and formal languages. Finally, pictorial representation, which does not assume a finite set of notation units, is included with regard to the analysis of the informational sign potential which also embraces the possibility of pictorial representation.

A further analysis of the significance of redundancy in informational notation is the subject of sections 8.1 - 8.3. A schematic survey of the relationship between linguistic, formal and informational notation systems appears in section 8.3, page 276.

As the use of informational notation is based on algorithmic organization, it also becomes necessary to investigate whether algorithmic "syntax" places semantic limitations on the use of informational notation. At this point, the comparative analysis must be taken a step further to include the relationship between the formal and informational representation of algorithmic procedures (sections 8.4 - 8.6).

7.3 Signal, sign and code - Umberto Eco

It is symptomatic that within linguistics, information theory is often seen as a theory of - physical - signals, which are either completely outside the domain of linguistics or constitute a borderline area. Eco, (1976), who defines semiotics in relationship to the subjects which are not those of semiotics, the signals of information theory, together with physical stimuli thus comprise a "lower threshold" which should properly be studied separately, although it can also be regarded as a "missing link" between "the universe of signals and the universe of signs".[4]

On the face of it, the reason for this distinction appears reliable:

The proper objects of a theory of information are not signs but rather units of transmission which can be computed quantitatively irrespective of their possible meaning, and which therefore must properly be called 'signals' and not 'signs'.[5]

Although well-established, this conceptual convention contains a number of difficulties, first and foremost that the physically defined signals which comprise information theory's "proper objects" are only available by virtue of a theoretical definition, an attribution of meaning. They are thus brought about by a semiotic activity.

Eco can also show that the relationship between this type of signal and other signs must rather be described as the relationship between expressions based on different coding procedures. The central distinction is therefore not the distinction between signal and sign, although Eco maintains this, but on the contrary between:

I: Formal code procedures such as

II: A superior code or

While the signal system, semantic system and response system are all formal code systems (designated s-codes, where s stands for system), the last coding comprises the semiotic code procedures which, unlike the s-codes, are not characterized by a definable structure, but on the contrary by bringing about the unity between signal code and content code (either a semantic set or a behavioural response), which can constitute a sign.[6]

Although we may accept Eco's concept of the missing structure as a basic characteristic of semiotic processes, his description leaves the problem that s-codes, which are assumed to be able to exist independently of any form of meaning or communicative purpose, are themselves based on signals or possible content entities which have been produced by a semiotic activity. They can thus not simply occupy a place in sign theory as an underlying material which creates the basis for a semiotic process.

Traffic lights have often been used to illustrate the theoretical difference between a signal system and a sign system, as importance is attached to the fact that the motorist need not subject the light picture to any interpretation. Signals are regarded in these examples as stimuli which produce a mechanical response. Although for the sake of the example we can ignore the fact that it would be extremely dangerous to react completely mechanically to traffic lights, the example provides no basis for the theoretical distinction. If the motorist can react mechanically to the light signals, it will depend on two things. First, that there is an exhaustive set of rules which prescribe an unambiguous interpretation of the total signal system. Second, the motorist is familiar with this total system and willing to accept the received interpretation. He asks no questions, is not in doubt, proposes no alternative possible interpretations. His behaviour is exactly the same as that of a man who receives a letter containing a message of which he takes note and then complies with any instructions it may contain. The acceptance is a semiotic process.

Whether this acceptance is established in seconds or through years of anxious consideration for and against with the participation of a larger or smaller number of people, it cannot motivate a theoretical distinction between signal and sign. The traffic lights are part of a sign function both for the motorist and for the authorities that have established the signal system.

One of the reasons that traffic lights have been considered as a signal system of a lower rank and outside the domain of sign theory is presumably because the message of the traffic lights is presented in a monotonous circularity and within an unambiguous rule system characteristic of commands. Although the messages change with high frequency, nothing very novel is communicated.

That an expression does not provide the receiver with anything new, however, does not mean that it has no semantic content, but simply that its content is already familiar. Familiarity - which in the case of the traffic lights does not, however, include the highly meaningful time of the message - cannot motivate any theoretical distinction between signal and sign, among other things because it would then be necessary to assert that a message only contains signs when read for the first time, but not the second or third.

It would therefore be more apt to describe the traffic signal system's notation as a notation where each individual expression unit is connected with a specific content meaning.

The semantic coding which indicates a physical entity (e.g. represented by the colours red, amber and green) as members of a notation system is connected with a semantic coding which connects each expression unit with a content form that in this system has a definitory and unambiguous character. The coding of this system at the same time includes a declaration of a set of rules which establish the legal relationships between the individual notation unit's content forms. These rules are not expressed in the system itself, but are necessary for coding and de-coding it.

Now the signal structure, as Eco points out, can also be described by itself and possibly used in completely different meaning contexts - the signal structure can be polysemic. It is apparently available as an independent, purely syntactic structure which is not itself based on a sign function. But this is only apparently, as the structure depends both on the definition of the units' physical value and legitimacy and on the mutual relational connections - in this case the choice of the opposition, red-green, the combination of red-amber as respectively both-and (warning) and either-or (the state between green and red) etc.

The simple - or "lower" - signal system (the s-codes) thus requires that the notation system is subject to two simultaneous, but different codings, in which the individual notation unit is defined as a notation unit and connected with other notation units through a more general, preordained rule system. In other words, this is a question of a genuine sign function and this coding procedure, as will be discussed in greater detail in section 7.8 and chapter 8, is at the same time also the common and characteristic, basic form of all formal symbolic languages.

The double code procedure is thus included not only in the relationship between a syntactic and a semantic coding, but also in the coding of each of the two forms of s-codes. Eco touches on the problem when he concludes this part of the analysis by demonstrating that, ultimately, it is impossible to decide whether one or the other type of coding comes first and that:

Signification encompasses the whole of cultural life, even at the lower threshold of semiotics.[7]

This also expresses one of the reasons why Eco more generally argues against the idea that scientific knowledge is a definite knowledge of phenomena.

The question is whether this reference to the chicken and the egg can simply remain for ever as a final reference, or whether the uncertainty in the conceptual foundation, which is connected here with the insoluble problem of origins (where and how did semiotics begin), perhaps also has its price for the ability of the semiotic theory to describe the difference between sign systems.

As we have seen, Eco uses the dubious distinction between sign and signal as a foundation for the semiotic theory in opposition to the mathematical "signal theory", (information theory in Shannon's sense) as a definition of a lower threshold for the subject area of semiotic description. It even appears as though Eco is closer to allowing traffic lights and other signal systems a place in human sign activity than the informational signals, because the informational signals can be studied independently of their content:

We are now in a position to recognize the difference between a signal and a sign. A signal is a pertinent unit of a system that may be an expression system ordered to a content, but could also be a physical system without any semiotic purpose; as such it is studied by information theory in the stricter sense of the term. A signal can be a stimulus that does not mean anything but causes or elicits something; however, when used as the recognized antecedent of a foreseen consequent it may be viewed as a sign, inasmuch as it stands for its consequent (as far as the sender is concerned). On the other hand a sign is always an element of an expression plane conventionally correlated to one (or several) elements of a content plane.[8]

Even if we now - erroneously - accept that information theory can describe informational notation independently of semantic content, it is not a well chosen criterion for separating informational signals from other signals, because we can also establish a corresponding signal consideration in all other expression systems. But nor is information theory concerned, as we have seen, solely with expression systems, it is also concerned with the development of a special - and new - type of relationship between expression and content forms.

Where as the traffic light system and all other formal notation systems are characterized by the simultaneous declaration of the individual notation units' membership and establishment of internal, syntactic and semantic relationships respectively, informational notation is characterized by a systematic distinction between the declaration of membership and the establishment of syntactic and semantic relationships respectively. While formal systems connect syntactic and semantic codes by attributing a semantic value to the individual notation, syntactic and semantic codes in informational notation are only attributed to a cohesive sequence of units.

As the use of formal and informational notation thus builds upon two different principles for the formation and connection of expression and content forms, this is not a question of two different kinds of signal, some of which are connected with a content meaning and some of which are not, but of two different sign functions, as expression form and content form are connected in two different ways.

While these differences can be described within the framework of the semiotic/linguistic sign concept, i.e. without regard to expression substance, the picture changes when the mechanical properties of informational notation are also included. Where the formal expression form allows variation in relationship to the expression substance, the informational expression form is defined by an unambiguous bond. It was, as we saw in chapter 5, precisely this demand which - combined with the demand for universality - made it necessary to convert formal notation to informational notation with the result that the informational expression is available in a form with other semantic variation possibilities, even in the cases where it is derived completely mechanically from a formal notation.

The physical definition of the expression form - the binding of the expression form to the expression substance - thus gives informational notation a special semantic potential which is directly connected with the physical-mechanical form of the expression substance and the properties of this form. The substance of the expression form is thereby included as a specific and constitutive part of the informational sign function in a way which separates this both from the sign functions of formal and common languages.

No matter what significance the expression substance has for common language and formal sign relationships, its significance for the informational sign relationship must lead to a re-interpretation of the structuralist sign concept.

7.4 Eco's sign concept - "Signals" and "signs"

The demand for a re-interpretation of Saussure-Hjelmslev's structuralist sign theory is not new nor in any way original. On the contrary, similar demands - and suggestions for such re-interpretations - appear repeatedly as a kind of lowest common denominator for post-structuralist semiotics, represented, for example, by Jacques Derrida and Umberto Eco, where the criticism in both cases finds a partial motif in developments within information technology and information theory, just as post-structuralist criticism also more generally aims at a formulation of sign concepts which include all forms of human (and possibly other biological) sign functions.[9]

None of these theories, however, have made the informational sign function the object of closer analysis and they are therefore included only to the extent that the more general considerations of the sign concept also apply to the significance of the expression substance for the informational sign relationship.

Although Eco's reformulation of the sign concept takes its point of departure in a discussion of a lower threshold of semiotics, he finds no basis for including the expression substance in the sign concept. On the contrary, he separates the sign concept from the expression form: What is left as a possible distinction between the signal and the sign, when we look more closely at the definition quoted above, does not find expression at all:

We are now in a position to recognize the difference between a signal and a sign. A signal is a pertinent unit of a system that may be an expression system ordered to a content, but could also be a physical system without any semiotic purpose; as such it is studied by information theory in the stricter sense of the term. A signal can be a stimulus that does not mean anything but causes or elicits something; however, when used as the recognized antecedent of a foreseen consequent it may be viewed as a sign, inasmuch as it stands for its consequent (as far as the sender is concerned). On the other hand a sign is always an element of an expression plane conventionally correlated to one (or several) elements of a content plane.

Every time there is a correlation of this kind, recognized by a human society, there is a sign. Only in this sense is it possible to accept Saussure's definition according to which a sign is the correspondence between a signifier and a signified. This assumption entails some consequences: a) a sign is not a physical entity, the physical entity being at most the concrete occurrence of the expressive pertinent elements b) a sign is not a fixed semiotic entity but rather the meeting ground for independent elements (coming from two different systems of two different planes and meeting on the basis of a coding correlation).[10]

With this definition the sign concept becomes wholly a concept of an inner, mental procedure which is both imagined independently of the external physical and perceptible manifestations and of the internal physiological realization. It is impossible to decide whether a manifest expression is a signal or a sign. The distinction depends exclusively on the question whether a given signal - an expression system - is mentally interpreted or not. Eco expresses this more indirectly in phrases such as "recognized by a human society" instead of "a human mind" and in a subsequent remark that, strictly speaking, signs do not exist, but only sign functions.

That this is the case can be confirmed through analyses of manifest expressions. At the same moment we begin to reflect about the borderline between signal and sign, the distinction disappears. We only have access to signals through interpretation, which immediately transforms them into signs. There is no divergence here from Eco's general sign definition "A sign is everything which can be taken as significantly substituting for something else",[11] but on the contrary it points out that it not only undermines the lower threshold Eco proposes for semiotics, but also transgresses that threshold which connects the general sign concept with a manifest expression. The sign concept thereby, as Eco mentions in a note, coincides wholly with the meaning "intelligence".[12]

This sign definition is so general that it includes every articulatory design, but this has its price, which is not willingly accepted in semiotic theory, namely that this sign concept provides little help in the analysis of the different semantic potentialities of expression systems.

Linguistic literature also contains many examples of spoken and written language being understood as one - often both natural and national (!) - language - even though the two expression forms can enter into very different communicative connections with different demands on the expressions which must be manifested in order to make an exchange of meaning possible.[13]

In Eco's theory the problem is proposed differently because he replaces the universal rules of language (Saussure's "langue" or Hjelmslev's "language system", or "scheme" or "building") with a multiplicity of different - underlying codes - which do not comprise one system and are therefore not affected by the many exceptions in the use of language. The ghost of linguistic theory is thereby moved from the expression system into the code which resides in consciousness.

But it pops up again, because the code, according to Eco's universal definition of the sign as a non-physical, conceptual definition, is itself a sign, although we cannot see and do not know how it - or other traits of consciousness - are manifested in the physiological system. Like all signs, the code is also a cultural convention and the hidden codes are subject to the same problem of meaning balance as other signs:

every time a structure is described something occurs within the universe of signification which no longer makes it completely reliable.[14]

For semiotics as a science, the consequence for Eco is therefore that "semiotics must proceed to isolate structures as if a definitive, general structure existed". When we only pretend that a definitive language structure exists, we naturally have a great deal of latitude, as we can pretend that this structure has a host of different forms. It is more difficult to find an appurtenant criterion for choosing among the many possibilities.

As will appear from the next section, it is impossible to carry through this "proceeding as if" without paying a price. The idea of a general structure is - in spite of its fascinating character and although this idea has often led to new insights - no longer tenable. It creates difficulties in linguistics because, among other things, it reduces the relationship between language and the non-linguistic to a marginal phenomenon both in connection with the relationship between expression substance and expression form as well as the relationship between language form, meaning form and meaning content.

The relationship to the non-linguistic is a many-headed monster which includes both the referential dimensions (to the contents of consciousness, patterns of thought, the outside world and meaning relationships between different linguistic entities) the expression form and the substance of articulation. The form-substance relationship reappears in all areas, but in the following the presentation is concentrated on the relationship between the linguistic and non-linguistic as manifested at the level of notation.

As will be evident, different notation systems can both distinguish themselves by using different expression substances and by using the properties of the expression substances in different ways, as this can both be a question of using the different properties of the same expression substance and of using the same property in different ways, just as, finally, different properties of substance can be used in the same way. As the notation units in all notation systems can act as semantic variation mechanisms, the relationship to the expression substance can consequently also be included in the description of the semantic potential connected with a given notation system.

Conversely, this connection implies that the functions which are handled by the notation system in some symbolic languages can also be handled through other means. Notational distinctiveness, which belongs to the expression form, can thus sometimes be replaced by semantic distinctiveness at the level of content form or content meaning. Notation systems do not therefore comprise an independent, closed level, subject to an invariant rule structure, on the contrary, they are included in the different symbolic languages as a facultative semantic variation potential.

Although the semantic choices can embrace the suspension of underlying notation rules and conventions, there are considerable differences between the different notation systems, as they use different forms of rule determination and rule suspension. As the possibilities of rule suspension and rule variation differ in the different notation systems, these differences must also be included, which again implies that it is not possible to provide a wholly rule based delimitation of the individual notation systems.

As semantic use is not wholly rule based, the notation systems will instead be regarded as redundancy systems and the different uses will be described as different ways of using notational redundancy. This point of view therefore makes it necessary to provide a clarification of what is understood by redundancy and by the relationship between the redundancy and rule concept.

7.5 The redundancy concept

Although the concept of redundancy is used in a number of disciplines, it is a controversial concept which people often try to avoid. While most scientists and scholars appear to agree in acknowledging the existence of redundancy forms, many are sceptical that the concept can be used with the necessary precision. The concept appears only sporadically in the older structuralist linguistics because redundancy is seen here as a peripheral phenomenon on the borders of, or outside, language structure. This use is, as such, consistent because the concept is used with the meaning recurring structures with weak or negligible meaning, bordering on the superfluous, while the repetitive structures which are necessary in the linguistic expression are described by the concept 'language system'.

The distinction between the concept of redundancy and that of a language system thus has nothing to do with the occurrence of a structure or a pattern, nor with the form of the structure. Both concepts are used of recurring structures, patterns or regularities which thus constitute a common core of meaning. The distinction between the two, however, builds upon the function of the structure, as a distinction is made here between necessary structures, which do have a function, and superfluous or random structures, which do not.

While the concept of a language system rests on the connection between structure and necessity, an almost scientifically obvious idea, the redundancy concept builds on a far less obvious idea, as regularity - the recurring pattern - is described here as something meaningless, superfluous and random. It is apparent that such an idea can only with difficulty be reconciled with a stringent scientific description which, almost by definition, must ascribe meaning to any kind of pattern formation and regularity in the phenomena described. In older structuralist linguistics the answer to the way this problem presents itself was provided through the distinction between language system and language use, as redundancy phenomena were applied to the latter category.

In more recent structuralist - and post-structuralist - linguistics, which have objected to the sharp distinction between a synchronic language system and diachronic sequences, attempts have also been made to modify the sharp contrast between the redundancy concept and the concept of a language system as - in a formulation from Greimas and Courtes - it has been acknowledged that redundancy, defined as "the iteration of given elements in the same discourse seems significant, for it manifests the regularities which serve its internal organization".[15]

Although Greimas and Courtes do not explicitly discuss the relationship between the concepts of redundancy and language system, they are working towards an approximation, as they not only ascribe a more central role to the redundancy function in the description of the structure of sentences, but also - as appears from their treatment of the concept "natural language" (Saussure: langue, Hjelmslev: schema) - find it necessary to view syntactic sentence structures as part of this construction.[16]

As the syntactic structures, similarly to the structures described by the concept of a language system are repeatable patterns, it is difficult to see how it is possible to differentiate this concept of the redundancy function from the concepts of syntax and language system. There are indications, however, that they only have a more limited, perhaps stylistic definition in mind.

That Greimas and Courtes still recommend that the redundancy concept should be avoided - and suggest instead "the more natural term, recurrence" - can hardly be due to this vagueness, but rather to their wish to mark a distinction from Shannon's - statistical - redundancy concept, which does not acknowledge the significance of redundancy for the internal organization of the message, as Shannon identifies redundancy with the superfluity of the signals. In Shannon's interpretation the superfluous signals were precisely those which occurred with fixed regularity because they represented the statistical structure of the language system, while those signals which occurred irregularly, conversely represented the meaning of the message.

While Shannon in his definition takes the point of departure in one of the two senses of the concept, namely the superfluity of the recurring structures, as this concept is extended to include all types of recurring pattern, and this means the total language system, Greimas and Courtes, on the other hand, take their point of departure in the other, namely the meaning of these structures. In this connection there is no criterion for distinguishing between redundancy structures from the recurring patterns which are regarded as part of the language system. Nor is any answer given to the question whether and possibly how a recurring structure can be connected with a changing meaning content. A possible explanation may be that the particular purpose only is to describe how a simple - for example, stylistic - repetition of a form can contribute to expressing a meaning content which would not be present without the repetition.

Although the information theoretical definition falls short, because in opposition to the theoretical definition it becomes necessary to acknowledge the significance of the redundancy function for the reception of the message, it nevertheless also points out - with the concept of the significance of the random occurrence - a problem for the semiotic definition, where meaning is connected to variations of fixed, recurring structures.

While the redundancy concept in both definitions is a concept of fixed, recurring patterns, they differ in their description of the significance and necessity of these patterns. The two viewpoints form here extremities in a semantic field which applies to the redundancy function's strength of signification. The two definitions can therefore only be reconciled if by redundancy we understand repetitive structures which can appear with a variable - and thereby generally indefinite, not pre-established - strength of signification. Although they individually fix themselves in a certain position in this field, (information theory views redundancy as having a meaning which is weak to the point of non-existence, while semiotic theory views it as meaning bearing), we must see this divergence as an expression of a property of the redundancy function itself and assume that redundancy phenomena can both be manifested with variable strength of signification and/or changing content of signification.

This is indirectly confirmed by Shannon's use of the 5 previously mentioned definitions of the redundancy concept, as these definitions refer to different variation axes (two axes for meaning, namely respectively independently of and in opposition to, one axis for the rule structure, namely the system determined part and one axis for the expression form, namely the statistically determined part).

Such variations are a well known linguistic phenomenon and there are hosts of examples in the stylistic and rhetorical literature. This reformulation of the redundancy concept therefore creates no great problems.

The difficulty is rather greater when it comes to the second component of the redundancy concept which is formed around the relationship between the necessary and the random. As a consequence of linking the redundancy structure and meaninglessness, information theory is forced to identify the concept 'meaning' with the concept of random, non-patterned - and therefore facultative - occurrences. Semiotics, on the other hand, connects meaning with (variations in the relationship between) regular occurrences, as here the random and non-patterned is connected with the meaningless and not the meaning bearing.

None of these conceptualizations, which conflict with each other, appears convincing, but they each point out a weak spot in the other view. While information theory points to the possibility of free choice as a necessary element, something which is allowed no place in the structuralist definition, the latter, on the other hand, points to the possibility of ascribing meaning to the recurring patterns.

This mutual contradiction is manifested as a consequence of using the same theoretical thought structure, as in both cases an absolute opposition is assumed between the invariant - preordained - pattern, repetition, and the random occurrence, deviation. The conflict can therefore only be resolved by abandoning the idea of an invariant border between the repeatable-regular and the facultative, random deviation.

This abandonment has already been anticipated here by connecting the concept of the random, facultative occurrence with the concept of deviation, as the latter concept, unlike the concept of the random, not only covers the free - meaning-bearing - choice as a variation in relationship to a pattern, but also the free choice as a variation in or of a pattern, in or of its meaning respectively. The clarification at the same time makes it possible to provide a definition of the redundancy concept which clearly distinguishes the concept of redundancy systems from the concept of rule based symbol systems, as redundancy systems can be understood as repeatable patterns, structures or systems which

The definition maintains the concept's two semantic components as two connected, but individually variable, axes of signification, as the one axis allows variation in signification strength, while the other allows variation and deviation in pattern formation. Variation on both axes can at the same time be connected with variation in signification content. As variation of signification content can both be produced through variation of signification strength and/or pattern and as the pattern variation conversely is not always connected with (a certain or any) meaning variation, variation of signification content must be regarded as a third, independent, variation axis. While variation of signification strength depends solely on the reinforcement or weakening of an existing meaning, variation in content can also concern discontinuation and new meaning.

That it is the connection between these independent axes which is central appears if we attempt to clarify the definition by focusing on one aspect or the other. If - like Greimas and Courtes - we emphasize repeatability alone, the meaning paradoxically coincides with the concept of regularity - with the Shannonian consequence that the system thereby becomes empty of meaning because it is completely rule defined and inaccessible to meaning determined choice. If, on the other hand - like Shannon - we emphasize weakness of meaning or the superfluous, the meaning conversely coincides with the conceptual contrast: random and meaningless background noise.

Together, these two poles indicate the extremes in a three-dimensional meaning structure formed around the variation in strength of signification, content of signification and pattern variation. In connection with strongly significant and invariant pattern occurrences the concept coincides with the concept of regularity, structure and/or a new content of signification. In connection with occurrences of incomplete repetitions characterized by weak meaning - deviations from or variations of patterns - the concept approaches the meaning 'noise'.

Although this determination of the redundancy concept has its point of departure in - and has been kept within the framework of - the ordinary scope of the term's meaning, i.e. the connection of repeatable structures with indefinite meaning, it has implications which can hardly be considered obvious on the face of things. It is thus not immediately clear that the concept can be used to describe certain phenomena at all, because it apparently suspends any possibility of speaking of invariance.

It is perhaps also the fear of this slippery conceptual slope, which weakens the concept of regularity, that lies behind the widespread scepticism regarding its use and which prompts Greimas and Courtes to accentuate the rigorous form repeatability in their - cautious - rehabilitation of the concept.

But if the need is greatest for semiotics, it is also the first to offer the help which can be found in the biplanar sign concept. Where information theory falls short, because it operates with equivalence between the expression form and content form and assumes that the symbolic expression is subject to a single - or several completely distinct and thereby parallel - rule systems, the semiotic understanding of the sign implies that expression form and content form be regarded as two different, interfering pattern formations or rule systems. It follows from this that a pattern deviation and/or suspension and/or meaning variation on the one plane can occur on the basis of a stabilization of patterns on the other. As it is the sign function itself which - alone - creates the connection between the two planes, pattern deviation on the one plane, however, can also produce pattern deviation on the other,.

Where "monoplanar" symbol theories can only operate with rule based stability, the biplanar understanding of signs allows rule deviation to occur without stability being broken down, just as this understanding allows the existence of several stable meaning hierarchies in the same expression which are not unambiguously connected because they are not subject to clearly separate rule sets.

Perhaps a metaphor can help to illustrate this kind of relationship. Imagine for instance the interaction between our legs when walking. The movement of the legs is well co-ordinated but in such a way as to allow the movements of each leg to be varied with a certain degree of freedom, which is basically constrained by the use of the other leg as the stable - and in the actual situation "redundant" part - of the system, while at the next moment the redundant part becomes distinct.

Some of these variations might cause a change (whether intended or not) both in speed, rhythm or even direction. Others will effect only the rhythm, or speed or direction and some changes might not result in any changes in these respects at all. It is also possible to use such variations for semiotic purposes, e.g. simulations (walking with a limp to draw attention to ourselves).

There are different kinds of constraints on these variations. While some variations may make us stagger or fall, others will make us stop walking and others make us run, or jump on the spot etc.

The metaphor illustrates a system consisting of two co-ordinated axes in which stability can be obtained in - at least three - different ways: based on the stability of one of the two legs, based on the stability of the co-ordinated movements of both legs at the same time. As a metaphor, however, it also illustrates a difference, in that the system consists of two axes of the same category (since both legs are legs) while in symbolic systems there will always be at least two axes of different kinds, since there must necessarily be both an expression system and a content system, resulting in a more complex set of possible interferences between the two axes of variation.

While sign theory thus provides a theoretical justification that it is possible to connect the definition of the redundancy concept given here with the necessary stability, it makes no contribution to clearing up the meaning of the redundancy function.

This meaning can be illuminated in the relationship between the redundancy concept and the concept of language system.

While, on the one hand, it is possible to describe any kind of rule formation as a stable pattern which is maintained for a shorter or longer period in a redundant system, on the other it is impossible to fit the redundancy function into a rule system based on pre-established, invariant rules or patterns.

This definition of the redundancy concept can thus contain all the form elements and rule structures which are included in the concept of a language system, whereas the concept of a language system cannot contain the possibilities of rule variation, suspension and variation in strength of signification which characterize a redundancy system. The redundancy concept can thus be seen as a more basic - and comprehensive - concept than that of a language system. The rules of a language system are at the same time manifested as a system which - contained in a redundancy system - comprise a set of facultative and variable pattern formations which can both serve as a stabilizing background structure and be made the object of distinct meaning articulation through variations in the strength of signification and/or in pattern variation. A repetition structure of this kind can both act as a regulatory stabilizer, as an expression for a specific meaning content and is also accessible to variation in the content of signification, strength of signification and facultative pattern variations.

The central difference between a description of language as a rule based, as opposed to a redundant, system thus lies in the circumstance that rule structures in redundant systems become facultative, accessible to variation, suspension and non-rule determined interlacement, as the maintenance and use of rules becomes connected with the formation of meaning.

These properties have an intuitive relevance for an understanding of language, as they reproduce the infrangible connection between rule generation and meaning articulation which characterizes all linguistic articulation. Through this, the redundancy concept also makes it possible to re-establish a bridge between the concept of a synchronic language system and diachronic language use, as the synchronic structures can no longer be understood as once-and-for-all established, invariant structures which exist independently of usage, but on the contrary as more stable patterns and language norms.

If it is possible to distinguish structures with completely stable, invariant patterns, the concept of redundancy will coincide with the concept of structure, form or system. Any identification of a redundancy structure, however, assumes an interpreter and the same is true of the identification of an invariant system. An invariant system thus only exists if the interpreter cannot imagine any instability.

The extent to which we can do without the idea of instability in the description of "monoplanar" systems will not be discussed in this connection, but the fact that it is difficult to do without in the description of biplanar or multiplanar systems such as the linguistic, for example, appears not only to be confirmed by our ordinary understanding of the unruliness of language, but also by the noise problem of information theory.

This intuitive relevance, however, is supported by the circumstance that we must assume that any linguistic rule structure has a history both of origin and development. Although many language patterns and norms have been maintained for long periods of time, they must nevertheless have originated at some stage. As we are not familiar with their genesis we cannot derive later language development from them, nor can we therefore base language theory on the assumption that the total set of linguistic rule structures was formed as a total and invariant language system which is available as a preordained condition for language use. Of the possible explanations, this appears the least probable.

The redundancy concept is equally as incapable as the concept of form, rule or system of providing any clarification of how the phenomenon itself originated. It is not claimed that there is a genetic explanation, but on the contrary that the indefiniteness which is connected to the genesis of language implies that the linguistic rule structures cannot be understood on the basis of themselves, but must be understood as (new) formations which occur in relationship to other, linguistic or non-linguistic, structures.

As any repetition, in the nature of the case, is a repetition of something, repetition implies that a repeatable form exists prior to the repetition. The rule is distinct, however, from simple repetition, as regularity only becomes regulatory when it is connected with or used for a purpose. This purpose is not contained in the form repeated nor in the repetition itself, on the contrary, it lies in the use of the repetition. The form that is repeated can therefore best be described as an available expression form which, with the intentional repetition, is connected with a - regulatory - content form. In other words, the repetition of the form gives this a new meaning dimension as an available pattern which can be connected with a regulatory purpose. It is thus not the rule concept that is a precondition for the sign function, but the sign function which is a precondition for the rule formation.

While a rule system assumes a fixed connection between the occurrence of a form, the repetition of this and the connection of the repetition to a regulatory content, a redundancy system, on the contrary, is characterized by the possibility of varying these relationships. Redundancy systems have therefore not only the three previously determined variation axes (1: strength of signification, 2: pattern and 3: content of signification), but also a fourth which ranges from the first, possibly random occurrence of a form, through the repetition of the form to the connection of the repetition with some other kind of regulatory function which again can be connected with further meaning variations. See section 7.7 for an exemplification and further elaboration.

That the sign function is a precondition for and thereby independent of rule formation is not only supported by the circumstance that we have symbolic languages with different rule structures - in other words, the symbolic forms can be connected with different regulatory content forms - but also because we can only unambiguously distinguish between rule structure and that which is regulated when confronted with formal languages. As far as common languages are concerned this relationship can only be registered as a difference in perspective of the view of the same expression. It is not possible here to distinguish between that part of the expression which represents "the programme" and that part which represents "data".

Put in another way, the regulatory structures in common languages are different to the regulatory structures which characterize formal languages. As formal languages assume that both the expression form and its meaning are entirely rule based and mutually connected, these languages allow only rule based variation, just as the mutual relationship of the rules in the form of extent, grouping or co-ordination are fixed. The formal sentence is in principle a general statement which connects the situationally determined content (data) with a general, invariant rule structure. In formal languages the rule structure thus has its own distinctive notation form and each individual expression unit has an independently defined semantic content which represents either a rule or a regulated value.

In common languages the same - sequences of - notation units can both represent the rule structure and the meaning content, which not only means that the same expression form has at least two overlapping determinations, but also that the rule formation can be modified, weakened or strengthened relative to the concrete situational and meaning determined content of the message. The regulatory is not bound to the expression form itself, but to its semantic use. The common languages thus allow all legitimate expression forms, including those of the rules, to be subjected to variation in strength of signification, extent and content of signification - such as for example is the case with the use of tense (as respectively a neutral narrative form or distinct indicator of time) and gender (as respectively a purely grammatical or biological indicator) in common languages.

While the formal languages operate with a rule based expression system, the expression system is used in common languages as a redundancy system in which the individual expression forms are subject to several simultaneous, mutually different and variable semantic purposes. Any rule structure can therefore also be subjected to meaning variations through inclusion in new sign functions.

Unlike the rule concept, the redundancy concept allows a necessary openness in the conceptualization of the relationship between the unique and the general and of the unsolved problem of the origin of and transition between levels, as it allows:

Redundancy structures are thus characterized by the possibility of distinguishing (and perhaps modifying) elements from a subordinate level as members of a superior level and by placing partially stabilizing elements between these elements, which again allows the establishment of a new level. The description of the basic structure of language as a redundancy structure also provides the advantage of allowing a continuous formation of new rule structures at new, higher levels through the modifying variation of the subordinate levels.

As rule formation is described as part of language use and meaning production, it cannot be excluded from the sign function either, which also appeared as a consequence of Umberto Eco's analysis (7.3) just as it is in accordance with stylistics' many examples of different forms of semantic exploitation of repetitive language patterns.[17]

The concept of style is incidentally - and not surprisingly - one of the concepts which forces Hjelmslev to the - in his theory, surprising - admission that it may well be - perhaps almost always is - necessary to encatalyze several mutually different language systems in the analysis of the same text.

In other words, in order to establish a simple model situation we have worked with the premiss that the given text displays structural homogeneity, that we are justified in encatalyzing one and only one semiotic system to the text. This premiss, however, does not hold good in practice. On the contrary, any text that is not of so small extension that it fails to yield a sufficient basis for deducing a system generalizable to other texts usually contains derivates that rest on different systems.[18]

While the style of the text prevents it from being accommodated in the house, the house itself becomes an element of the style, as it is the style which determines how many houses are necessary, how they are used and how they are connected with each other.

While Hjelmslev's language theory demonstrates how his own monoplanar calculus understanding of the language system entails that when analysing an arbitrary text we must assume that there is an unarranged quantity of mutually unconnected systems, it thereby indirectly reveals the existence of an underlying language potential which makes any rule formation and language norm accessible to stylistic exploitation and semantic choice. It is the existence of this potential which justifies the redundancy concept as the most suitable, most adequate concept for the basic structure of language formation.

The concept of style hardly plays the same role in all symbol systems, but it always plays a certain role. The style concept is sometimes used in formal symbol theories as an argument for preferring one - more elegant solution - to another. There is a long-standing tradition in mathematics for supporting the argumentation for the truth of a mathematical proof with its beauty. Probably not all mathematicians would claim that this, in itself appealing, idea of the importance of style can be ascribed an independent - or basic - status in understanding formal languages, but we can certainly note that there is an inner relationship between the formal languages and a certain style concept, namely the concept of the pure and simple, non-contradictory expression.

With our point of departure in Hjelmslev's description of formal languages as "monoplanar", we find here a further indication of the assumption that the transition from multiplanar to "monoplanar" symbol systems - with full equivalence between expression form and content form - is closely connected with a reduction or elimination of that redundancy structure which is the basis of the multiplanar symbol system. Such a reduction (also including the elimination of the linguistic gender and tense functions, for example) is also a central element in the operative procedure for producing formal expressions.

If this assumption is correct, it can explain why Hjelmslev, who attached himself to this ideal of style, could overlook the paradoxical contradiction between this monoplanar stylistic ideal and the biplanar phenomenon of language he wished to describe. Moreover, it can also create the basis for a description of the difference between common languages and formal languages, as formal languages' identification of the expression form and content form builds upon a freezing up of the four variation axes of the common languages' redundancy systems (strength of signification, pattern formation, content of signification and the axis from the first, random occurrence through repetition of the form to the connection of the repetition with regulatory function and possible further meaning). Formal languages only allow rule based variation - which has been declared in advance. As these declarations are carried out at the level of notation, any notation variation is thereby connected with a rule based meaning variation. While the use of notational redundancy is a precondition for common languages (and other informal uses of notation systems) formal languages are based on wholly rule based notation, in which redundancy forms, however, can appear at higher semantic stages.[19]

This difference also explains - the generally accepted assumption - that all formal expressions can be translated into common language expressions, whereas the opposite is not possible. Common languages have a variation potential which cannot be represented in formal languages.

As it is thus reasonable to assume that the redundancy concept can be regarded as a key concept in the description of structural differences between expression systems, the theoretical definition of it given here will be used in the following sections to describe the different redundancy structures which characterize the linguistic, formal and informational uses of notation systems.

7.6. Redundancy in notation systems with limited inventories

The difference between common and formal language notation was described in the preceding section as a relationship between the use of the notation system as a redundancy system based on the use of a limited inventory of notation units, each of which is empty of meaning, and as a rule determined system based on the use of an unlimited inventory of individually meaning-defined units. This difference was described as a difference between a symbol system, in which rule set and meaning content are connected with the same expression constellations, and as a symbol system which builds upon a systematic distinction between rule expression and the expression of that which is regulated.

While this description is adequate for distinguishing between common languages and formal languages, it is not adequate for describing the relationship between linguistic and informational notation, as in both cases they use a limited set of notation units which are empty of meaning, so that meaning is only connected with sequences of expression units. In both these uses, meaning variation can still also be produced through the variation of an individual expression unit. In other words, the individual notation must be able to represent a meaning distinction without itself containing any meaning. In both cases, the limited inventory of legitimate figurae comprises a set of semantically empty, semantic variation mechanisms.

To these similar features yet another can be added, as the variation potential of the notation system is not only concerned with meaning content, but also, as will be discussed in greater detail in chapter 8, the rule structures.

These very striking and comprehensive similarities appear on the face of it to confirm one of the assumptions on which efforts to artificially simulate "natural" languages (designated common languages in the present work)[20] have been based. It must therefore immediately be noted that the similar features mentioned here will not bear such a far-reaching interpretation. The relationship is rather the contrary, as simulation theories operate with formal notation, while it is precisely the similarities between linguistic and informational notation indicated here that distinguish these from formal notation. The way this problem presents itself therefore gives occasion for a more detailed analysis of the relationship between common languages and the use of informational notation.

Here it is most appropriate to take our point of departure in Hjelmslev's commutation test. Hjelmslev formulated the commutation principle as a method for deciding whether an expression unit is semantically distinctive, as what is tested is whether a change in the expression also changes the meaning of the expression. The method is a suitable means of delimiting the smallest units of the semantic variation potential and it becomes possible in this way not only to indicate the phonemic and graphemic expression units, but in the case of - spoken - language also a number of other semantic variation mechanisms such as intonation, stress, glottal stops and hesitation, at the same time as the method makes it possible to separate semantically empty expression variations such as individual differences in the articulation of the "same" sound. At this level the commutation test can be used to distinguish the variation potential used for semantic purposes from the - more comprehensive - variation potential offered by the expression substance.

Hjelmslev used the test himself to distinguish the "figurae" at the disposal of sign formation, as in his formulation of the law of the relationship between the sign and the figura he states:

the transition from sign to non-sign never occurs later than the transition from unlimited to limited inventories... Language is thus so organized that with the help of a handful of figurae and through continuously new juxtapositions of them, a host of new signs can be constructed.[21]

The definition implies, continues Hjelmslev, that language should not first and foremost be understood as a sign system, but as a figura system which is built up around a limited number of figurae and used for sign formation, as the figura system comprises the foundation for the immanent functions of language.

Hjelmslev thus saw the figurae as the material of sign formation, as at the same time he defined the concept of a language system as a set of invariant rules for the mutual organization of the figurae. As mentioned in section 7.5, he was thereby forced to draw the conclusion that any, even slightly longer text, must presumably be described as a conglomerate of elements from several language systems, whereby an important part of his point is lost.

We can naturally - like Hjelmslev - refer any deviation from a delimited, invariant system to another system. The consequence will be that the described phenomenon "everyday language" in such a case becomes an aggregate of a very large number of mutually unconnected language systems, while the ability of everyday language to contain these mutually unconnected constructions remains undescribed. An obvious example is variation in pronunciation.

It is a well known fact that many individual pronunciation variations in spoken language are precisely only pronunciation variations which are not used as semantic variation mechanisms. It is far more difficult to draw a clear borderline between dialectal and sociolectal pronunciation variations (as well as those characterized by age and gender), which can both form part of spoken language as messages with weak meanings connected with the speaker's background and as an emphasis with a less strong meaning of this background (perhaps intentional in the situation), or as a central aspect of the point of the message (such as in jokes).

The circumstance that everyday language contains individual dialectal and sociolectal pronunciation variations, which are sometimes manifested as semantic variation mechanisms with a positive result in a commutation test, is seen by Hjelmslev as a less essential feature of language.

The occurrence of dialectal and sociolectal sound variations, however, leads directly to a basic question of linguistic rule formation because this is a question of a non-rule determined, semantically facultative break between different dialectal or sociolectal rule structures (for the use of phonemes). Such breaks are not only general occurrences in the individual use of language, they also create a foundation for comprehensive and far-reaching cultural struggles for the upholding of some rules rather than others. While the struggle regarding linguistic rules is also carried on in language, such struggles cannot be fought in formal languages. That such a struggle can take place is in itself a good example of the importance of the redundancy function for the use of linguistic rule structures, as it is a question of variation in the rules' strength of signification, extent and content of signification, just as these features assume the possibility of semantically motivated rule suspension.

In Hjelmslev such features create a foundation for the concept of language norms, which on the one hand fulfil regulative purposes on a par with the invariant language system, but on the other are accessible to variation. Although the normative rules also regulate language use, they are not included in Hjelmslev's concept of a language system, but on the contrary are included in the use of the language they regulate. In other words, the language norm is a significant property of language which is not incorporated into Hjelmslev's concept of a language system. As this property can not only fulfil the same - regulatory - purpose, but can also create a foundation for rule deviation and rule suspension, it not only gives occasion to ask whether there is a need for a concept of an invariant language system at all, it also raises the question as to which criteria create the basis for separating a set of invariant rules from the variant norms.

In Hjelmslev the distinction between variants and figurae, which creates an invariant system that is independent of norm changes and variations in use, appears solely as a consequence of the theoretical model. Hjelmslev, however, can only identify the elements of the system with the help of the commutation test, which is empirically bound. It cannot thus be used to distinguish an invariant set of figurae, as it contains no criterion which can determine whether a given, unused variant could be used in another case.

While Hjelmslev believed that the test could be used as a means to distinguish a delimited set of linguistic figurae which could be utilized for sign formation, it is, on the contrary, a means for distinguishing a set of actually used figurae from a set of possible substance forms.

Hjelmslev's use of the commutation test to distinguish the elements of the system is not only problematical because it is empirically limited, it is also problematical because he overlooks the fact that the commutation principle he is forced to use to distinguish the invariant system figurae only works on the condition that these figurae actually occur as semantically facultative variation mechanisms.

Where Hjelmslev claims that the figura system is invariant, as the used figurae form a closed, delimited system, the test shows on the contrary that the border between used and unused figurae depends solely upon the question as to whether a given figura is actually used as a semantic variation mechanism.

The figurae of a language system are in other words not themselves defined by the language system, they - and thereby also the system - are on the contrary defined as the semantically used parts of the figura variation possibilities which are contained in the expression substance.

It could now be objected that the commutation principle is only a - necessary and sole - analytical means of discriminating the figurae theoretically and that the analytical procedure provides no information on how the figurae are used in language. Although the commutation principle prescribes that we regard the graphemes /h/ and /c/ as semantically distinctive graphemes which are incorporated in the language system's figura set, as we for example can differentiate between /hat/ and /cat/, the respective meaning content of the two words is not connected with the two distinct figurae, but to the total constellation.

We are also only able to point out the graphemes /h/ and /c/ as semantically distinctive because this distinctiveness is relative to the subsequent - in this analytical context, semantically non-distinctive - graphemes -at.

The result of the test is independent of whether the chosen words occur in contexts where they can be confused. It therefore provides no information on the individual grapheme's function in a given use. The grapheme, however, has a more distinctive value when it occurs in contexts where the mistake of a single grapheme also changes the meaning.

As an example, we can take a not unusual error in writing the word intention as /intension/. If the word appears in a text, whose subject has not yet been revealed, the reader will be in doubt as to whether the writer was thinking of the concept of intension (as distinct from extension), or whether it is rather an error for the more widespread concept intention (which has no definite opposite concept). In this case the 's' is manifested as a grapheme with strong meaning - so strong that it causes doubt. If the word, on the other hand, appears in a text whose subject has been revealed, the reader will not experience a problem of understanding - or will easily 'skip' the error. In this situation the 's' is manifested as a grapheme with weak meaning - so weak that doubt does not arise or can easily be ignored.

The difference between the analytical procedure which is independent of the actual context and the way in which we use language ourselves does not alter the fact that we can only use this procedure (and have no other) because the figurae of language are semantic variation mechanisms. It is the possibility of semantic variation which decides which parts of the variation possibilities of the expression substance that are used in language. If we do not use this criterion we cannot distinguish the figurae which can be included in the language system from the figura possibilities of the expression substance. If we do use this criterion we must also draw the conclusion that the rule structure of a language system is rooted in a figura system in which each individual element is defined through the possibility of semantically motivated variation which depends both on strength of signification, pattern variation and content of signification, not only for the individual figura, but for the total expression.

The problem with Hjelmslev's theory is thus that the means he uses to provide the theoretical construction with an empirical foundation itself assumes the semantic bond the theory denies.

It is not difficult to see that the contrast between /h/ and /c/ may be decisive for an understanding of the content of the sentence, while in other situations it may be the surrounding graphemes (a or t) which handle the more distinctive function relative to the distinctions between hat-hit, cat-cut, hat-ham, cat-cab, for example.

The individual grapheme is thus manifested at one and the same time as semantically distinctive relative to the surrounding graphemes and relative to other possible graphemes in the same place. But it is manifested as less distinctive or redundant in relationship to the surrounding, more distinctive graphemes, as we distinguish hat from hit, cat, as well as ham.

In other words, it is only in the test situation itself that we can isolate the distinct from the redundant. What distinguishes /hat/ and /cat/ unites /hat/ with /hit/ and these are distinguished by one of the elements which unite /hat/ and /cat/. As the examples can be supplemented with /cat/cab/ and /hat/ham/ we have an example here in which commutation is positive for all graphemes in the words cat and hat.

The individual grapheme is manifested as distinctive in contrast to other graphemes, which are manifested as redundant through the same contrast. But at the same time it acts itself as a redundant background for each of the others. The graphemes enter into a simultaneous reciprocity as each others' foreground and background.

It is the surroundings, and not the grapheme itself, which make it possible to define the individual grapheme's semantic distinctiveness in the actual figuration. Semantic distinctiveness is therefore also manifested as a variable relative to the grapheme's own possible occurrence in other surroundings (including the possible occurrence at another place in the same expression).

Although the meaning is connected with the whole word and although the different meanings do not necessarily have any graphemic representation at all - words with different meanings can be spelt similarly (such as bow, for example = a knot with two loops, the front of a ship, a lowering of the head etc.) - the marking of the difference in meaning relative to the context (which here both includes the meaning and the actual surrounding graphemic expression forms) is clearly one of the important functions of the grapheme.

The commutative test shows just as little as other methods that certain graphemes are always and only distinctive, on the contrary, it shows that it is true of any semantically distinctive grapheme that it can only be semantically distinctive because it can act less distinctively in other surroundings and, at the same time, act as a redundant background for the distinctiveness of the surrounding graphemes. The individual grapheme's distinctiveness is thus manifested in a double redundancy structure where on the one hand it is determined in relationship to its own possible occurrence as more or less distinctive in other circumstances and, on the other, as both distinctive and redundant relative to the surrounding graphemes.

That it is redundant does not mean, however, that it can simply be omitted from the expression, although this may be possible in some cases. But this can only be determined by finding out whether meaning is lost by omitting it. Although a certain grapheme is superfluous in one context, it is not given that it is in another. The same figura constellations, even in the same word, can act with a variable strength of significance - as more or less necessary for maintaining the meaning content and/or rule structure in different occurrences.

The distinctive unit in common language can only appear with the meaning "more" distinctive and a more distinctive unit can also appear as "less distinctive". If a given grapheme could only act distinctively, it need not be manifested relative to redundant surroundings.

Moreover, as will be described in more detail in chapter 8, it is precisely this second possibility which is the foundation of the formal notation systems, where the individual figure's semantic distinctiveness is ensured by definitory precepts which are outside the expression. The formal and informational notation systems do not operate with the same more-less polarity and the thereby connected variation potential.

Conversely, in linguistic notation, external definitions of the individual figures' distinctive meaning are not used, here distinctiveness appears, on the other hand, in a double redundancy structure.

The redundant occurrence is the condition for the distinctive occurrence, as this both assumes redundant graphemes in the surroundings, (redundancy in usage) and redundant occurrences of the same grapheme in other expression contexts (which in Hjelmslev's terminology should mean that redundancy is also constitutive in the language system).

For Hjelmslev it is only the distinctive function which is included in the language system. The redundant function is not recognized as an important feature of the structure of the language system. Redundant figurae are treated as unused figurae - although they are actually used as conditions for the manifestation of the semantically distinctive figurations and as semantic variation potential.[22]

In a given context, as far as speech is concerned, it is also possible to use expression substance variations in the form of dialectal and sociolectal variants. Where writing is concerned there are fewer possibilities for using substance variation, and in printing still fewer, but they are found, for example, in the form of italicization and certainly in some choices of type faces, typographic styles and page layouts. It could also finally be discussed whether spaces and division into sections should be regarded as blank signs, i.e. as independent figurae, or as variations in substance similar to the choice of type face and typographic style.

There is thus no definite rule structure which determines how the smallest semantic variation mechanism of language can be connected with meaning variation. The linguistic notation figurae are each determined by their potential use as semantic variation mechanisms and the use of them in language is characterized by the possibility of variation along several axes:

The semantic variation potential connected with this includes, finally, not only semantic variations within the framework of the language system, but also this system, as - exactly like meaning - it is itself manifested as an organization of notation units which are defined by their use as semantic variation mechanisms. It is quite true that there are several different forms of rule based notation sequences with rules of inflection as the most rule determined, while the notation sequences of words are subject to the syllable criterion.

The syllable criterion implies that there must be a vowel (although vowels need not be manifested in all written languages) and very little else. To this, the national languages each add their rather arbitrarily delimited set of customs for legitimate and illegitimate syllable forms.

Roots and inflection forms are thereby subject to different types of regulation of notation sequences and the two forms largely act independently of each other. But not completely, as there may be interference from inflection form to root. It appears moreover that every rule has a least one exception. While the individual notation units are in principle semantically empty, the vowels /i/ and /a/ (i, ø and å, in Danish) are also used as meaning bearing words.

Unlike the graphemes of the roots, the graphemes which present the rules of inflection have been given a further semantic determination as rule notation. But although they are regulatory they are not regulatory in the same way as the operators of formal languages. The graphemes of the inflection system do not represent a programme which transforms one set of data to another. On the contrary, they represent a supplementary semantic determination which can also occur with variable semantic values, such as is true of the use of the present tense, for example. It can hardly be by chance - and is certainly not without significance - that the inflection system is manifested with the help of - a selection of - the notations which are also used to manifest the roots, whereas formal languages systematically distinguish between rule and data notation units. In the latter case, a line is drawn between two separate semantic rooms, where in the first there is an interference.

The rules of language are similar to many other social rule systems, they are not rules which carry out themselves, but rules which are - perhaps - respected and which can be respected to a greater or lesser extent, and rule formation often has the character of analogy - sometimes almost on the principle, if you can get away with it, all well and good. This is impossible to get away with in a formal system.

Although the separation between root and inflection form is unavoidable and invariant, it is not unavoidable in the expression system. For a great number of words (some) inflection forms are identical with the root. The inflection form can thus also occur as a purely semantic determination as regards content which, among other things, allows an inflection category such as the dative case almost to disappear from a language, such as has happened with modern Danish, for example.

The same expression form can in these cases therefore also occur with variable semantic values. The semantic distinction is not stabilized through the inflection system, but solely through the actual syntactic and/or semantic context, which is thus sometimes used as a means to suspend the use of the inflection system's notation rules.

Under any circumstances the linguistic use of the notation system is characterized by a set of possibilities for exchange between rule distinctiveness, custom distinctiveness and semantic distinctiveness, as all notations can serve on all three sides, often simultaneously, although in several different ways and with more or less weight.

In other words, there is an indissoluble discrepancy - and structural difference - between expression form and content form which cannot thus be described as homologous. The variation potential of the expression form is not bound to the content forms. The change of a single expression unit can dissolve a content form which includes a word, a sentence or a rule.

As the relationship between rule structure and meaning content can neither be wholly rule based nor wholly unconnected, the two levels can be regarded as reciprocal redundancy structures, i.e. as a system of variation axes in which each axis has its own variation criteria and where the relationship between the individual axes constitutes an independent variation axis which establishes the meaning and function of the variations.

Double redundancy and the simultaneously redundant and distinctive occurrence comprises one of the specific characteristics of alphabetical writing. It does not occur in formal notation systems which are characterized by the elimination of all redundant graphemes and it does not occur in pictorial expression systems which neither use a delimited notation system such as the alphabet, nor in an unlimited system where the individual members must be declared, such as in formal notation.

It thus appears that the redundancy which must be included in linguistic theory's criterion for sign distinctiveness comprises an extremely central and characteristicinguistic feature which permits a conceptual distinction with regard to other semantic systems such as formal and pictorial systems.

Although Hjelmslev's description of linguistic notation as a use based variation of an invariant set of asemantic relations between a limited set of notation units provides a great deal of leeway for normatively established, but principally variable, structures and relationships, his theoretical interest in the normative is peripheral and he has no more detailed considerations regarding the relationship between the smallest semantic variation mechanisms, rule formation and meaning variation.

A comparison with informational notation shows, however, that there is a characteristic difference here. Linguistic notation shares the limitation of inventory and the demand for semantically empty, but semantically distinctive notation units with informational notation. The smallest semantic variation mechanisms are not only defined in different ways, however, they also allow different forms of semantic variation, because linguistic notation also depends on the use of notations and notation sequences which are indefinite or have weak meaning or open meaning. Thus phenomena such as syllables, relationships between vowels and consonants, the frequent occurrence of preferred consonant constellations and the absence of others, as well as the use of inflection forms are only of relevance for a description of linguistic notation.

It is possible to further isolate this difference with the help of the commutation test, as in this way we can ascertain that it is possible to eliminate quite a number of graphemes from a written text without the meaning being lost, whereas the omission of only a single informational notation unit can only be made without loss of meaning if a set of control codes has been added to the total message. This difference is again related to the circumstance that informational notation in binary form always uses the entire expression inventory, where language, step by step, uses only a small selection. The two different notation systems are in other words characterized by different stabilization structures.

Where language is concerned this stabilization is characterized by a limited use of rule determination which mainly only occurs in inflection systems, while most other notation sequences are determined by tradition or meaning. The notation system is used as a redundancy structure which allows the individual notation units to be manifested as determined by conventions, by purposes of meaning and by rule structure and where the individual notation's function can serve several purposes and vary with the contextually determined meaning.

Informational notation, on the other hand, is highly subject to rule determination, which includes both the unambiguous demands on the physical form and the formal semantics that is used to stabilize the notation's legitimacy. This semantics can be separated completely, however, from the semantic regime in which the message is produced. Formal semantics acts here as a redundancy structure with weak meaning seen in relationship to the meaning of the message, while it at the same time acts as a means, with strong meaning, of ensuring the notation's legitimacy. The separate part of the message can therefore not be used as a semantic variation potential in relationship to the meaning of the message either. Finally, informational notation is also subject to a rule based demand on the syntactic organization which stems from the demand for mechanical efficacy.

Hjelmslev's system theory therefore appears - curiously enough - to provide a far more apposite description of informational notation than it does of the linguistic, as in the first case we can clearly distinguish between the definition of legitimate figurae and the definition of their function and meaning. The definition of the figurae is at the same time a definition of their mutual - asemantic - and oppositional relationship. This definition determines notation at the physical-mechanical machine level, while the definition of their function and meaning is a subsequent semantic determination which establishes the function and meaning of the notations at the level of the protocol, programme and use. The informational notation units can therefore neither be varied individually nor as a total system through use, whereas spoken language allows such variations, which can act both as individual and dialectical and sociolectal variations, just as it is also possible to assimilate formal notation systems. The latter also holds true of written language, just as various diacritical notations can also be introduced here. In print, the individual variation of graphemes is limited to the choice of typefaces which are not semantically distinctive, whereas italicization and underlining, for example, can be used in a semantically distinctive way. Something of the same is also true of handwriting where individual variation, however, can also be read as a personality trait.

Although both notation systems are bound to the use of a limited set of notation units, this restriction is manifested in two different ways. Informational notation does not use more or less superfluous notation units which are weak of meaning, whereas linguistic notation is characterized by frequent occurrences of more or less superfluous (but potentially meaning bearing) notation units. The informational use of notation units is rule based, each individual notation unit has a definite physical value and function - with regard to the mechanical procedure - while the linguistic utilization uses the notation system as a redundancy potential.

Excursus: In several of these respects the linguistic use of notation units is related to the function of notes in scale-based music, where the musical expression is bound to a sequence of notes although the expression is changed through variation of the individual note. Such variations can both have the effect of a deviation from a given scale, which is common to many works, or of a variation of the thematic structure which characterizes the individual work. While the scale establishes a sonar background structure (not necessarily explicitly manifested in the individual work) as an invariant basic pattern for the musical expression, the themes which characterize the individual work are expressed through the repetition of a limited and chosen set of the possible combinations. The relationship between these two repetition patterns is not, however, fixed. The thematic variation, which can include overlapping between themes and variations of the individual themes, can be carried through right up to the dissolution of the theme. It can also lift the musical expression out of the scale-based tonality (we could say over to another scale, although this is perhaps only represented by a single note) and both pattern structures (that of the scale, which is common to many works, and the choice which characterizes the individual work) can become the objects of corresponding variations in strength of significance.

In scale-based music the individual notes are defined by a certain frequency which additionally defines the musical borderline between noise and legitimate musical sounds. The unlimited possibility for varying the patterns which create music thus does not depend on a continuous, gliding sound transition, but on the circumstance that the pattern itself is produced as a compositional, facultative structure of distinct expression units. This holds true not only of the thematic patterns which characterize the individual work - and its relationship to other individual works - but also of the harmonic scale pattern which establishes a tone structure for a greater number of works.

Although the musical sound value of this music has a well-defined physical form and a well-defined relation to other sound values established by the scale, the musical expression cannot be described as monoplanar sound symbolism.

The individual notes are defined both by frequency, by scale and by thematically determined relationships to other notes. At all three - individually variable - levels this is a question of conventional pattern formations through which sounds are defined as music - i.e. legitimate - sounds.

The similarity between the symbolic systems of language and scale-based music lies in the circumstance that the linguistic and musical rule structures are established, on the one hand, in a subdivided layer of sequence structures, (those of the scale, the work's basic theme and the thematic variations) which on the other hand is realized in an expression form which makes it possible to arrange these structures in variations, ranging from complete regularity to complete dissolution, as all structures are produced through a combination of singular facultative or variable expression units.

Now it is difficult to imagine that it would be at all possible to create music or language if this should be done by selecting expression units one by one. But although neither language nor music appears conceivable without restrictive conventions for the composition of expression units, in both cases there is a need to limit and stabilize the potential choice and not for a set of rules which can define the musical or linguistic field. The rule structures which are included in the individual musical work or the linguistic expression respectively, do not circumscribe the musical and the linguistic, on the contrary, they are contained in the expression and manifested in the expression systems which in both cases are accessible to variation which transgresses the rules.

This possibility of varying and suspending rule structures, which holds true of all symbol systems that 1) use a finite number of expression units and 2) allow rule formation to be manifested in the same expression units as meaning content, is thus based on the circumstance that the smallest expression units are defined as semantic variation mechanisms, but have no definite semantic rule or meaning value.

Although the individual work will always use only a very limited number of the possible variations, it is not possible to establish definite limits to variation at any of these levels which are common to all music. The limits which appear through a description of a given body of works thus do not represent a description of the musical "essence", they represent, on the contrary, the intentional, semantic considerations of the communicative purpose and ensure that the message can be understood and received.

The purpose of this parallel is not to emphasize the music of language, but to emphasize that kinship between language and music which lies in the central importance of the redundancy function for the symbolic use of what - in both cases - is a limited set of expression units. The kinship is not, however, interesting solely because of the similarity, but also because of the differences.

No attempt will be made here to describe what can be understood by the meaning content of music, nor the content forms of the musical sign function; there can, however, hardly be any reason to deny that the musical expression is only musical because the expression is part of a sign function and must therefore be described as a biplanar or multiplanar symbol system. This is why John Cage could compose (and we can listen to) a piece of music by declaring only its duration (four minutes and some seconds) using no sounds at all. If nothing else, this work illustrates the ultimate and sole limit to musical expression, that of the substance. In the broadest sense of language, music is a language. The difference between speech and music, however, is not only a difference at the level of content meaning and content form, but also at the level of the expression form, although speech and music both use the same ethereal substance. We can therefore not speak of more or less superfluous occurrences of notes in scale-based music, each individual occurrence of a note is subject to the composer's choice and the musical expression is also bound to a far more rigorous demand on the physical definition of the notes. In other words, this is a question of two different criteria for distinguishing legitimate forms in the same expression substance.

Whereas it is possible in spoken language to use the forms of the expression substance as a semantic variation potential, the scale-based musical expression is bound to a sharply delimited set of legitimate substance forms. While the expression substance variation of the individual sounds is included in the redundancy structure of linguistic notation, it is not included in the scale-based musical redundancy structure - apart from that timbre which distinguishes the same sound when played on different instruments. In scale-based music all other variants and deviations from the rule based substance forms are, on the contrary, always defined as noise.

As a consequence of the precise tone definition, scale-based music can also be represented extremely precisely, note for note in the form of musical notation. The difference between the tone and the equivalent note is simply a difference in substance. Although there are probably people who can enjoy a comprehensive and lively musical experience by reading a musical score, music cannot normally be understood with the eye. The sensing of the form is conditioned by and bound to the substance in which the form is expressed.

In an article on musical notation as a means of knowledge representation (seen as a kind of "precedent" for binary notation) Henrik Sinding-Larsen notes that the musical information in the score "apparently as a paradox" grew in step with the development of a notation system in which the individual notation unit "contained less and less information" up to the point where the notes had become "exact digitalized symbols in a well defined system". This development, claims Sinding-Larsen, is typical of semiotic systems, as these develop in a continuous abstraction in which the semiotic and syntactic systems take on greater and greater importance, while the individual element correspondingly loses information content.[23]

While this description is perhaps adequate for a possible line of development in a formal notation system such as the musical score, which is the formal re-presentation of a tonal system, it is inadequate as a general model. First, because it allows no room for the difference between notations which have independent semantic value and notations which do not. Second, because it connects the "falling information content" of the individual notation with less weight in relationship to the total system. The relationship is rather the opposite, as a notation without an independent information content has a potential use of far greater semantic reach. The less the value of the notation is preordained, the greater the potential for its use as a semantic variation mechanism. Third, the individual note's notation value is defined by its place on the line, which is part of the rule determining formal system.

It is exactly at these points that alphabetical writing and informational notation differentiate themselves, because they use semantically empty notation units, while the tone (and thereby also the note) is bound to a definite relationship in the tonal system. As musical note notation is bound to a scale - and not to its own expression substance - it cannot be regarded as an independent notation system. The relationship between the phoneme and the grapheme is different from the relationship between the tone and the note. Writing does not have the same relationship to speech as that of the score to the music.

The music of language clearly distinguishes itself from the language of music, but the language of music is also used for linguistic meaning articulation. We have no difficulty in distinguishing spoken language from song, song from other musical expressions or singing a song from song-like sounds such as humming, for example. The relationship between these symbolic expression forms is not a relationship between two different symbolic expression forms with clearly delimited rule systems which do not overlap. Not only can we break into song and thereby connect the musical and linguistic norms with the same physical sounds, we can also exploit musical structures as expression forms for linguistic meaning articulation.

That we can connect linguistic and musical norms with the same sounds is not quite so obvious as it - sounds, as the scale-based, musical sounds are defined by a precise frequency, while language works with both dialectal, sociolectal and individual variants of the "same" sound. Nevertheless the common expression substance allows an amount of interference between musical and linguistic sound symbolism. The exploitation of musical structures in linguistic meaning articulation, however, is even more interesting because it is a question of a linguistic use of a non-linguistic expression form.

If we wish to maintain the concept of an invariant language system, we must therefore introduce musical structures as part of this system and indicate invariant thresholds for their linguistic use. The question then is whether these thresholds, if they could be shown, would make the gateway to language systems so high and the door so broad that there will no longer be any room for a wall.

The comparison with scale-based music shows that the use of the expression substance by spoken language is not only different from that of music, but also that this special relationship to the expression substance can be used as a semantic variation mechanism. End of excursus.

Hjelmslev does not eliminate expression substance and notational redundancy from the structure of language because redundancy is not part of the expression form. The explanation can rather be found in Saussure's sign concept, which propounds the opposition between expression and content as an overall, controlling perspective in considering the expression side. Through this perspective the relationship between semantic distinctiveness and redundant expression figurations is arranged in order of precedence on the basis of content distinctiveness which - in a short-circuit - is directly connected with the preferential position of expression distinctiveness as the exclusively semantic part of the expression. Content distinctiveness, however, becomes manifested in the polarization of redundant and distinctive manifestations.

If we wish to describe the specific linguistic utilization of alphabetical notation, we cannot omit this redundancy structure. Hjelmslev's omission of it is also closely connected with the fact that he saw notation as an insignificant expression material for language, except for the circumstance that the number of permissible figurae was limited. This limitation, however, is not invariant and not systematically determined.

It is also in the same - i.e. reversed - fashion with the content side, where Hjelmslev's system separates language system from meaning, as he simply writes off the importance of the linguistic redundancy structure for interference between language system and meaning.

If we maintain Saussure's terminology - and precisely from his assumptions - it becomes clear that the substance depends on the form to such a degree that it lives exclusively by its favor and can in no sense be said to have independent existence.[24]

In spite of this almost religious rhetoric,[25] which so appositely expresses the theological roots of his idea, Hjelmslev shows immediately after, with the sentence "I do not know" in Danish, English, French, Finnish and Eskimo, how the same meaning de facto exists in different languages, expressed in different content forms which "stress different factors within the amorphous "thoughtmass"".[26] There is a further discussion here on an arbitrary relationship, which must mean that the meaning exists in such a real sense that it both has different features - so that it is not completely amorphous - and can be included in various relationships with a content form.[27]

The sign concept is thus formed through a double delimitation: on the expression side in relationship to the manifested redundancy, described as sign parts, non-signs, or figurae and on the content side in relationship to the complex meaning concept, described as an amorphous mass.

The semantic field, however, stretches across both these borders. Although meaning is understood as an amorphous mass, in Hjelmslev's theory structured meaning elements are included as a necessary precondition. It is such elements (and not content forms) which are used in the commutation test, which also only works because it uses meaning change as a form distinctive criterion. It is also structured, i.e. a specific, meaning content which is decisive for the sign definition itself, for the distinction between sign and non-sign and for any analytical segmentation of the language forms, both at the level of content and that of expression.

When all is said and done, it is only the meaning which distinguishes any kind of symbolic form from any other kind of form. It is also only the meaning in a form which turns it into in-formation. Hjelmslev's language theory does not include the semantic tools of analysis he uses to express his own theory in linguistic form.

Although Hjelmslev emphasized the linguistic form as the concern of linguistics in opposition to transcendental, meaning bound language descriptions, he also used meaning as a means of deriving the language system, in spite of his claim that the system existed independently - and transcendentally - of meaning.

The transcendental precondition is contained in the axiomatic postulate that it is possible to claim that any linguistic sequence can be understood as the manifestation of a language system.

While no linguistic sequence can exist without an underlying system, there may, it is said, be language systems which exist without there being a text constructed in that language, i.e. virtual texts without realization in the form of theoretically possible systems.

It is thus impossible to have a text without a language [system] lying behind it. On the other hand, one can have a language [system] without a text constructed in that language [system]. This means that the language [system] in question is foreseen by linguistic theory as a possible system, but that no process belonging to it is present as realized. The textual process is virtual.[28]

It would now be highly appropriate to discuss how a mental language system without linguistic features could possibly exist. Under any circumstances, the idea of the primacy of the language system contains a residue of the same transcendental precondition that Hjelmslev wished to dismiss.

If, in accordance with Hjelmslev's intention, we wish to establish an immanent view of language, we cannot lay the foundation by declaring that there is a language system which exists in the form of a linguistically well-defined island which is completely delimited from the surrounding non-linguistic sea and prior to any linguistic articulation.

When we deny that the language system is produced by language usage, we are left with the question as to where, when, how and by whom it was created. Without an answer to these questions, the declaration lacks the foundation it assumes itself. That this lack has often been accepted is perhaps due to the fact that the idea of a fully created, closed system is ideally suited to the deep-lying cultural assumption expressed in the idea of a divine creation.

It was at this point that Chomsky (probably without knowing it) broke with Hjelmslev's theory in proposing the hypothesis that humans were equipped with a physiological "language motor" in the form of an innate, universal grammar.[29] By identifying the system with a motor Chomsky resolved the schism between the invariant, static system and the dynamic sequence. But the theory does not describe how the physiological system can produce a grammar. It fixes a long, unknown history of development in a single, giant leap from the physiological system to a physiologically rooted grammatical system in which it is no longer necessary to see the physiological process as a potential source of meaning which can work both with and against the grammatical motor.

Although Chomsky is a Darwinist in the sense that he places the innate grammar in the physiological system, he maintains a classical dualism with the idea of an autonomous, mental - in this case, grammatical - form which is elevated above (and conceived independently of) material substance. The form concept, however, is itself determined by a cognitive discrimination which distinguishes certain elements in the matter as part of a form, a structure or level.

If there is a grammatical motor in the physiological system - and this is still a speculative hypothesis - it does not represent the beginning of linguistic competence, but a late stage in its development. As the motor has not always existed, it cannot be particularly universal either, much less inaccessible to new, non-linguistically motivated change.

The immanent, scientific viewpoint must also go beyond this transcendental residue in the understanding of form and take steps to look at form creation, including that of language forms, in relation to the immanent, non-linguistic "surroundings". The relationship between the linguistic and the non-linguistic is not only a question of how it is possible to use external matter to depict the external world in the form of language which is distinct from both matter and meaning, but rather a question of how linguistic forms are generated in the field of tension between matter and meaning.

Probably nobody would deny that it is possible to construct languages which follow a limited set of given rules, or that any linguistic expression can assume some kind of regularity. The problematical point in these assumptions lies, on the contrary, in the implicit precondition that any linguistic rule system always constitutes a coherent, theoretically reconstructable and, in this sense, closed system. It is the same problem which motivates Hjelmslev to suspend further analysis of linguistic redundancy with the term 'figura'. If a linguistic sign is created in the establishment of a distinction between semantically more distinctive and more redundant figurations, it is impossible to maintain Hjelmslev's - transcendental - concept of a language system, as the minimum linguistic condition in such a case consists of the distinction between semantically distinctive and redundant figurae and not of any particular rule system. The redundancy structure thus appears to comprise the smallest identifiable condition of language.

This assumption is completely in accordance with the description of a sign as something that can stand for something else, as that which must stand for something else can only do so by standing slightly less for itself. It thereby conflicts with the idea that only signs can produce signs, in what Peirce described as an infinitely continuing, self-dependent semiotic process.

That we can only speak of the world through language and that any referentiality has a debatable quality, does not mean that the thus dubiously referred to and always only re-presented world around us can be eliminated or marginalized in linguistic theory. On the contrary, it means that the semantic meaning field stretches across the gulf between language and non-language also including, as is the case with informational notation, that of the lower threshold to the expression substance. The elimination of the non-linguistic is only made possible by the groundless claims on behalf of a sign concept based on transcendental, theoretical premises which legitimizes taking the sign as exclusively given as its own cause.

Whether we motivate the autonomy of the science of signs with the concept "langue", "language system", or "code" cannot change the fact that in all these cases, with these terms, we carry out a groundless separation of a special linguistic fragment of consciousness from the rest of the contents of consciousness - and also from the physiological manifestation form of consciousness which comprises the mental expression substance.

In the definition of the sign function as a relationship between two different levels, an expression and a content level, both seen as purely linguistic dimensions, linguistic theory eliminates its possibility of understanding the meaning of the non-linguistic for the way language works. This holds true at the internal, mental level and at the level of the expression and therefore also for the sign concept which is defined as the connection between them.

The idea is not in this way to be able to solve the problem of meaning in the form of a definition of the referential status of various sign systems, but on the contrary to investigate the ways in which the relationship to the non-linguistic is included as an element ]in the linguistic.

7.7 Linguistic redundancy structures

I have claimed in the preceding that redundant figurae are an irreducible part of the sign's expression form and of the semantic structure of language.

The redundant manifestation of figurae as a foundation for the manifestation of the more distinctive figurae is in itself an important functional property, but it also creates the foundation for other characteristic semantic features.

It is well known that an abundance of sign elements considerably aids readability. We are thus often able to ignore printer's errors, mispronunciations and speech variations (or ascribe meaning to them) and decipher indistinct signs, whereas notation systems without redundant sign elements - Morse signals for example, or binary notation - are much more vulnerable.

This meaning stablilizing effect can hardly be underestimated, but on the other hand, it is not of such importance that it can explain in itself why language has retained its redundant elements. If redundancy only served to support meaning recognition, it would be reasonable to expect redundant expression units to disappear in step with increasing reading proficiency - whether in the form of abbreviations or linguistic innovations which omit certain sign sequences. Words which are used in a group are often subject to this type of change in pronunciation or spelling, because the need for distinct marking declines as a given meaning expression becomes a custom. A good example is a Danish usage which apparently grew up among children of kindergarten age. Here, we not only encounter 'børnehaven' (the kindergarten) referred to as /'børneren'/ (literally 'the kinder'), but also 'fjernsynet' (the television) referred to as /'fjerneren'/ (the 'tele', or 'the telly' as it is usually spelt), 'døgnkiosken' (24-hour service kiosk) as /'døgneren'/ ('the 24-hour'er'), 'fritidsinstitution' (the recreation centre) as /'fritteren'/ (the 'rec') - and a number of other similar innovations.

The - Danish - example not only tells us something about the linguistic creativity of children - which is often seen by adults as vulgarization - but also something about the redundancy function. It is immediately obvious that these changes follow the same rule for the elimination of superfluous sign elements. But it is also clear that the familiarity which makes it possible to omit the entire second part of a number of compound nouns is not only a linguistic familiarity. The regularity which permits the elimination is, on the contrary, a regularity in the world of children, where the kindergarten, television, 24-hour service kiosk and recreation centre in the same period have become common and basic areas of daily life experience.

The example thus shows that a distinctive expression can become redundant relative to the non-linguistic (in the actual a case a new lifestyle). But it also shows that expression redundancy is relative to the content form. The two different expression forms (the television/the telly) correspond to a semantic difference, although it may be difficult to define this difference. One possibility is to regard it as a - subjectively motivated - stylistic difference, but it could also be claimed that the stylistic difference represents a more comprehensive semantic distinction, /the telly/ indicates a relational experience, a familiarity, which is not contained in the concept of /television/.

A "sui generis" explanation could attach importance to the fact that the different examples are formed in accordance with the same rule, which could thus be regarded as part of the language system. The rule could be formulated as something like: the second part of compound nouns is subject to the same tendency towards loss of distinctiveness that we are familiar with in connection with many suffixes in Danish. There is, however, no rule for when this rule comes into force and when it does not, for which words it affects and which it does not and this is because it can only come into force as the consequence of a semantic choice made by a language user and then accepted by so many other users that it becomes adopted. The semantic choice of the form, the first use, occurs under any circumstances before the formation of the rule, just as the establishment of this expression form as a rule structure contains yet another semantic choice.

The use of the rule in the examples we have seen here can only be explained by referring to the specific context. The transition from distinctiveness to redundancy is not only fluid, it is determined by semantic decisions which are not solely subject to linguistic rules. The redundancy structure is conversely precisely a structure which permits such an interference between the linguistic rules and non-linguistic influence on rule structure and rule formation, because it permits both new and old expression forms to be manifested with semantically motivated, variable values.

The sign economy of the linguistic expression is thus closely connected with both meaning and the non-linguistic world in which and of which meaning is formed. Where there is great familiarity with regard to meaning between sender and receiver, distinctive sign sequences lose some distinctiveness. This does not necessarily mean that they are no longer manifested, but rather that they are manifested as redundant sign sequences which can later be eliminated or retained with the possibility of becoming distinctive once again.

Expression redundancy thus constitutes an extremely important aspect of the plasticity of language relative to the highly variable consensus between the senders and receivers of language. That which is expressed is a semantic function of the non-expressed, not only on the content side, but also on the expression side.[30]

Finally, herein lies the fact that the relationship between redundant and distinctive manifestations need not necessarily coincide for the sender and the receiver or for different receivers.

Complete coincidence, on the other hand, is an exception which rarely or never occurs. We never hear or read the precise meaning expressed, we hear or read it in more or less conformity with the sender's intention or explication. The question therefore arises as to how one and the same linguistic - and not least written - expression can contain this semantic openness at all, as the expression is produced in a completely closed form.

In answering this, reference has often been made to the fact that linguistic understanding depends on an interpretation community, which in some way permits meaning to be received as a copy of the message transmitted and then interpreted. But the reference to an interpretation community, which is not completely inaccurate in itself, provides no answer to the question of how language can contain several meanings in the same expression. The reference to an interpretation community, however, is not quite accurate either. If we already possess a common understanding, communication would only be a confirmation of this concord. In this case the only reason to communicate would be to confirm that there is no need to communicate at all. Conversely, we can state that a basic motive for communication is to establish common interpretations or to explore differences.

Nor will it help to regard the expression on the basis of the semantic-distinctive sign manifestations, because this view either implies a semantic unambiguousness or complete randomness in the relationship between the expression and the content form, whereas the relationship between the sender and the receiver is neither unambiguous nor completely random. Polysemy must at once be made possible in and limited by the expression itself.

But nor is it adequate to simply add that redundant sign sequences are also included, if we thereby imply that a given expression is characterized by an - intentional or unintentional on the part of the sender - completely defined relationship between redundant and distinct manifestations. This would imply that all semantic variations permitted by the expression would be variations of an opposed character. Where the sender defined a distinctive relationship, the receiver would have to read this as redundant, with complete randomness as a consequence.

The only possibility which remains is to assume that the same notation sequence permits variation in reading the relationship between the more or less distinctive.

This variation is not limited to the circumstance that many words can be used with different meanings and that different shades of meaning can be manifested in certain uses. This form of polysemy, connected with semantic entities such as the word - or sentence - is well known and obvious. In these cases it is a question of a semantic content form which is connected with a (variable) register of possible content meanings (old meanings may disappear while new are created). This type of variable reading (polysemy) thus concerns variation in the relationship between content meaning and content form.

But in addition to this there is a possible polysemy which is connected with the smallest semantic variation mechanisms. It is well known that it is possible to change meaning in spoken language by changing tone or emphasis. In this case the change of content meaning is brought about by changing the expression form. The interesting point now is, that such a change need not necessarily be manifested in written language. While the difference between /en vis person/ (a certain person or a wise person) in spoken Danish is expressed by a phonemic distinction (the former is pronounced something like [vis] (as in] 'this') while the latter is pronounced something like [vees] (unvoiced 's'), the two persons today usually have the same expression form in written language.glutural stop, bedre eksmp4ele på viis The difference can be represented either by using the archaic /ii/ (en viis person, der er klog - a wise person who is clever) or by italicization (en vis person, der er bestemt - a certain person), but this is not necessary and not usual.

While meaning distinction in speech is represented here by an expression difference, in writing it is only borne by the meaning context. The phonemic marking of semantic distinctiveness in spoken language is substituted by a purely semantic distinction which has no explicit manifestation in writing. The individual grapheme can in other words have different semantically distinctive values in the same constellation. If we use the commutation test on this example the peculiar result is that in written language we have genuine commutation between the grapheme /i/ in vis (wise) and the grapheme /i/ in vis, (certain) which are thus both identical and different graphemes.

While such a case strains the idea of an asemantically defined graphemic system, it confirms the description of figurae as semantic variation mechanisms which are included in a redundancy system in which the individual figurae can occur with a variable content of significance and/or strength of significance and that notational distinctiveness can be replaced by semantically determined distinctiveness.

The example, however, also gives occasion for a closer look at the relationship between the spoken and written expression.

Writing - a system of expression and/or a language?

Hjelmslev's language theory concerns the description of what he refers to as the "so-called "natural" spoken language". We could immediately ask, however, whether the spoken language, on the whole or solely, uses sign elements in the form of phonetic figurae in the sense that Hjelmslev assumes. Although it is true that it is possible to establish relatively clear phonetic inventories as typical, and the understanding of spoken language also presumably assumes a certain correspondence between the speaker's and the listener's phonetic inventories, spoken language equally indubitably permits a far greater (individual, group determined, dialectal, stylistic etc.) phonetic variation than is expressed in these inventories, just as at the same time it offers a number of other, corrective possibilities for distinguishing semantic distinctiveness (tone, facial expressions, gestures, pre-established social expectations in the communicative context) which are regarded as peripheral by Hjelmslev.

As spoken and written language not only use different substances, but also use substance forms in different ways, it is not possible to speak of an expression system common to both without further ado, nor to take either speech or writing as a model for "language".

A more cautious interpretation therefore prompts us for the present to regard the graphemic redundancy structure as a redundancy connected with the alphabetically expressed language, where the manifestation of redundant sign elements is the necessary precondition for the manifestation of semantically distinctive signs.

That this is a characteristic of alphabetical writing does not necessarily imply that it is also a characteristic of spoken language or of language as such. Havelock, for example, claims that it is wrong to identify writing with language and suggests that the term "language" should be reserved for spoken language. Further to this he describes alphabetical writing as a translation of the phonemes of speech into a visual expression which depends on - compared to speech - a very recently developed civilizational competence.[31]

According to Havelock, a true alphabet can be defined by three requirements which must be fulfilled simultaneously: First, that all the phonemes of spoken language must be covered. Second, that the total number of graphemes (letter shapes) must be limited to between 20 and 30. And third, that a given grapheme need not handle more than one task, the individual grapheme must be connected with a fixed and invariable acoustic identity.[32] The central point in this definition is that the visual representation of spoken language in the Greek-Roman alphabet is a re-presentation of the spoken language's phoneme system.

This translation depends on the one hand on a theoretical, analytical conceptualization of the basic acoustic components of spoken language, its "atomic structure", with the deciphering of the vowels as the sonant element, to which are added con-sonant start and/or stop conditions and, on the other, on the written notation system being based on a set of distinctive forms which have no semantic content. The graphemes of writing, letters, must on the contrary be seen as visual signals which mechanically release an acoustic picture in the consciousness.

The bond, which can connect speech and writing, thus lies in the demand for a rigorous correspondence between phonetic and graphemic manifestation, a correspondence in the elementary particles of the expression system. According to Havelock, it is this asemantic relationship between speech and writing which makes it possible to represent many different spoken languages in the same written notation system. That the number of necessary graphemes can be defined with such relative clarity as being between 20 and 30, finally depends on a combination of a mnemonic need to reduce the number of immediately recognizable basic forms as much as possible with the demand for complete representation of the possible number of phonemes, which again is determined by the biologically contingent, physiological articulation possibilities.

Havelock thus assumes that the expression elements of alphabetical writing "ideally" correspond to those of spoken language, but he also claims at the same time that acoustic recollection can hardly have the form of a - limited - phonetic inventory, as he sees the spoken language as a biologically handed down disposition comprising the mental ability to retain the enormous number of acoustic picture constellations of spoken language. But this view is not without its problems either, because it conceals the question of the spoken language's acoustic side in biology, even though the art of speaking has by definition, so to speak, artificial dimensions. This at the same time implies that the description of the limited phonetic inventory also in this theory is perhaps rather a projection of the much later developed alphabetical notation.

On the other hand, both Hjelmslev's and Havelock's theories create the, in this connection, regrettable problem that writing is not understood as language. In Hjelmslev this only appears implicitly from his repeated emphasis on the claim that the primary linguistic subject area is spoken language, although he otherwise appears to assume that linguistic theory is so general anyway that it includes all languages. The lack of clarity in his view of the relationship between spoken and written language is not only shown by his refusal to consider written language as a separate subject, but also by the fact that when referring to the physical material (usage) he is thinking of speech, but is mainly and perhaps exclusively writing about the "text":

The objects of interest to linguistic theory are texts. The aim of linguistic theory is to provide a procedural method by means of which a given text can be comprehended through a self-consistent and exhaustive description.[33]

It is not difficult to understand the motive behind this textual reference to spoken language which proposes the description of language sui generis as a goal. While the written language, precisely on the expression side, appears sui generis, the spoken language has no such "existing" property as a manifest object. Writing exists, as a fixed manifestation, speech is unique and can only appear as an object in a mediated and reconstructed form.

That this is a question of a deeper confusion also appears from the quite informal and uncommented use of examples from Latin, just as all examples which are used in the book therefore appear as written representations, while there is a complete lack of any attempt at all to describe oral communication. This confusion cannot be explained as a careless lapse. It is, on the contrary, the result of the theoretical construction, as speech and writing are viewed as two different usages, i.e. as two, for language, external and random expression substances, or as Hjelmslev gradually defines them: as substances for an expression system of a linguistic schemata,

Thus, various phonetic usages and various written usages can be ordered to the expression system of one and the same linguistic schema. A language can suffer a change of a purely phonetic nature without having the expression system of the linguistic schema affected, and similarly it can suffer a change of a purely semantic nature without having the content system affected.[34]

There is no basis for denying these possibilities which, according to Hjelmslev, explain, "that it is possible to distinguish between phonetic shifts and semantic shifts on the one hand, and formal shifts on the other". On the other hand there are no possibilities either for denying that both phonetic shifts and semantic shifts can also produce formal shifts. In Hjelmslev's theory this can only happen as an external cause whose effect in the language system is exclusively determined by "the immanent algebra of language".[35] This abstraction, however, cannot be observed as there is no other way of studying the language form than through the study of notation and meaning changes.

By isolating the language form and reducing the physical medium to an amorphous substance, the central question as to whether it is possible to explain rules for which shifts at one level can produce shifts at one of the other levels, disappears, partly because the relationship is seen as peripheral, but particularly because the idea of an amorphous substance implies that we must ignore the structural properties which characterize the relationship to the expression substance and provide speech and writing with different semantic potentialities.

Where Hjelmslev is silent (but does remark that written language has still not been studied at all and is perhaps just as "original" as speech), Havelock offers a number of conceptual - and historically motivated - distinctions, including the descriptions of the development and mutual relationship of the two expression systems in ancient Greece. For Havelock this distinction implies that we cannot use writing as a paradigm for the description of spoken language, but at the same time he also introduces the two systems into a mutual hierarchy where speech is seen as a biological invariant, while writing systems are seen as specific, artificial and external notation systems.

A successful or developed writing system is one which does not think at all. It should be the purely passive instrument of the spoken word even if, to use a paradox, the word is spoken silently.[36]

As different articulation possibilities are attached to each of the systems, it is not obvious that writing is only a passive, external medium for speech and is not seen as language. No clear reason - over and above the biological background - is given and it is perhaps limited, ultimately, to a manifestation of that logocentrism which, according to Derrida, is expressed in a tacit preference for speech as against writing, an invocatory gesture intended to conceal the gulf between meaning and expression which is attached to the sign concept in which the presence of the sign is a manifestation of the absence of the thing. Whether the way the problem presents itself here can be clarified must remain unanswered in the present work. The problem, however, marks a possibility for regarding alphabetical writing as a specific language.

As far as the redundancy concept is concerned, it is therefore obvious to ask, moreover, how the sign organization of alphabetical writing relates to the spoken language. Does spoken language possess double redundancy parallel to that of written language, or is the redundancy structure of written language, on the contrary, a specific function which only corrects problems in converting visual forms to the mental recollection of the spoken language's phonemes?

Probably both. It is well known that written language is far from capable of reproducing spoken language when read at the level of expression units. Linguists operate, on the contrary, with a special phonetic notation which is subject to a far higher variability than written language. In this respect Havelock's correspondence theory represents an idealization of limited durability, as any child who has learned to spell knows.

In some circumstances, redundant grapheme occurrences are undoubtedly connected with a need to correct the incomplete correspondence of written notation to acoustic recollection, but this does not imply that a similar redundancy does not also hold true for the phonetic inventory. The difficulty here is that there is no obvious symmetry between the concepts of phoneme and grapheme.

While graphemes, in their capacity of explicit and physically fixed forms, are constructed as distinctive and manifest forms, the concept 'phoneme' is perhaps only a theoretical abstraction whereby we make the acoustic aspect of spoken language accessible to analytical operations. There thus appears to be a question in both Hjelmslev and Havelock of a description of the phonetic structure on the basis of the alphabetical notation. While written notation is based on a sequential, single-stringed organization of discrete elements, spoken language is under any circumstances at least two-stringed. The distinction between consonants and vowels in writing is here parallel to a co-ordination of at least two simultaneous (and complex) physical processes: the production of acoustic waves and the modulation of variations which can be both continuous (sonant) and discontinuous (con-sonant). The speech situation at the same time contains a number of other, simultaneous and mutually interfering physical expression possibilities. A wink can influence the speaker's construction of a sentence, or be used to give expression to one or more meanings etc.

That we can still claim that redundancy is not simply a function of written notation, but is included as constitutive for language formation, is due to the fact that redundancy is a necessary precondition for any articulation in this world. The acoustic picture of the spoken language can - just as the musical picture - only be manifested as a choice of repetitive modulations in a sonant sounding board.

Redundancy and regularity

In the description given here of the notational redundancy structure, the emphasis has been placed on the functionality of redundancy seen in the relationship between the linguistic and the non-linguistic, on the one hand in relationship to Hjelmslev's "meaning" (intentions and references) and on the other in relationship to the physical manifestation of language. The relationship between the linguistic and the non-linguistic, however, cannot simply be understood as a "national border" between distinct territories such as has been done through the well-motivated attack on the view of language as a mimetic mirror, or as a means of perfectly reconstructing the world around us.

Hereby falls the idea of the possibility of a given language being described on the basis of the jurisdiction that is indicated by the concept of language system. The building itself is built, the rules are themselves subject to regulatory changes in a process which is at once produced by signs and non-signs which breed new signs. This affects not only Hjelmslev's dream of a language theory which would

be of use for describing and predicting not only any possible text composed in a certain language, but, on the basis of the information that it gives about language in general, any possible text composed in any language whatsoever.[37]

it affects all theories which describe language systems as invariant, structural precepts for language use.

It is quite true that there are many linguistic features which have not changed much, if at all, for a period of 50, 100 and perhaps 1000 years, for example the nexus structure of the principal clause. This shows that to a very great degree language utilizes stabilizing rules. It does not, however, show that there is an precept which is independent of the manifest usage, nor that the functionality of the nexus relationship is only connected with the internal organization of the sentence.

As long as we only consider the repetitive use of the same rules, the choice between describing them as part of a language system, or as an expression of stabilization in a linguistic redundancy structure, is perhaps arbitrary, but the arbitrariness is dissolved when we consider the relationship between redundancy and distinctiveness. If we see repetition as part of a transcendental language system, in relationship to usage, we create an unbridgeable gulf between the - in such a case redundant - part of the linguistic expression which represents the system and that part which represents meaning. To each part there must belong an individual set of sign sequences, as the rules of the language system cannot determine all sign sequences, if it is to be possible to read a meaning into the expression.

It is not possible, however, to carry out such a complete division of sign sequences, but it is possible, on the other hand, to show that the sign sequences of written language are subject to several simultaneously operating rules and that they are included in several simultaneous relationships. Distinctive occurrence goes hand in hand with redundant occurrence, linguistic certainty goes hand in hand with non-linguistic certainty and linguistic certainty can itself embrace several levels, from grammatical choice to that of genre and style.

Abandoning the idea of a transcendental language system does not therefore imply that it is impossible to speak of rules, but on the contrary, that the relationship between rules and the determination of their reach and use is itself part of the sign formation process and that linguistic rule formation takes its point of departure in the repertoire of existing forms whether they are already defined in one or several - possibly overlapping - ways or only exist as redundant or potential forms.

It could also be said that the common spoken and written languages are characterized by a semantic rule formation, that this is part of the practice it regulates and that rule formation occurs in the form of a shifting balance between several different, available linguistic rules and non-linguistic interferences.

The relationship between what is preconditioned and that which is expressed is not a relationship between a precept and an execution of the programme, but a semantic choice which delimits the expressed relative to an intention and a receiver. Further to this comes the fact that the concept of linguistic redundancy itself is, in an important sense, contrary to the distinction between a programme and an execution. On the one hand the redundancy function constitutes an alternative to precepts. Redundancy brings about a stability which, in its absence, would have to be filled in by a programme. On the other hand, it is not possible to speak of the concept of redundancy before there is a manifested expression, as redundancy can only be determined relative to physiological and semantic distinctiveness.

It is therefore not satisfactory, as Paul Ricoeur does, to simply supplement semiology, understood "as a science of signs in systems" with "a semantics, or a science of usage, of the use of signs in sentence position". Ricoeur motivates his distinction with the point of departure in the poly-semic character of language which

in purely synchronic terms... signifies that at a given moment a word has more than one meaning, that its multiple meanings belong to the same state of system.[38]

while in diachronic terms polysemy is the actual result of an ongoing semantic exchange of meaning, which is again determined as follows "that the word is a cumulative entity, capable of acquiring new dimensions of meaning without losing the old ones".

While the diachronic and semantic dimensions are thus characterized by "a factor of expansion, and, at the limit, of surcharge" the synchronic system dimension becomes "the mutual limitation of signs within the system" seen as a necessary brake which means "that the new meaning finds its place within the system".

It is clear here that Ricoeur is wavering between the view of synchronic description as a description, with regard to meaning, of a transcendental form system "which can be treated without any reference to history" and as a "thumbnail sketch", a certain stage in a process - and hence a history - in which the system is included as an acting force. He describes the relationship between the synchronic and the diachronic as a collision process between two completely separate systems, where the former changes the latter, but itself remains untouched.

The condition which allows the system to work limitationally in relationship to the semantic expansion, however, is that it is semantically sensitive itself. The meaning of the one word cannot fall into place unless the system permits continuous and unpredicted semantic changes in the linguistic surroundings, i.e. changes in the extent of the rules and/or changes in the content form and/or expression form without which a change in meaning cannot be manifested.

That language can contain this polysemy at all, which according to Ricoeur is the characteristic proper of language, is due to the fact that the regularity of language is formed in continuous modulations and crystallizations in redundancy structures which permit the same expression elements to be both rule-bearing and meaning distinctive, often at the same time, but also in a mutually variable relationship. This implies that the entire structure, and not only meaning, is included in the semantic dimension. The synchronic description must therefore be seen as an idiomatic, photographically frozen picture of a specific state whose relationship to preceding and subsequent states is open to semantic variation and to the introduction of new rules and structures, or the suspension of old. Polysemy includes the rules of language, which only exist if they are accepted and are only accepted if they further a semantic relationship between a sender and a receiver.

If the rules of language were available in the form of an invariant rule structure, language would be highly suitable for presenting unambiguous messages, as there would be a declarative expression rule for each meaning entity. In such a - for example mathematical - language, an expression such as "goddag mand økseskaft" ("hello, man axe-handle") cannot be articulated, although in Danish this phrase is actually used to tell people that they are talking nonsense. Nor would a critical reading of such a text be possible.

7.8 The redundancy structure as a criterion for distinguishing between semantic regimes

If we were asked to name the last 5-10 words - or the last sentence - we had read, we would generally have to think for a while, it is easier to reproduce a meaning than to repeat an expression we have read. If we were asked instead to name the last 5 or 10 letters, or to spell the last word, this would also require some thinking. The path to the recollection of the letter appears to go through the recollection of the word and the path to the recollection of the words to go through the recollection of the meaning. While the distance between word and meaning corresponds to great freedom to choose words to express a meaning, the distance between the word and the letter with regard to recollection is more striking, as there are fixed bonds between the word and its literal manifestation.

Things are different in spoken language. It is often possible to repeat without difficulty something which has just been said. On the other hand, we do not possess the same fixed codex for dissolving words into a phonetic inventory. Whether it is possible to carry out a phonetic or phonological dissolution of words into sound components plays no important part in language competence. While spelling is a facet of the ordinary learning of written language, phonetic transcription is a purely professional accomplishment in spite of the colossal importance we attach, individually and collectively, to correct pronunciation.

It is clear that the phoneme does not play the same role in oral language competence as the grapheme does in writing, but where does this difference lie?

One possibility is that there is a structural difference between the auditive and the visual sensory apparatus. But it is difficult to see why visual mediation should demand closer ties between the written word and its graphemic representation than the auditive mediation demands between the spoken word and its phonemic representation, not least if, with Havelock, we see the alphabet as a visual representation of the phonemic structure of spoken language.

It is therefore more reasonable to view this difference in the light of the different communication structures of the spoken and written word. Whereas speech - with the air as its medium - is transient and the relationship between speaker and listener is contemporaneous, writing is fixed and the relationship between writer and reader is non-contemporaneous.

As contemporaneousness between speech and hearing implies physical closeness between speaker and listener, the speaker is also able to use other possibilities to express himself. The phonetic inventory does not exist alone, it is accompanied by accentuation, stress and gesticulatory signals as means of articulating meaning, just as the speaker can utilize the receiver's reactions as part of the stabilization and clarification of the message.

These structural differences determine a difference in the expression economy of speech and writing. While the speaker, in speaking, can both use multiple auditive, visual and possibly also tactile means of expression and economize with the expression under the impressions of the signals which are emitted by the receiver and the surroundings, the author of the text can only use graphemic means of expression and must himself, in advance, establish his interpretation of the necessary relationship between redundancy and distinctiveness in the expression.

It appears from this difference not only that the grapheme must handle many more tasks than the phoneme, the graphemic manifestation must also transpose the simultaneous manifestations of speech (and those which are not linguistically expressed, e.g. 'shown' meanings, gestures, for example) to successive sequences. The fixed graphemic structure of words, which in writing is further emphasized by the blank sign which separates graphemic blocks from each other, are not equivalent to the phonemic structure of speech.

There is thus also an exceptionally good reason why the phoneme does not play the same role for spoken language competence as the grapheme does for competence in writing. The phonemic inventory is simply not the elementary particle of spoken language in the same way as the grapheme is for writing. There are three reasons for this.

First, the phoneme as a unit is larger than the smallest possible semantic expression unit. Different accentuation, (voicing, stress, the Danish glottal stop, strength and volume of voice), of the same phoneme can be semantically distinctive.

Second, the phonemic manifestation is subject to great individual and group variation. Handwriting too has its individual variations, but this variation appears to permit far from the same rich set of possibilities for semantically distinctive use. The individual variations of handwriting have also traditionally been seen as a stylistic phenomenon which may characterize the personality of the writer.

Third, consonant articulation, which in writing is represented by separate graphemes, is precisely a con-sonant modulation of vocalization. We simply cannot pronounce separate consonants without a minimum of a sonant resonator. Distinctions are always distinctions in something.

Whether phonemes actually exist at all as a clearly delimited, acoustic entity can be discussed, whereas the existence of graphemes as manifest, graphic entities is indisputable. The difference also appears indirectly from the difference between phonetic notation and written language, as phonetic notation produces many phonemic variants of the same word, while written language uses an almost complete - semantically - invariant graphemic manifestation.

It is clear that fixed spelling serves to make word recognition easier. As a consequence of the fact that this occurs in a different way in writing than in speech, the economic alleviation argument must be seen in the light of the written communication structure and not as a manifestation of a general economic law of language.

Where writing with the blank sign and the graphemic invariance of the individual word support the word as a far more invariant and distinctive entity than speech, it expresses a difference between the semantic potential which lies in the different time structures of the two languages. This difference in time structures is given in and with the properties of the expression substance.

It is correct that, as a whole, speech, like writing and reading, can be regarded as a linear sequence in time, but it is not correct that the expression elements of speech are articulated (or understood) in a linear succession similar to that of writing.

The multi-dimensional time-space of speech is only possible because speech elapses in time, unlike writing which appears as a closed and simultaneous manifestation of the entire expression. Correspondingly, we can only understand speech at the time, place and in that order it is pronounced, whereas the reader can read at any time or place and is completely at liberty to turn the pages backwards and forwards, skip a page, put the book down or read it again.[39]

Whereas the reader, however, must take note of what he reads, put away the text or make objections post festum, the listener has a broad range of possibilities for intervention: from the continuous confirmation of understanding, through quizzical facial expression, interruptions, supplements, amplification, dialogue, objections, contradictions, to argument, fighting, or departure - or bloodiest of all - murder. The solitude of writing, however, does offer the author the clemency of being able to exploit the distance of time - and thought - to correct or - perhaps - protect himself before the message is sent out into the world.

The graphemic freezing and sequencing of the contemporaneous field of speech thus constitutes a micro-structural difference in speech as a dialogic and writing as a monologic medium. This micro-structural difference remains, although speech can be monologic or writing dialogic. In speech the expression is not alone and is accessible to variation as it is produced. Writing, on the contrary, - in order to stand for itself - must use a certain expressional invariance speech does not need. As expression systems, speech and writing are separated by their semantic variation possibilities.

The difference between speech and writing is therefore basically a difference in the redundancy structures of the two expression forms, as the expression substance offers different semantic variation mechanisms. Although this structural difference can be modulated, the two expression forms drawn closer together, it is not so plastic that the one system can be made to cover the entire expression potential of the other. Many sentences can without further ado be produced in both systems, but both systems also permit meaning expressions which cannot be produced in the other. Here we are cut off from the possibility of providing genuine examples of spoken language which cannot be expressed in writing, but the present text is an excellent example of a written expression which cannot be produced in spoken language.

The difference reaches further that the difference in production potential. Not all expressions can be translated either, once they have been produced. It is quite true that it is possible to read any text aloud, but a number of texts have been written which could not be understood if they were read aloud, such as theoretical texts which operate with hierarchic sentence structures, highly specific concept formations and low meaning redundancy.[40] Conversely, written language can in many cases reproduce spoken language through a detailed linguistic (and sequentially ordered) account of the many non-linguistic (and simultaneously expressed) elements which are included in the meaning expression, but not in what is pronounced in language. In this case, it is not the complexity of the sentence structure which hinders representation, but the complex, non-linguistically expressed - meaning distinctive - situation, whether the meaning is given by an existing interpretation community or is only produced during the act of speaking.

Speech and writing have different relationships to Hjelmslev's "purport" and "substance", both on the expression and the content side.

Where the clear meaning in spoken language builds upon a complicated, non-linguistic context, this context is not expressed in the spoken language even though it is semantically distinctive. The circumstantiality with which such a speech must be retold or written down for others reveals that contemporaneousness, which determines a possible interaction between the event and the narrative and/or between the narrator and listener, also confers a chronological dimension on the spoken language's redundancy structure which is unknown in invariant writing, although it is both produced and read in a one dimensional, linear progression in time.

The difference which exists between the linguistic competence of writing and speech corresponds to a difference between their redundancy structures, which implies a difference between the distinctive potentialities of the two languages.

The two languages, however, are at the same time each other's subset. Seen in relationship to other sign systems this kinship appears characteristically as a kinship in the same area, which mutually separates them, namely the redundancy structure.

While written language is distinguished from spoken language ]by the redundancy structure of graphemic notation, writing and speech have a simultaneous manifestation of redundancy and distinctiveness in common. These two languages thereby distinguish themselves from both pictorial and formal expression systems.

Written language shares the manifestation's spatial two-dimensionality with other pictures, but not the linear sequencing of space. All relationships are manifested at once in the picture, but are not bound by any succession sequence. Although the distinctive features - the forms - appear against a background and in relation to other forms, no fixed redundancy structure is included in the pictorial expression, as no delimited notation system exists.

It is true that colour in a certain sense constitutes a kind of equivalent to the linguistic redundancy structure, as forms can only be manifested as differences between colours. These differences possess a plastic variability, but the relationship between colour and form itself is invariant. Even though the form can be determined through the critical thresholds for colour transitions, the relationship between colour and form is different to the relationship between redundancy and distinctiveness. Colour cannot be manifested as form, nor form as colour, as the form always and only manifests itself as a difference between colours. The relationship is not open to semantically motivated change, whether the colour is seen as the form's - random - substance or colour variation is seen as the material structure of form.

In a certain sense it could be said that picture formation, similarly to language formation, is characterized by over-determination (overlapping rules), by the simultaneous effect of several norms and rules, but picture formation is also characterized by irregularity rather than the possible suspension and variation of the extent of the rules. While the individual picture constitutes a complete, closed and ordered entity, the picture as an abstraction has no definable order structure. No classification of the pictorial expression can be made on the same scale as for spoken and written language because the pictorial expression is not bound to well-delimited notation systems.

This does not mean that certain pictures cannot be classified on the basis of a notation structure. On the contrary, it is quite possible to classify certain types of picture in this way, as distinct from others, including groups of pictures which use other notation structures. A typical example in this connection is the difference between a television picture and a computer generated picture on a monitor which are precisely and solely distinguished through the two different - invisible in themselves - underlying notation (or signal) structures.

Although the grapheme is a picture form which as such can become the object of aesthetic consideration and variation, it is at the same time subject to an acquired interpretation regime which includes the separation of the graphemic forms, for example in the form of an abecedarium and an established rule set for reading - for example in the form of a linear succession. It is not possible, on the other hand, to distinguish the letter from other pictorial forms simply by pointing out the letter's arbitrary, non-iconic character, as all pictorial forms can be dissolved into non-iconic form elements with division into individual points as the most radical subdivision.

The graphemic picture is thus determined by its belonging to an established inventory and by a chronologically defined, usually one-dimensional reading order. Herein also lies the fact that the grapheme is not defined by its invariant form. That this is the case is also shown by the way we can recognize with surprising certainty a great number of different A's as "A" and also distinguish many similar manifestations as "not A", whether "not A" is another grapheme or a non-graphemic pictorial form.[41]

The continuity of possible pictorial forms constitutes the redundant background for the distinctive occurrence of the grapheme. Writing thus rests on a simultaneously redundant and distinctive utilization of pictorial forms. The recognition of the individual grapheme, however, is at the same time supported by the manifestation of other graphemes, which in this connection act as a manifested graphemic redundancy.

While the notation system and the social bond between form elements distinguishes the graphemic picture from other pictures, the picture's contemporaneousness has a counterpart in spoken language. But where the picture's contemporaneousness is established by freezing the expression, (and separating the sender from the receiver) the contemporaneousness of spoken language exists between the sender and receiver who are related in a sequentially developed semiotic relationship which allows variation of the expression during the articulation.

On the face of it, it may be surprising that pictorial and formal expressions, which appear to be diametrical opposites, have in common that they distinguish themselves from language through one and the same circumstance, namely the absence of structural redundancy which is a characteristic of linguistic expressions. The absence of this redundancy at the level of physical manifestation also has a different - form.

While pictorial structures appear with no relation to the redundancy structure of language, (the redundancy structure of writing has, on the contrary, pictorial structure as a precondition) formal notation appears through the elimination of linguistic redundancy. The means to this elimination is a prescriptive declaration of unambiguous rules, the purpose of which is to overcome the polysemy of language.

While language on the one hand is characterized by the fact that any element in the language system can be subjected to variation - just as any rule in a computer programme can become data - on the other hand, unlike the programme, it is characterized by the fact that variation appears as a result of a semantic operation which is manifested as a shift in the relationship between redundancy and distinctiveness. This shift can, as will be evident, occur through variations on one or more axes: as a new utilization of a random form through repetition, as a variation of a pre-established pattern, through its strength of significance and/or through its content of significance. That this is a semantic shift implies that it need not - such as in the programme - be declared ]prior to its effectuation.

With the preceding unambiguous rule declaration the formal representation is given a redundancy structure which is distinct from that of language, as the rule simply defines the distinctive expression by distinguishing the indefinite redundancy potential as superfluous. While the formulation of the rule occurs as a semantic operation in linguistic form, the expression of the rule occurs in a formal form through a replacement of the linguistic notation by a formal notation.

As both the redundant content and expression elements are thus distinguished from the formal expression, this expression does not have the same semantic variation potential. To the chronological distinction (the declaration of rules always precedes the execution) belongs a structural or logical distinction between the open, semantic operation and the formulation of the closed, formal expression. All transitions between redundant and distinct occurrences thereby become subject to a sequential time relationship where these transitions in language can be defined in a simultaneous relationship with the definition of redundant features.

Now the definition of any redundancy structure necessarily contains the definition of distinctiveness. It is the relationship which defines each of the features in the relationship. It might therefore also be tempting to regard the semantic potential of the formal expression solely on the basis of the programme which is rooted in the semantic structure of the language, as this can only be formulated with a linguistic articulation as a starting point and working means.

This, however, is not sound. Although the distinct formal expression - the operational procedure - is characterized by the fact that the semantic content, the establishment of the relationship between redundancy and distinctiveness, is defined in advance - and outside - the distinctive, formal expression, the expression appears as a distinct linguistic procedure subject to a delimited, specific to the expression, set of semantic variation rules. This set is not simply a chosen set of linguistic variation rules, it is a set of rules which as a whole is characterized by a different relationship to other rules than that between linguistic rules.

This different relationship to linguistic rules is manifested in a structural difference in the definition of graphemic expressions, rules for sign sequences and in the linguistic and formal sentence construction. In the formal expression it is necessary to declare the semantic value of each expression unit. Although the alphabetical notation units are often used, the individual notations do not appear with their alphabetical value or function, they no longer belong to alphabet of language. In the same way, the rules of language for notation sequences are also rejected in favour of the demand for a specific definition of the relationship between a given notation and the next. Finally, where a linguistic utterance can be a single sentence, a formal expression always requires at least two.

Even though, seen in isolation, the formal expression can be described as a defined relationship between defined entities, in the most literal sense the expression has the definition as a precondition. The semantic analysis of the formal expression is only possible if this precondition is taken into account.

The bipartite formal sentence structure is not equivalent to the principal clauses and subordinate clauses of language, as these are not subject to the same declarative definition of the redundancy structure. With the demand for declaration, the formal expression is connected with and part of language, but with this declaration an expression system based on non-linguistic rules is created.[42]

While we thus in the relationship between language and picture have two separate expression forms where the structural connection - as far as written language is concerned - is limited to the notation level, in the relationship between linguistic and formal notation we have two separate expression forms which are both included in a historical and structural internal connection of a syntactical and semantic character. The formal expression form is an expression of a linguistic meaning content and the formal expression's content is specified through a linguistic expression form.

As the formal representation overcomes the polysemy of language through the elimination of the - for language - bearing redundancy structure, the relationship between the two expression systems necessarily contains a tense negation with comprehensive and often discussed epistemological implications.

The relationship between the ]linguistic structure of these two languages, however, has played a surprisingly modest role in these discussions, often subordinated to transcendental considerations of truth. The relationship between linguistic and formal representation has either been seen as a variant of the relationship between everyday language and scientific language, or as a difference between language and non-language, which, for example, could be described as the history of arithmetic or the use of signals, where a weak parallel to written language is only drawn in the introductory reference to the extent of this history.

The explanation of this circumstance should, however, hardly take the form of a criticism of tradition. That the formal representation - in spite of its thousands of years of history - only rarely gave rise to linguistic considerations shows first and foremost that it has been far from obvious - and perhaps not particularly relevant - to regard formal representation in its - semantic - relationship to language.

Whether formal representation creates a foundation for a special language can still not be taken as given. On the other hand, it is given that the dramatic expansion of formal representation competence over the past 50 years also includes in-depth changes in the relationship between linguistic and formal representation.

These changes, however, are based on the appearance of informational notation which, among other things, is distinct from both linguistic and formal notation because it can contain them both in the same expression form.

As this revolution marks a significant historical change in symbolic representation competence and has its centre of gravity in a new definition of the concept of information, the new symbolic competence will be treated here separately under the term informational representation competence.

Through a coincidence, which is perhaps more than a coincidence, a crossing of a historical and structural perspective in informational representation leads to one and the same starting point, namely the redundancy structure of informational representation. While the structural path to here starts with the relationship to language, the historical path starts with Shannon's theory which, with its establishment of a mathematical scale for measuring informational redundancy, became one of the theoretical starting points for the informational revolution.

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Notes, chapter 7

  1. The distinction between expression substance and expression form is Hjelmslev's. He viewed phonetics as the study of the spoken language's expression substance and phonology as the study of the spoken language's expression form. Unlike Hjelmslev's understanding of the "linguistic" as independent of the expression substance, the relationship between expression substance and expression form is interpreted here as a semantic relationship which differs in different symbolic languages.
  2. There is a similar argument in sections 7.6 and 7.7 regarding the difference between spoken and written language, which are thus regarded as common languages with partially different semantic potentialities.
  3. C.f. also L. Hjelmslev, (1943) 1961: 110 ff., where a similar criticism - but in other terms - is advanced against Rudolf Carnap's "monoplanar semiotic".
  4. Umberto Eco, (1976) 1979: 21.
  5. Umberto Eco, (1976) 1979: 20.
  6. Umberto Eco, (1976) 1979: 36-47.
  7. Umberto Eco, (1976) 1979: 48
  8. Umberto Eco, (1976) 1979: 48.
  9. In Derrida, among other things, as part of the considerations of the alphabetical script's linearization of the structure of thought and regarding the conclusion of the alphabetical script's period. Derrida (1967) 1976: chapter 3, p. 74 ff. The idea of a general sign theory, however, is far older and is also found in both Saussure, Hjelmslev and Peirce. It is therefore rather more appropriate to speak of yet another unclarified borderline - or an inner tension - between the attempts to formulate a single, overall sign concept which characterizes all forms of sign formation and attempts to differentiate the sign concept.
  10. Eco (1976) 1979: 48-49.
  11. Eco, (1976) 1979: 7.
  12. Eco, (1976) 1979: 31, note 5. The transition from Hjelmslev to Eco at this point is not as great as it may appear on the face of it, because Hjelmslev's concept of the expression form is also a concept of a mental content. The concept designates a set of mental "codes" for using the phonetic or graphic expression substance. Hjelmslev, however, assumed that these mental codes comprised a closed linguistic system which could be described "immanently", i.e. without including the mental environment. In his argumentation for this view, Hjelmslev claims, among other things, that it is not a question of individual, and thereby psychological, but social, common codes, that language is a social institution. But we are forced to ask - in spite of Luhmann - where this social institution is located, if not in consciousness?
  13. Havelock, 1982: 48, who views the alphabetical signs as visual representations of sounds, actually claims that it is as good as impossible to obtain a clear distinction "between speech and the visible symbols of speech" from linguistic theory. After Derrida, (1967) 1976, who sees the idea of oral primacy as a logocentric illusion, Saussure has been given the main responsibility for this weakness. Saussure saw written language as a distortion of 'natural' or 'genuine' spoken language: These phonetic distortions do indeed belong to the language but they are not the result of its natural evolution, Saussure, (1916) 1983: 31 (54).
  14. Eco (1976) 1979: 129.
  15. Greimas and Courtes, (1979) 1982: 259.
  16. "It is becoming necessary today to bring the concepts of natural language [as a pure taxonomy or schema] and of competence together. This rapprochement seems to demand an explicit integration of syntactic structures in the definition of natural language [or in the terms of Saussure: langue, and Hjelmslev: language system/schema]. Ibid: 170.
  17. In a 1960 "Danish stylistics" it is said of "repetition" that it 1) is the primitive expression of powerful emotional agitation, 2) produces a stronger effect if it does not 3) conversely weaken the effect, that it 4) is related to gradation, that it can be 5) lulling in its monotony, or actually 6) platitudinous. The work also contains a syntactically based classification of a number of classical repetitive figures based on the repetition of the same figure (epizeuxis, anaphora, symploce, epanastrophe, antimetabole, polyptoton, as well as "several other types", to which can be added repetitions based on variations of the thus only partially repeated figures. Albeck, 1960: 155-179.
  18. Hjelmslev, (1943) 1966: 101-102. English translation: (1953) 1961: 115. After the above quotation, Hjelmslev introduces a number of largely stylistic examples, but also those features which distinguish various national languages. He responds to the problem by describing these features as connotative features which can be omitted from the elementary description of "everyday language" which are conversely - and rather surprisingly - defined as purely denotative language.
  19. The concept of monoplanar symbol systems is actually imprecise, as this is rather a question of symbol systems where any given expression form always only corresponds to a single, given content form, or several mutual, but clearly distinct forms. It is used here to distinguish this system from other multiplanar symbol systems which operate with variation in the relationship between expression and content form.
  20. The terminological pedantry in this connection is not only due to the difficulty of accepting the concept 'natural' in connection with certain cultural phenomena as opposed to others, but also to the fact that the use of the concept as a designation for language appears to be based on a scientific understanding of rules, in accordance with which the observance of the rule is given by the rule itself. Although this holds true as a condition of formal languages, it is not true of most other cultural phenomena, if any, because the execution of a rule assumes the overcoming of "noise".
  21. Hjelmslev, (1943) 1966: 42-43. This passage - in fact nearly a whole page - has been omitted from the English translation. In Hjelmslev's terminology, a figura can both be a phoneme and a syllable. The phoneme and the grapheme are also described as 'functives', where Hjelmslev differentiates between their occurrence in a process, in which the various letters co-exist in a "both-and" relationship (a function Hjelmslev calls a relation) and their occurrence in a system, in which they enter into an "either-or" relationship with each other (a function Hjelmslev calls a correlation). Ibid. pp. 34-44, English translation: 36-48. These definitions apply at the starting point of the analysis, where an approach is made to a definition of a formal language theory. At the other end - where the formal theory is applied to language - the phoneme is identified with the term a 'taxem', i.e. the possible (virtual) expression inventory.
  22. As Hjelmslev, in continuation of Saussure, defines the sign concept on the basis of semantic distinctiveness, the inner composition of the sign is subordinate. Whether the sign is manifested through one distinctive grapheme, or a root which is manifested in many graphemes, is considered secondary. Behind the terms, non-sign, part sign or figura lies a mixture of figurae and some of the functions the figurae can occupy in the sign's composition.
  23. Henrik Sinding-Larsen, 1988: 97.
  24. Hjelmslev (1943) 1966: 46. English translation (1953) 1961: 50.
  25. "by its favor" is a translation of the Danish "af dens nåde", which has reference to the grace of God.
  26. The amorphous "thoughtmass" is also referred to as "the meaning" or (content) "purport" - residing outside the language system, but totally dependent on it.
  27. See the examples with "børneren" (the kindergarten), "døgneren" (the 24-hour service kiosk), and "fritteren" (the day-care institution) in 7.7 for further explanation.
  28. Hjelmslev (1943) 1966: 36-37. English translation, (1953) 1961: 40.
  29. Chomsky, 1957.
  30. This function is also frequently manifested in the use of "empty places", for example the omission of one part of the nexus relation often used in newspaper headlines: /[ ] Sends suggestion to committee/. /[ ] Died of drink/. /Peter Hansen [ ] court tomorrow/. Here it is left to the reader to encatalyze the missing parts. The reader's capability to do this is considered, in Hjelmslev's theory, as confirmation of the existence of the language system. It is not possible, however, to encatalyze the correct word without take meaning into account, just as the possibility itself of working with "empty places" provides language with a characteristic property. We could perhaps cautiously compare this to the meaning of the number 0, which is different to nothing.
  31. Havelock, 1982: 39-59, 316.
  32. Havelock, 1982: 61, 77.
  33. Hjelmslev (1943) 1966: 16. English translation: (1953) 1961: 16. The term 'text' is used throughout and naturally in Prolegomena, while when referring to the fact that it is the spoken language that is the subject, this appears in more emphatic connections. In the original Danish text, the two reference systems sometimes meet in one and the same sentence, thus towards the end we find: a demand for a sure method of describing a given limited text composed in a previously defined "natural" [spoken] language, has, in the course of our presentation, with logical necessity, had to make way... Hjelmslev (1943) 1966: 110. English translation (1953) 1961: 125. The English translation uses "language" for Hjelmslev's sprog/ dagligsprog/talesprog (language, ordinary or everyday language as well as for spoken language).
  34. Hjelmslev, (1943) 1966: 93. English translation (1953) 1961: 105.
  35. Hjelmslev, (1943) 1966: 72. English translation (1953) 1961: 80.
  36. Havelock, 1982: 55.
  37. Hjelmslev, (1943) 1966: 17. (1953) 1961: 17.
  38. Ricoeur, (1969) 1974: 93-94.
  39. This difference can still be maintained in a modified form even though there are means (recitation, telephone, radio and tape recorder) to repeat and/or transmit speech at a later time and/or another place.
  40. This structural difference becomes very extreme if we also include in writing numerical-algorithmic and mathematical notation, which can only be handled to a limited extent without writing.
  41. Stjernfeldt, 1990, discusses this, taking as his point of departure Douglas Hofstadter's question, what is A and I? Hofstadter, 1985. With support from J. Petitot, Stjernfeldt suggests a topological description of graphemes, as he assumes that the topological categories have ontological status: "The categorical perception of writing and its base in a combinatory of topologies seems to indicate that the reason for categorization of letters is the same as for the categorization of the phenomenal world - thereby suggesting an interface intermediating the two being topology". Stjernfeldt does not explain, however, how topological mathematics - or simply J. Petitot's idea of a mathematically describable categorical perception - deserves such an ontologically privileged position rather than a number of other transcendental form concepts. As the human perception apparatus itself has a history of origin and development it is not easy to see how an invariant topological picture of perceptual structures can be applied. The difficulty is indicated by the use of the concept "combinatory of topologies" because these combinations are not themselves contained in the topological description. But I must admit that as far as I know there is no other satisfactory explanation. However, it can hardly be unreasonable to assume that an explanation must, under any circumstances, operate with indefinite, critical - mental - thresholds for the transition between physical form and symbolic form, pictorial form and grapheme, between graphemes mutually and, as far as notation systems are concerned, indubitably also semantic components, as the distinction of notation systems assumes a significant competence in making symbolic abstractions which can hardly be explained without reference to pre-existing symbolic activity based on less established, "semi"-discrete means of expression.
  42. In formal expressions at least one decision - as a condition - has been made which need not have been made in a linguistic expression, for example that two + two are four, while "two by two" in language can both be four, but also, for example, refer to a procession with an indefinite number of participants who move - two by two, or to phenomena which often occur between two, such as, for example a widespread and well known reproductive procedure where 1 + 1 can both become 2, 3 or 4, or almost overwhelming.