Blurring (speech)

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The vagueness of a linguistic term is used when it is difficult to clearly assign it to a certain lexical or grammatical category . In linguistics, the terms "vagueness" or (also outside of the English-speaking world ) "fuzziness" are generally used for this :

"We speak of the vagueness (syn .: fuzziness, vagueness) of a natural language expression [resp. of a term] if there are no clear conventions for certain areas of application and situations as to whether the term can be used to designate a certain object, fact or process or whether its use is excluded, or if certain potentially relevant aspects of the statement that is formulated by the expression, remain open. "

Then a term is "fuzzy" ("vague" or "fuzzy"),

  • when the scope ( extension ) is imprecise;
  • if there are objects of which it cannot be said with certainty whether they belong to the set of objects that are denoted by this term or have the properties denoted by its predicates (borderline cases of categorization).

In addition, one speaks of “vagueness” (“vagueness” or “fuzziness”) when a term or a predicate describes a phenomenon to which the Sorites paradox applies.

About the term "term"

In linguistics / psycholinguistics and in psychology is meant by a "term" or "concept" (English. Concept a mental grouping individual) entities (objects, situations, events or relations), the common features ( " classification "; cf. . also categorization ). In other words: by means of classification (also: classification) “given objects are identified with regard to certain features and structures and assigned to a certain class or subclass”. Hadumod Bußmann also defines a “term” as “a conceptual concept gained through abstraction [the most varied of experiences], by means of which objects or facts are classified based on certain properties and / or relationships”. A term or concept is "accordingly a cognitive unit that results from the processing of information."

Fuzzy extent (extension) of terms

A term can first be defined by its scope (its extension ), i.e. H. the totality of all objects that have all the characteristics of this concept. In many cases, however, this “totality” cannot be clearly determined. Many terms such as “medium-sized car”, “large”, “blue” or “grossly negligent” are used blurred. For example, a car of a certain type may generally be regarded as a (element of the class) “ compact car ”, while for many observers it is already a “ middle class ” car . Similarly, a baby can be “big” to parents, yet it is small compared to a school child; also, a person can be rather tall for one viewer and rather not tall for another viewer. This is independent of whether the viewer only knows the approximate or exact size of a person.

Communicative conflicts resulting from the use of fuzzy terms - e.g. B. "blue" - are mostly solved by "negotiation" or subsequent (conceptual) clarification or accepted as borderline cases:

A: Das blaue Auto gefällt mir.
B: Welches blaue Auto?
A: Na das da hinten, das dritte von rechts.
B: Das ist doch grün.
A: Na schön, das blaugrüne Auto da würde ich jedenfalls gerne haben, wenn ich es mir leisten könnte.

On the other hand, whether a certain act was “grossly negligent” or not can often only be clarified through judicial negotiations between the public prosecutor, defense counsel and expert.

So it is not the “phenomena” (the car, the baby, a certain action) that are “fuzzy” or “vague”, but their classification by the viewer (as “middle class car”, “blue”, “large” or "Grossly negligent"). To put it bluntly: "Vagueness is not a property of terms, but a wrong interpretation of non-vague phenomena."

Fuzzy definition of terms

The fuzzy scope of a term can also be described as the fuzzy delimitation of this term from other terms. For example, while some objects are clearly perceived or referred to as “ chairs ” or “ armchairs ”, others appear, e.g. B. a rocking or a desk chair, rather than "something in between" a chair and an armchair. The categorization of such an object is not unique ( crisp ) but "fuzzy" or "blurry" ( fuzzy ). In the same way, grammatical categories such as “past”, “completed action” or “reference to the present” are not clearly defined, that is, fuzzy.

The technical term fuzziness originally comes from mathematics or cybernetics ( fuzzy logic ) ( Zadeh 1965). If it is not used synonymously with vagueness , as in the definition at the beginning of this article, it explicitly denotes the “continuous” or “gradual” class affiliation of entities to linguistic terms that can be mathematically recorded. A robin belongs more to the class of "birds" than a penguin, which has many characteristics of a "bird", but does not have the characteristic "can fly", and is still biologically a "bird".

Psychologically, these facts are presented as follows: All phenomena of the world (" objects ") that we perceive, i.e. objects, processes, colors, sounds, etc., are never perceived as objects in themselves , but always as realizations of certain originating from our experience Abstractions that can be described as classes of objects (“categorization”). Thus the meaning of an expression like chair “is not an individual idea; it results from the similarity of the individual ideas as a social phenomenon ... ”. To perceive a concrete object as a “chair” means to recognize it as an element of the class “chairs”. In doing so, questions like the following are answered unconsciously: What properties does the chair have to have in order for it to be recognized as such and accordingly labeled? Which function (s) does it have to fulfill? How level and how horizontal does the seat have to be? How many legs must or may he have and how high must or may they be? The corresponding requirements for a “chair” or a “non-chair” are obviously conventionalized , they correspond to intuitive ideas. We intuitively assign borderline cases either to one or the other category or make this borderline character the topic (“negotiating” meanings as in the above examples of the “blue” car or “gross negligence”).

In any case, native speakers or otherwise competent speakers of a language have much more and much more detailed intuitive knowledge of the vocabulary or the grammar (regularities) of this language than can be determined in a linguistic language description. In these language skills, the life experiences made so far are combined quite unconsciously with the linguistic experiences associated with them (see feeling for language ).

Incidentally, experts in a specific field also meet outside of the usual language , e.g. B. a craftsman or a housewife who follow their (experience-based) intuition in many of their decisions , not always sharp yes-no decisions. Often they decide, like a fuzzy-logical computer program to control a technical device, on the basis of gradual manifestations of certain criteria ( more liquid, a little oil, a handful of flour), so act intuitively and are usually successful.

The Sorites Paradox - The Blurring of the "Heap"

At this point, a special case of “uncertainty” should be mentioned: the Sorites paradox ( paradox of the heap ). It shows up when trying to identify something as a "heap". If you remove z. B. A single grain of sand from a heap of sand still remains a heap; likewise if one removes another grain. Strictly speaking, since there are no termination conditions or no transition point, this means that a single grain of sand also forms a heap. The same applies to a "large" object that is made smaller millimeter by millimeter. The reason for the paradox of the heap is that the shape of a heap is not determined by the number of its elements and, in principle, cannot be determined. On the other hand, our life experience, which also includes the language used by our fellow human beings, tells us that a single grain of sand and five or ten grains of sand do not form a “pile of sand”. However, a gray area begins somewhere within which we can speak of “borderline cases”. In any case, the Sorites paradox cannot be solved logically-definitionally and thus unambiguously.

Linguistic fuzziness in linguistics

There are a number of approaches to explaining and describing linguistic fuzziness. The most influential so far are:

Prototype semantics

The prototype semantics as the theory of word meaning ( lexical semantics ) provides a now generally accepted explanatory approach for certain vagueness phenomena: terms or conceptual categories are not described as meaning spaces with clearly defined boundaries, but as a kind of topological space with a core - e.g. B. the "kitchen chair", which we can see as a prototype of a "chair" - and flowing transitions to a periphery to which z. B. "high chair", "swivel chair" or "rocking chair" belong.

According to György Fuhrmann, a “prototype” is the most representative element of a certain category. A kitchen chair is certainly a highly representative representative of the “chair” category, while a high chair is also a (peripheral) representative of the “chair” category, but not one of the (much smaller) “typical chair” category. In contrast, a “stool” is actually not a chair, but “somehow” it is closer to the chair than z. B. an "elevator". There, on the periphery, for some it may still be an element of the (fuzzy) category “chair”, while others see it already outside this category and thus as an element of another “topological space”. As a borderline case, the “stool” can in any case give rise to discussions about its class. The further, i.e. more dissimilar, an object is to the prototype of the term, the more unclear or controversial is the assignment of this object to the term. “In general, the center of a category appears to us to be firmly established and clear. The borderline cases of categories are not as unambiguous and clear, categories tend to be fuzzy or fuzzy at the edges and overlap with adjacent categories. "

The vagueness of word meanings such as big , immature , cool or young cannot be explained with the help of prototype semantics. On the one hand, formalisms of fuzzy logic can be used for this purpose , while, since the 1990s, contextual factors, i.e. H. the context dependence of terms, uses (see below).

The theory of fuzzy sets

Since the mid-1970s, the approach of fuzzy logic with its concept of “ fuzzy sets ” (also: sets with “fuzzy boundaries”) has been used to explain the “fuzziness” of linguistic terms and rules as well as the intuitive “ feeling for language ” .

In the language of the - greatly simplified - fuzzy set theory , a clearly recognized chair (e.g. a kitchen or dining room chair) has a class of "1" and a in relation to the category (or quantity) "chair" Object that is clearly not a chair (e.g. an elevator), the value "0". "Belonging" ("1") and "Not belonging" ("0") are the categories of classical set theory. The fuzzy set theory, on the other hand, also applies to objects that - such as B. a swivel chair or a rocking chair - are not clearly identifiable as a "chair", a mathematical way of describing it: a swivel chair has a class affiliation of perhaps 0.7 or less in relation to the category "chair". Such a fuzzy set theory does not work according to the so-called bivalence principle , which only knows the values ​​“0” or “1”.

Each element of a fuzzy set or subset A can be assigned a number between 0 and 1 (“in the interval [0,1]”) which represents the degree to which element x belongs to this set. More accurate:

"A fuzzy subset A of a set X is characterized by its membership function μA: X → [0,1], which gives each element x from X a number μ A (x) in the interval [0,1 ], which represents the degree of membership of x in A. "

A small subset of the fuzzy set of "chair" can thus be described as follows:

A (chair) = {(kitchen chair, 1), (dining chair, 1), (swivel chair, 0.7), (rocking chair, 0.5), (...)}.

Adolf Grauel introduces the term “fuzzy relation” for fuzzy relations when connecting two fuzzy sets, i.e. fuzzy relationships between two and more objects, facts, sizes, etc. As an example he cites the "color-ripeness relation", which he uses in the form of a "relationship matrix between color x and ripeness y of a fruit with the possible colors X = {green, yellow, red} and ripeness degrees Y = {immature, semi-ripe, ripe} ”, which he interprets as follows:“ IF a fruit is green, THEN it is unripe. IF a fruit is yellow, THEN it is half-ripe, or IF a fruit is red, THEN it is ripe. ”“ But it should also be formulated that a certain percentage of a green fruit can be regarded as half-ripe, for example with gradual affiliations ", Then the following representation can result:

μ R (green, immature) = 1.0, μ R (green, half-ripe) = 0.5,
μ R (green, ripe) = 0.0, μ R (yellow, immature) = 0.25,
μ R (yellow, half-ripe) = 1.0, μ R (yellow, ripe) = 0.25,
μ R (red, immature) = 0.0, μ R (red, half-ripe) = 0.5, and
μ R (red, ripe) = 1.0.

Terms like “green”, “immature”, “semi-mature” are so-called linguistic variables , according to Hans-Jürgen Zimmermann, essential elements of the theory of fuzzy sets. “Their values ​​are not numbers - as is the case with the usual numerical variables - but words and expressions (terms) of a natural language. Since words are not as precise as numbers, they are represented by fuzzy sets. ”As an example, he cites room temperature, the values ​​of which correspond to a set of terms such as“ cool ”,“ pleasant ”or“ warm ”. These fuzzy terms can also be defined mathematically. In the classical theory, however, this range could only be specified as a sharply delimited interval, e.g. from 19 to 24 degrees Celsius. “Then, for example, a temperature of 18.9 degrees would be classified as not pleasant, which does not correspond to human perception in this form. In our example, 18.9 degrees would be assessed as 'maybe not so pleasant anymore', which means that this value could belong to the vague set of pleasant room temperatures with a level of 0.8. ”As further examples of linguistic (lexical) fuzziness of meanings Zimmermann calls expressions such as “tall man”, “hot day” or “stable currency”. "The meaning of these words results from the context, that is from the person of the speaker and the reference in which the respective expression is used."

Fuzzy function for a person's age

It is similar with the age of people. In years, the age of a certain person may be exactly given; however, whether a thirty-two year old is referred to as “young” or a sixty-four year old as “old” depends on many factors, not least the age of the observer. The age of a “young” or “old” person cannot be clearly defined, terms such as “young” or “old” are fuzzy. These relationships can also be represented graphically as a fuzzy function with values ​​between “0” and “1”. According to the adjacent figure, which can only apply to so-called "standard situations", i.e. regardless of the specific situational and contextual conditions of a concrete situation, a thirty-two year old with a degree of affiliation of slightly below 0.5 falls into the "young" category. , a sixty-four year old with a degree of approximately 0.6 in the “old” category.

Going beyond such descriptions at the word level, Burghard Rieger (1998) generally calls for the development of “fuzzy linguistics”, because the analysis of specific linguistic performance data can only adequately be carried out empirically with the help of fuzzy (performance) modeling, not with the help of traditional, i.e. H. Competence of theoretical sharp categories: “The quantitative description and numerical analysis of linguistic elements, units and structures [with fuzzy categories obtained from performance data] is useful when it comes to determining properties of their use, their use and the associated relationships can be described as (not directly observable) derived functions of their (observable) occurrence. In connection with the fuzzy-theoretical possibilities of modeling [KGK93] [Nov89] these methods allow the definition of elastic units [Zad75] - corresponding to the soft constraints [Smo89b] in sub-symbolic models - linked by numerical specifications and increased resolution of degrees of membership with larger tolerances of categorization and processing [Zad94]. ... Fuzzy categories are called those abstract assignments whose (empty) structures as well as their possible fillings appear as the results of processes that can be represented in the form of procedures. "

Seen in this way, the cognitive interest of “fuzzy linguistics ... is an integrative one that focuses on a theory of performance . However, this is not primarily based on the ability to produce correct sentences, but on the communicative competence of the sensible use of pragmatic-functional, i.e. H. meaningful linguistic utterances. The object of investigation form (verbal / written) certificates of situated verbal communication, and the methods of investigation (all the techniques of blurred fuzzy ) include modeling, including such procedures used by the moderns linguistics , computational linguistics and quantitative linguistics be used. "

This problem of the pragmatic-functional context dependency of expressions / terms / utterances has led to more and more criticism of the explanatory and descriptive approach of the fuzzy set theory since the 1990s. Further considerations of traditional approaches even deny the fuzzy set theory any possible explanation for the phenomenon of linguistic fuzziness and instead focus on the context-dependency of expressions / terms / utterances.

See also


  • Hadumod Bußmann : Lexicon of Linguistics (= Kröner's pocket edition . Volume 452). 2nd, completely revised edition. Kröner, Stuttgart 1990, ISBN 3-520-45202-2 .
  • György Fuhrmann: m-Fuzziness in brain / mind modeling. In: Zétényi, 1988, pp. 155-202.
  • Adolf Grauel: "Fuzzy Tutorial: Fuzzy Logic in Theory and Practice". Online here (accessed March 15, 2017).
  • Hannelore Grimm and Johannes Engelkamp: Speech Psychology. Handbook and Lexicon of Psycholinguistics. Erich Schmidt Verlag, Berlin 1981.
  • Ingemund Gullvag and Arne Naess: Vagueness and ambiguity. In: Marcelo Dascal, Dietfried Gerhardus, Kuno Lorenz and Georg Meggle (eds.): Philosophy of language. Philosophy of Language. La philosophy du langage. An International Handbook of Contemporary Research. Second half volume, Berlin / New York: de Gruyter 1996, pp. 1407–1417.
  • Rosanna Keefe and Peter Smith: Vagueness. A reader. Cambridge: MIT Press, 1999, ISBN 0-262-61145-7 .
  • Geert Keil : "vagueness". In: Markus Schrenk (Hrsg.): Handbuch Metaphysik . JB Metzler, Stuttgart 2017 ( ISBN 978-3-476-05365-7 ), pp. 97-102 (with further references).
  • Theodor Lewandowski: Linguistic Dictionary. 3 vols. Heidelberg, Wiesbaden: Quelle & Meyer, 6th edition 1994.
  • Martina Mangasser-Wahl: Prototype theory in linguistics: application examples, method reflection , perspectives . Tübingen: Stauffenburg 2000, ISBN 3-86057-706-9 .
  • Klaus Mudersbach: “Terms from the point of view of the language user”. In: Rudolf Wille (Hrsg.): Conceptual knowledge processing: basic questions and tasks . BI-Wiss.-Verl .: Mannheim [u. a.], 1994.
  • Ralf Pörings and Ulrich Schmitz (eds.): Language and Linguistics. A cognitively oriented introduction . Tübingen: Narr, 1999 ( ISBN 3-8233-4975-9 ). Online here with a link to download the book (accessed March 15, 2017).
  • Burghard Rieger : "Theory of unsharp sets and empirical text analysis" in: Wolfgang Klein (Ed.): Methods of Text Analysis (= medium literature 3), Heidelberg (Quelle & Meyer) 1977, pp. 84–99. Online here (last accessed July 8, 2017).
  • Burghard Rieger: “Why fuzzy linguistics? Considerations and approaches of a computational linguistic reorientation ”. In: Dieter Krallmann / H. Walter Schmitz (Ed.): Perspektiven einer Kommunikationwissenschaft. Lectures at the International Gerold Ungeheuer Symposium, Essen 1995 . Vol. 1, Münster: Nodus 1998, ISBN 3-89323-651-1 , pp. 153-183. Online here (last accessed on April 15, 2017).
  • Eleanor Rosch and Barbara B. Lloyd (Eds.): Cognition and categorization . Hillsdale, NJ [u. a.]: Erlbaum, 1978, ISBN 0-470-26377-6 .
  • Michael Smithson: "Possibility Theory, Fuzzy Logic, and Psychological Explanation". In: Zétényi, 1988, pp. 1-50.
  • Philipp Stoellger: "vagueness". In: Gert Ueding (Hrsg.): Historical dictionary of rhetoric . Darmstadt: WBG, 1992ff., Vol. 10 (2011), Sp. 1364-1377.
  • Johannes-Peter Timm : "The" fuzziness "of language as the basis for holistic, functional, experience-oriented grammar lessons". In: Johannes-Peter Timm (ed.): Holistic foreign language teaching. Deutscher Studien Verlag, Weinheim 1995, pp. 120–148.
  • Wolfgang Wahlster : "The representation of vague knowledge in natural language systems of artificial intelligence". Online here (accessed March 12, 2017).
  • Timothy Williamson: Vagueness . London: Routledge, 1994.
  • Lotfi Zadeh : “Fuzzy Sets”. Information and Control , 8, 1965, pp. 338-353.
  • Tamás Zétényi (Ed.): Fuzzy sets in psychology . Amsterdam: North-Holland, 1988.
  • Hans-Jürgen Zimmermann : "Principles of Fuzzy Logic". From:, March 1, 1993. Online here (last accessed April 11, 2017).

Further literature available online

  • Geert Keil and Ralf Poscher (project leaders): Research project “Sensible handling of blurred boundaries. Phenomena of vagueness and indefiniteness as a challenge for philosophy and law ”. Online here ; extensive bibliography: online here ; Comprehensive index: online here (all last accessed on December 15, 2018).
  • OTH Regensburg: "Fuzzy Systems". Online here (last accessed on April 3, 2017) (only available to registered users on December 15, 2018).
  • Burghard B. Rieger : “Fuzzy modeling of natural language meaning. On a computational linguistic reorientation of semantics ”(1998). Online here (last accessed on April 3, 2017).
  • Roy Sorensen: Lemma "Vagueness". In: Edward N. Zalta (Ed.): Stanford Encyclopedia of Philosophy . Online here (accessed on April 3, 2017; heavily revised since April 5, 2018).


  1. Wahlster: "The representation of vague knowledge", p. 18.
  2. ^ Lewandowski: Linguistic Dictionary 2. S. 538; sv classification.
  3. Bussmann: Lexicon of Linguistics ..., p. 128.
  4. Grimm and angels Kamp: psychology of language ..., S. 190th
  5. Mudersbach: "Terms ...", p. 117.
  6. As the Wikipedia entries “ Stuhl ” or “ Armchair ” show, the extension of these terms can be quite different in different countries (Germany, Austria, Switzerland).
  7. Timm: "The 'fuzziness' of language ...", p. 123 f.
  8. ^ Lewandowski: Linguistic Dictionary 1 , p. 137; sv "meaning".
  9. Sorites = "heaping up" to sōròs "heap": "Name of Cicero for the aporia going back to Zeno: 'How much does the heap begin with?'" (After: Duden. The large foreign dictionary. Origin and meaning of foreign words . 4., current edition, n.d. [2007], p. 1263.)
  10. Fuhrmann: "m-Fuzziness ...", p. 167 ff.
  11. ^ Pörings and Schmitz: Language and Linguistics ..., p. 19.
  12. Rieger: Theory of fuzzy sets and empirical text analysis. P. 84ff (online)
  13. "Due to the arbitrariness in the choice of this function, the fuzzy set theory is a very subjective method, which is therefore particularly suitable for the representation of human knowledge." (After: Informationsfusion # Fuzzy-Logic , accessed on April 19, 2017) - Such values ​​between “0” and “1”, which can vary from one speaker of German to another, naturally require an empirical check based on a larger sample.
  14. See also uncertainty # logic and language theory
  15. Grauel: "Fuzzy Tutorial ...", p. 14.
  16. Grauel: "Fuzzy Tutorial ...", p. 60.
  17. Grauel: "Fuzzy Tutorial ...", p. 62.
  18. Grauel: "Fuzzy Tutorial ...", p. 63.
  19. a b Zimmermann: "Principles of Fuzzy Logic" (online).
  20. Figure taken from: Example of a non-linear fuzzy function ; accessed on May 6, 2017.
  21. Rieger: “Why Fuzzy Linguistics?”, P. 14.
  22. Rieger: “Why Fuzzy Linguistics?”, P. 24.
  23. Uli Sauerland: Vagueness in Language: The Case Against Fuzzy Logic Revisited. In P. Cintula, C. Fermüller, L. Godo, P. Hájek (Eds.): Understanding Vagueness - Logical, Philosophical, and Linguistic Perspectives. (Studies in Logic 36), College Publications, London 2011, pp. 185–198.
  24. See Fuzzy Logic # Fuzzy Set Theory .