A Reply to Löfgren's Comments on my Proposed "Structural Language"


PO-PESP, Free University of Brussels, Pleinlaan 2, B-1050 Brussels, Belgium


Löfgren's criticisms of the "structural language", based on his "linguistic complementarity", are considered. Though the impossibility of complete description and the "non-detachability" of language are acknowledged, it is argued that a complementaristic conception does not provide a sufficiently clear understanding of the limitations encountered when determining the meaning of a representation. In the structural language, meaning is represented by distinctions, which are determined in a bootstrapping way by the other distinctions to which they are connected. The number of distinctions that can be included in the description is open-ended. That makes it possible to continuously adapt or extend the description, thus overcoming some of the limitations imposed by languages based on combinations of primitive distinctions.

INDERX TERMS: Structural language, linguistic complementarity, bootstrapping, distinctions, open-endedness, meaning, description.


In a Letter to the Editor15, Lars Löfgren analyses and criticizes my proposal in this journal to tackle the conceptual problems of physics by means of a "structural language"5. Löfgren's analysis is based on his "complementaristic conception of language", which he has been developing for many years11, 12, 13, 14. This "linguistic complementarity" expresses a number of fundamental restrictions on the completeness of any language, and, hence, according to Löfgren, also on the "structural language". The fact that the structural language replaces a subject-predicate scheme for modelling by a network of connections appears irrelevant to these limitations, and, hence, Löfgren objects to my claims that the structural language would be able to provide a more complete picture of the quantum mechanical observation process than the one provided by the concept of complementarity. Finally, he wonders whether the structural language is a language at all, since it does not have any explicit requirements of finite and stable representation, necessary to make it a vehicle for communication.

In this letter I will try to respond to Löfgren's quite pertinent remarks. Fundamentally, I agree with the existence of the limitations that he enumerates, and my attempt to design a new type of language were motivated by similar concerns. Yet I hope to show that the structural language does evade part of these restrictions, albeit in a different way than one would expect, and without any pretense of completeness of description.


Let me first try to recapitulate Löfgren's conception of language the way I have understood it. A language in this view is conceived as a description process, representing potentially infinite and dynamic ideas by finite and static strings of symbols, together with an interpretation process, going in the opposite direction, and deriving the meaning or interpretation of the symbolic descriptions. Description can be seen as the construction of an appropriate symbolic representation for a given phenomenon. Interpretation can be seen as either the construction of a corresponding phenomenon on the basis of the plan provided by a symbolic description (e.g. the development of a phenotype on the basis of its genetic description), or as the checking of the appropriateness or truth of the symbolic description by relating it to the phenomenon it is supposed to describe (e.g. the observation process in quantum mechanics).

The principle of the linguistic complementarity11,12,14 implies that no language can completely describe its own interpretation process. In some cases, there exists a metalanguage that can provide the description, but the interpretation processes of the metalanguage itself requires yet another level of description, and, in the best case, this leads to an infinite regress.

As I have previously argued myself7,8, this problem can be clearly illustrated by the quantum mechanical observation process. In order to completely describe the observation process, we need to completely describe the observation apparatus. But in order to describe the apparatus we need a second apparatus that would measure the microscopic state of the first one. That second apparatus on the other hand would still be incompletely described, and that would incite us to introduce a third apparatus to measure the second one, and so on. Since the result of the measurement does not only depend on the state of the system that is to be observed but also on that of the measuring instrument (unlike measurement in classical mechanics), the conclusion is that we will never be able to completely predict that result. This leads to the well-known indeterminacy of quantum mechanics.

Bohr1 has tried to capture this difficulty by introducing the concept of complementarity: since no single observation can give us complete information about a quantum system, we need to take into account different observation set-ups (e.g. one for measuring the velocity and one for measuring the position of a particle), if we want to completely characterize the phenomenon. However, those set-ups and, hence, the corresponding observation results and descriptions, are incompatible. It is this feature of descriptions being mutually exclusive, yet jointly necessary, which Bohr calls "complementarity".

In my paper, I have criticized this approach as obscuring what is really happening at the physical level. In practice, the philosophy of Bohr's "Copenhagen school", has led to a superficial pragmatism among physicists: let's not worry about the fact that we do not really understand quantum phenomena, since anyway it is in principle impossible to get a complete description. I want to argue that there is a difference between "understanding" and "completely describing" a phenomenon. Bohr's philosophy is an attempt to reach understanding, but the meaning of complementarity as a concrete term remains quite vague and ambiguous. Heisenberg's indeterminacy principle, expressed as an inequality on the product of measurement uncertainties, is much more precise, but it has the disadvantage that it limits itself to specific physical variables (e.g. position and momentum), and, hence, cannot be generalized to other domains. Löfgren's concept of the linguistic complementarity is an attempt to generalize Bohr's concept to other domains, while attempting to make it more precise. Yet it still lacks the formal clarity and concrete illustrations characterizing a well-established theory.


Let me elaborate on why I think that complementaristic approaches are in a number of respects more obscuring than elucidating. The basic idea of complementarity is that you start with two (or sometimes more) distinct parts or aspects of the phenomenon you want to understand. In the case of Bohr, this might be a "wave-like" and a "particle-like" description of a quantum system. In the case of Löfgren, it would be an interpretation and a description as fundamental characteristics of a language. Then you come to the conclusion that the sharp distinction, or mutual exclusion that seems to hold between the two aspects of the phenomenon does not really hold, since both aspects are jointly necessary to characterize the phenomenon, and you cannot have the one without the other. In Löfgren's terms15: "The linguistic complementarity [...] refers to language as an ultimate whole, and its nonfragmentability within itself into parts, descriptions and interpretations [...]." In other words, you start with distinguishing or "fragmenting" the whole into parts (descriptions and interpretations) and then you come to the conclusion that the whole cannot be fragmented.

This can be interpreted as some deep mystical truth, expressing fundamental limitations on our understanding of Nature or Mind. Such an interpretation tends to lead to an attitude of intellectual laziness: let's stop analysing what is happening, since it is in principle impossible to model it.

My interpretation would be different: if you start by distinguishing separate parts, and it turns out that those parts cannot be separated, then there is something wrong with the way you make distinctions. One might eliminate the problem by either making different distinctions, or by acknowledging that distinctions are in general not objective or invariant, and by trying to understand the mechanism by which they vary. I have argued6,8 that most conceptual problems and paradoxes associated with "non-classical" models (quantum mechanics, relativity theory, thermodynamics, ...) are artefacts of our implicit assumption that distinctions are invariant or, what I have called "conserved". In real life, distinctions are very seldom conserved. Insistence on modelling non-distinction-conserving phenomena by classical (distinction-conserving) representations necessarily leads to strange, "complementaristic" situations, where you have both a multiplicity of different, mutually exclusive representations, and the certainty that you all need them in order to represent the same phenomenon. The problem of "incompatible" representations of a quantum system is well-known. Let me therefore propose an example from another domain.

A fundamental characteristic of relativity theory is that temporal distinctions loose part of their invariance: an event that is in the future for one observer, may be in the present, or even in the past for another observer who is travelling with a different speed. This can be modelled by two different classical representations, or reference frames, with different time axes, where the projection of the event on the one axis gives a positive time coordinate, while its projection on the other axis gives a negative time coordinate. Now, one might try to solve the problem by postulating the "complementarity of past and future" or the "complementaristic conception of time", and argue that time is not fragmentable into future and past. The solution proposed by relativity theory is more precise, though. First, it is noted that both representations (and all other, equivalent ones) can be transformed one into the other by Lorentz transformations. Second, it turns out that the only structure that is invariant under all Lorentz transformations is the light cone. Third, the light cone is used to define a new conception of time, where time is a partial order rather than an absolute, or linear, one. Though the distinction between past and future is variable, the distinction between events inside, on, or outside the light cone is invariant, and that makes it possible to construct a perfectly precise and unambiguous theory of space-time processes (which I have partially reconstructed in the structural language5).

In this particular instance, Löfgren would probably remark that the "past-future complementarity" is transcendable, i.e. that there exists a metalanguage (the light cone model, or space-time language) which can fully describe the interrelations of the "fragments", but that we cannot expect such a metalanguage to exist in general. My opinion is that it is always possible to have a metalanguage describe "complementary" distinctions, but that that metalanguage must be able to describe the "dynamics of distinctions"3,4,6,8, that is to say the processes through which distinctions change with the passage of time, or with the shift from one observer to another one.


Löfgren also states that if a metalanguage exists, it is itself subject to the linguistic complementarity, and hence cannot describe its own interpretation process. In order to better understand what that means, we will have to analyse what is meant by interpretation.

Instead of speaking about descriptions and their interpretations, I prefer to reformulate everything in terms of distinctions. A description, according to Löfgren, consist of a string of symbols. A description or symbol, say D, represents a class C of phenomena that are distinguished from all other phenomena that do not belong to that class. The interpretation process is that process which decides for a given phenomenon whether it belongs to the class or not (or the process which generates an instance of that class). The class C can be seen as the interpretation or meaning of description D. However, remark that both D and C are distinctions: the symbol D too is a class of phenomena which is distinguished from all symbols, or phenomena in general, that are not recognized as "D". Many utterances spoken by different people, or graphical patterns printed on paper in different sizes or styles, will all be recognized as the symbol "D". Both description and interpretation are processes that connect one class or distinction to another class or distinction. It is this connection or reference relation that determines the "meaning" of a symbol or its associated distinction.

In natural language that meaning is not fixed or invariant: it depends on the context, which may include the sentences spoken before or after the linguistic element in question, background knowledge the reader or hearer is supposed to have, the setting or situation in which the element was uttered, and so on. For example, the words "it" or "he" may be interpreted in the most diverse ways. If the previous sentence was "The dog attacked me", we might gather that "it" refers to "the dog"; if a colleague just left the room, we might assume that "he" refers to that colleague. In such cases there is no objective procedure to determine what precisely is meant, and the same word will correspond to different classes of phenomena in different situations. Expressed differently, the distinction represented by the description is not invariant.

In scientific modelling we wish to make our descriptions as precise and unequivocal as possible, and therefore we try to avoid context-dependent meanings, by defining linguistic elements formally or operationally. A definition is an attempt to explicitly formulate the distinction represented by a symbol. A formal definition expresses the distinction as a combination of other symbols and the distinctions they represent. An operational definition expresses the distinction in terms of operations or procedures that are to be carried out in order to distinguish a phenomenon belonging to the class. In either case, the characterization of a distinction relies on other distinctions, whether they are symbolic (like in formal definitions) or procedural (like in the operational case). For example, you might define the symbol "2" as a combination of two other symbols: "1 + 1". Or you might define the class represented by the description "has a weight of 1 kilogram" by the procedure "Put the phenomenon on a balance. If the meter stabilizes at the value 1, then the phenomenon belongs to the class. Otherwise, it does not." Such definitions are meant to make the distinction objective or invariant, so that different people in different contexts would come to the same conclusions as to whether a phenomenon belongs to the class that is described or not.

However, a distinction can only be defined in terms of other distinctions, and for it to be invariant, those other distinctions also need to be invariant. In the two examples above, we assume that the symbols "1" and "+" have the same meaning for all observers, and that they all use balances that are calibrated in the same way. But in order to ensure that the latter distinctions are invariant, we again need to define them as invariant combinations of further invariant distinctions. For example, the balances might be calibrated on the weight of 1 litre of water at a temperature of 4 degrees Celsius, but that demands a definition of the distinction "1 litre" and "1 degree Celsius". "1 Litre" could be defined as a volume of 1000 cubic centimetres, but that demands a definition of "centimetre", and so on. This leads to an infinite regression, since no distinction can be taken as a priori invariant.

The conclusion is that it is never possible to give absolute or complete definitions. The quantum observation process that we discussed is a good illustration of this difficulty: determining a distinction by measurement requires that one distinguishes the state of the measurement set-up, but that requires additional distinctions, and so on. We now have come to the point where we have discovered limitations similar to those expressed by Bohr's or Löfgren's complementarity principles. The process of invariantly determining or "fixing" a distinction is infinite, and, hence, cannot be completely described.

The situation would be different if distinctions were always conserved, as classical mechanics assumes6,8. In that case it would suffice to postulate one set of primitive distinctions, say elementary particles and their basic properties of position and momentum, and all other distinctions could then be derived from those primitive elements and their combinations in an invariant, "distinction-conserving" way, through a mapping or correspondence. In a process conception of language or reality, on the other hand, no such invariant correspondences can be assumed, since distinctions are continuously being built-up or destroyed.


The motivation of my attempt to define a structural language was to go beyond the statement of a limitation principle, and try to analyse the phenomenon at the most profound level. The essence of the structural language is the idea that distinctions are determined in a bootstrapping way: in order to determine distinction A, you need to determine distinction B, which requires the determination of C, etc., which again requires the determination of distinction A. For example, in a dictionary, you might find word A defined in terms of word B, whereas word B would be defined in terms of A. Distinctions always depend on other distinctions, and there are no primitive distinctions. This means also that there are no a priori privileged classes of distinctions, such as "descriptions" or "interpretations". The "meaning" of any given distinctions arise solely from the other distinctions it is connected with.

In the structural language elementary distinctions are called "arrows", and each arrow is determined by its set of input arrows and its set of output arrows. From a certain point of view, the input set of an arrow A might be seen as its extension (that is to say the set of phenomena that imply A), and its output set as its intension (the set of phenomena that are true if A is the case)10. The movement from input to A might be seen as a "description" of the input set, the movement from A to its output might be seen as an "interpretation" of A. However, the terms "input set" and "output set" have a much more general meaning than these purely "linguistic" processes.

Determining the "meaning" of A occurs in first instance by exploring its input and output set. This may lead to the identification of A with another arrow B if both have the same input or output sets (this means that they cannot be distinguished5,10). However, the elements of input and output sets are themselves distinguished only by their connections with further arrows, and so a further exploration of A's meaning will also involve these "neighbours of neighbours", and further "neighbours of neighbours of neighbours". The process does not have an end. Yet in practice we are not interested in completely determining A's meaning: it suffices that we can situate A with respect to a smaller or larger "context" or "neighbourhood" of related distinctions.

The descriptions of the structural language do not have the pretension of being complete, as Löfgren seems to have understood15. In the sentences from my paper he quotes, I merely mention "satisfactory" or "holistic" descriptions, not "complete" ones. The structural language only tries to avoid all a priori restrictions, by providing an open-ended representation scheme. No description can ever be complete, but the idea of the structural language is to make it infinitely extendible. Every extension is supposed to add a little bit to our understanding, and in practice we will stop when we are satisfied with the level of precision we have reached. The continuous extension of a structural description is not like chasing a rainbow, which, however far we move into its direction, always remains at the same distance. Each addition does improve our understanding, and though we know we will never reach complete understanding, at least we are not frustrated by finite restrictions, of the type "until here, but not beyond".

Such restrictions do arise in traditional languages (which I have called "subject-predicate" languages), because they start from primitive elements (words) with a given meaning (distinction). Though we might be able to generate an infinity of descriptions from a finite number of elements, we can never produce distinctions that cannot somehow be reduced to static combinations of the distinctions determined by the elements. In a language that only contains words for describing positions and instants you might define volumes, velocities or durations, but you would not be able to express colors or weights.

In natural languages that difficulty is circumvented by setting up a context: the person to whom you want to convey a new distinction that cannot be expressed as a combination of already known distinctions is made to undergo a certain process, by reminding him or her of previous experiences or by showing concrete phenomena, and then that experience is labeled with a new symbol. It is assumed that the person will be able to generalize from that experience and thus will associate the symbol with the right class of phenomena. The ambiguity or context-dependence of natural language makes it possible to refer to phenomena ("that" or "it") for which no label exists as yet.

This is not possible in traditional scientific languages, since the elements of these languages are supposed to have fixed meanings independent of any particular context. The novel phenomenon can only be incorporated by changing the language, introducing new words and rules. The aim of the structural language is to synthesize the advantages of both natural and scientific languages, by expressing "reference to the context" in a formal way, by means of the so-called "bootstrapping axiom". The way this is achieved is by moving to a metalevel: the axioms and definitions of the structural language do not determine the meaning of any particular elements (arrows) of the language; they merely characterize the processes by which arrows get their meaning (distinction) through their connections with other arrows, and that is a potentially infinite process.

In order to make your description more complete you do not have to add another metalevel, for describing the interpretation processes of the structural language. The structural language is supposed to be able to describe distinctions and their dynamics in general. Hence, it should also be able to describe its own distinctions and distinction-making. Although that is not implemented yet in the description I have proposed5, the structural language is expected to become its own metalanguage3. Self-application of metasystems is a technique that is being applied in computer science to generate more powerful compiling programs2. Although Löfgren correctly argues that no self-reference can ever be complete13, the process of self-application can make a system more complete.

That is another illustration of the properties of bootstrapping and open-endedness that characterize the structural language's approach towards the inherent incompleteness of any representation. Instead of halting at the border of what can be expressed by the combination of elements with fixed meanings, and noting that the only way to transcend the limitation - if one exists - is by a discontinuous jump to a different language or metalanguage, the structural language proposes a way to continuously expand the domain of distinctions that can be expressed, remaining basically within the same language scheme.

A basic assumption is that any distinction, however novel or unexpected, must always be observable in one way or the other. That implies that there exists a continuous process which connects the new distinction with some distinction that is already known or understood, e.g. the read-out of an observation apparatus. That process can then be represented in the structural language as a network of connected arrows.

As an illustration, let us look once again at quantum observation. As shown by the paradoxes of Schrödinger's cat and Wigner's friend, a basic difficulty in understanding the observation process is determining at what point it finally stops: when the measuring apparatus clicks, when the researcher looks at the read-out, when he tells his friend what the read-out was, when the friend tells him what the read-out means, ..., ? The conclusion seems to be that either there is an infinite regress of observers observing observers, or that there must be some unanalysable terminating point, when the observation reaches the consciousness of the observer. In the structural conception, on the other hand, an observation process is merely an unlimited sequence of connected distinctions: the distinction between the observed system having a particular property or not is transferred to the distinction between the observing apparatus being in a certain state or not, and that is transferred to a distinction in the eye, and then the optical nerve and the brain of the observer. The distinction between two neural patterns in the brain of the observer may lead to a distinction in the way the observer will behave, and so on.

The only thing that is strange about this process from a classical viewpoint is that these distinctions are not completely conserved: there is some loss and gain involved, so that effectively new distinctions are developed along the way. This can be understood by the fact that the process is not linear, but branching or network-like: different distinctions (represented by arrows) come together (are added), then other distinctions go apart again (are subtracted). For example, the distinction made by the observation apparatus does not only depend on the state of the phenomenon being observed, but also on the (unknown) state of the apparatus itself. This means that the same state of the phenomenon may lead to distinct observation results (distinction creation), or that distinct states of the phenomenon may lead to the same observation result (distinction destruction)4,6,7,8.

If you want to understand the observation process you must model all these intermediate stages, and see how distinctions determine new distinctions. The "meaning" of the observation is something that is continuously being built up during the process and the interactions between different distinctions. It does not have any specific spatial or temporal location or boundaries. The structural language is designed to explore that on-going development of meaning, not to describe the ultimate or complete meaning of what has happened.


The answer to the above question, raised by Löfgren15, depends obviously on how the concept of "language" is defined. Löfgren prefers to call the structural language a "modelling scheme" and that is a term I cannot disagree with. But what is the difference between a language and a modelling scheme?

Löfgren15 is worried by the fact that no finite representability is required for the structural language, a property which is needed in order to use the language for communication. What I wanted to express was that the "open-endedness" of the language does not imply either finite or infinite cardinality. The cardinality of a structural description is rather variable or indefinite, and can be expanded without limit. Of course, every practical description at a certain moment in time will be finite, but we might imagine a computer program that is continuously generating or expanding structural descriptions, and will continue to do so until the end of time.

It is partly in that sense that I have called the descriptions in the language "dynamic". The other sense, as Löfgren rightly notes, is more of a confusion between the description itself (an "arrow", which is represented as a static symbol) and what the description describes (a process). The "arrows", when drawn on a piece of paper, or represented by conventional symbols, are obviously not dynamic. On the other hand, an arrow might stand for a pointer or link in a computer representation (e.g. a semantic network or a hypertext)9,10, and in that case the traversing of the link can be called dynamic. The "dynamicity" of structural descriptions is in that sense rather potential than actual.

Löfgren15 is further concerned with the requirement that a description must be independent of time for as long as it is under interpretation or further analysis. Otherwise it might change before its intended meaning is interpreted. In the first interpretation of the word "dynamic" (the continuous extensibility of descriptions), the structural language does not obey that requirement. I do not see this is as a grave problem, as long as a history of the changes is kept, so that it always possible to reconstruct the changes that the description has gone through. In practice, in everyday spoken communication, descriptions and interpretations do change while the message is being transmitted, if only because the utterance of a description changes the context to which the utterance refers. This is dangerous because it can lead to misunderstandings. However, when both parties agree about the procedure according to which the change takes place, all misunderstanding can be avoided. Again, we see that the structural language tackles the difficulty on a metalevel, by describing the process through which distinctions arise, rather than trying to represent any given, fixed distinctions. The description of the process itself, however, is independent of time, and that makes it possible to consider structural descriptions as being sufficiently invariant and objective to allow communication.

Löfgren15 also concludes that I do not believe in the "non-detachability" of language, on the basis of his (mistaken) assumption that I believe in the possibility of complete descriptions. But on the contrary, the structural language is especially designed for being "non-detachable", since it explicitly proposes to model the processes of interpretation and description which connect the language with the phenomena it attempts to describe. The physical implementation of a language can happen in many ways: a description can be carried by characters or diagrams on a page, by spoken utterances, by computer programs residing in RAM or ROM, by electronic circuits, or even by complete observation set-ups. The farther we move away from conventional written or spoken symbols, the more fuzzy the distinction between "language" and "non-linguistic phenomena" becomes. Is a machine designed to produce or register the occurrence of certain phenomena a description of those phenomena? Is a natural process that produces, or reacts to, certain phenomena a description of those phenomena?

The structural language consists of a set of procedures for designing or analysing distinction producing processes, that can be implemented in the most diverse media. The philosophy behind it is that there is no strict distinction between the "symbolic" descriptions and the "physical" phenomena being described. The only criterion I accept to call something a "description" (or "model" or "representation") is that it would allow some form of control or anticipation of the system being described8. But in that case about everything can become a description of something else, and the separation or "detachment" between language and reality becomes very relative. Indeed, A might describe B in this generalized sense, whereas B at the same time might describe A, and, therefore, indirectly describe itself. Traditional formal languages will quickly get hopelessly confused when trying to deal with situations like that, because they make a strict separation between object level (interpretation) and metalevel (description), as requested by Russell's theory of types. The structural language, through its bootstrapping architecture, was designed to overcome these restrictions.

Whether it will succeed in that remains to be proven. At present, it offers, in addition to a process philosophy of modelling, not much more than a few rules and procedures for making distinctions, with some applications in reconstructing the fundamental distinctions of physics (space-time, causality, the light cone, particles). Though this particular domain of application appears rather esoteric, the basic thrust is practical: to design a tool for representing, structuring and reorganizing knowledge (models, representations) about arbitrary complex problem domains. The most promising way to implement the tool is in the form of a computer support system, based on hypertext and semantic networks9,10. That system would support one or several users in their interaction with each other and with the computer in order to expand and ameliorate problem representations. Much work still remains to be done in that field.

Concerning the answer to the above question: in view of the many issues that still remain to be solved, and of the decidedly unusual architecture of the structural language, I should perhaps better switch to a more humble formulation. Taking over Pask's term16, I might rather call it a protolanguage.


The philosophy behind the structural language does assume the inherent limitations of any modelling scheme implying that no description can ever be complete, and that a description can never be completely detached from the thing it describes. But rather than trying to capture those limitations by formulating a complementarity between separate aspects which cannot be separated, it proposes an open-ended, infinitely extensible framework, overcoming the restrictions of traditional languages which assume that all distinctions can be reduced to invariant combinations of primitive distinctions. Bootstrapping allows the formal specification of a distinction system in which no distinctions are primitive, and where the context-dependence of expressions can be represented explicitly. That makes the framework inherently dynamic and adaptive, without any apparent constraints. Though no finite description in the structural language can be exhaustive, there are no phenomena that in principle evade description. Such a foundation should make it possible to get a much more profound and detailed understanding of typically paradoxical or "complementaristic" phenomena, characterized by non-conservation of distinctions, such as the quantum observation process, however, without pretense of offering completeness in the sense of perfect determination or prediction.


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