ISSN 01476882, Scientific and Technical Information Processing, 2010, Vol. 37, No. 2, pp. 127–131. © Allerton Press, Inc., 2010. Original Russian Text © F.V. Nersterov, 2010, published in NauchnoTechnicheskaya Informatsiya, Seriya 1, 2010, No. 6, pp. 1–6.
On the Definition of Definition F. V. Nersterov Received March 24, 2010
Abstract—An attempt is undertaken to define the word “definition.” The correlation of concepts, such as definition, term, discourse, and frame is discussed and a systematic definition of the term “definition” is given. Key words: sign, term, mapping, representation, element of the World Universe, concept, image, definition, frame, meaning, information DOI: 10.3103/S0147688210020061
Terminological problems, despite all the discussion about them, continue to exist. Somebody said that the definition of definition is obscure. Let us try to prove the contrary. The simplest definition of the foreign word defini tion is given in [1]. Unfortunately, other dictionaries, including Wikipedia, give very brief or contradictory information about the word definition. According to Glossarii.ru, a definition is a logical way to set the typical and specific attributes of an object that make it possible to distinguish it from other objects. In this case a linguistic expression (a term) can be an object and then a definition is a logical proce dure consisting of attaching an exact meaning to a lin guistic expression (a term) by means of known and already comprehended terms. Unfortunately, in the given definition the differ ence between a word and a term, as well as the defini tion of a word and the definition of a term, is not clear. According to Wikipedia, a definition is a formula that explains the content or sense of something. A sen tence is also included in the definition in which the sense of an expression or a name is elucidated. By def inition we mean the procedure of defining a concept in the form of a logical procedure for setting a term’s sense. Unfortunately, the given definition does not make it clear what is spoken about in this case, a concept or a term. It does not have the distinguishing features of objects under consideration, such as expression, name, concept, term, as well as the sense, content, essence, and meaning of the given objects. It is hardly possible to support the idea from Wikipedia that one should dis tinguish such an action as defining from other similar actions, in particular, from describing (itemizing dis tinguishing external attributes that are helpful in iden tifying an object among others) and characterizing (itemizing proper important attributes) an object, since both are included in the notion of define.
Commonly, the definition of an object (a word) is considered to be either a logical procedure of defini tion (attributing) or as a set of a definiendum (a word to be defined) and a definiens (a defining phrase) that are related by their equivalence. One may state that a word or a phrase (a word or a sign, data below) consisting of linguistic signs, includ ing letters, can be defined by means of other words (expressions). Since words are polysemic, when more than one meaning can correspond to one word, then the words to be definitely defined must have the status of a term. To a first approximation, we will accept that a term is a word included in a terminology (a terminological system) that has only one meaning in the form of a certain expression (unambiguously perceived text). In a terminological system, terms are related and ordered in some way. We accept that terminology is a system of terms concerning people’s activity in some field, within which one can identify not only terms, but also rules set to define them. Terminology is necessary so that people can trans fer knowledge to new generations, communicate at different levels, including international communica tion, and take account of new terms. The latter is of exceptional significance, since the rapid development of science and engineering makes terminology com petitive. Countries using outofdate terminology might fail to maintain their development. Terminolo gies are used by people working with engineering equipment, those who design it, or those who are engaged in research. Terminology is divided into engi neering jargon, proper engineering terminology, and juridical terminology. In the absence of purposeful work on the coordination of the development of termi nology, some countries could fall behind advanced countries where terminology is paid great attention.
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NERSTEROV real element
sign object
mental object
Fig. 1. Triangle of the elements of the World Universe.
sign of a real element
sign of a sign
sign of an image
Fig. 2. Triangle of signs.
sign of real element mapping
sign of mapping of images
sign of sign mapping
Fig. 3. Triangle of signs of mapping.
To correctly solve this problem, one should eluci date what the objects to be defined are. Words only map images of the surrounding reality and the existing world in human consciousness. One can identify the elements of reality (things, phenomena, subjects, pro cesses, etc.) as well as their images in consciousness. The elements themselves also can have meanings. We state that the elements of reality are mapped in human consciousness in the form of objects that are chosen subjectively and are mapped in verbal form. Such objects can be considered as images and/or concepts
mapping the elements of reality. Therefore, we can fix the following hierarchy: elements of reality, their men tal images, and the sign images of these elements of reality, images (concepts), and/or signs, respectively. In addition to the real world, one can distinguish the existing world of signs and the existing mental world. All three worlds can be united as the elements of the World Universe. These elements are also mapped in human consciousness in the form of words. Since any element of the World Universe can be mapped by means of terms, then these objects can be words, thoughts, and/or real elements. In this connec tion a question can be posed: are real elements or mental objects more important? What should be mapped in a professional terminology? Is it changing reality or our theoretical thoughts about it? In our opinion, a terminological system must map all three parts, viz., reality, thoughts about it, and the signs by which it is mapped. It is impossible to ignore language development; e.g., the word SMS cannot be ignored in the Russian language. Some special scien tific words mapping scientific mapping theoretical concepts should be introduced in practice. In a similar way, some engineering words must be introduced in laws and vice versa, engineers cannot avoid juridical terms in their practice. Like the wellknown Frege triangle [2], one can present the triangle of the World Universe in whose angles sign object, mental object (concept), and real element (Fig. 1) words are placed. We distinguish between such objects as functional objects, viz., a con cept and a structural object, or an image. One might not understand what is mapped but have its image. For instance, a child can have an image of God but he does not have an idea of what God is. Each of the elements of the World Universe can be designated by a sign. In this connection we can build the triangle of signs presented in Fig. 2. In its turn, mapping in consciousness includes in a general case both mapping of real elements and signs (terms), as well as mappings that are mapped in the form of corresponding signs. Furthermore, we can build a triangle of mapping signs (Fig. 3) wherein the mapping sign of real elements, the sign of mapping, and the sign of mapping of mapping (an abstract object) are shown. The first two signs are ideal objects. We deal with the definition of words and the defini tion of terms. In this case the definition of words is considered to elucidate a word’s meanings and defini tion of terms consists in attributing one meaning to one term. Since a word can have many meanings one should be able to choose or create just one optimal one. Among these terms there is a group that does not correspond to any real elements. The words of this group name ideal or abstract objects. In contrast to the definition of a term, the defini tion of a word can comprise any object and include any number of meanings. In this case mapping can com
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term
detonation sign
sign meaning discourse
sign value
frame
Fig. 4. Triangle of sole meanings.
Fig. 5. Triangle of sign features.
prise not only ascription but also attribution and/or measurement. The definition of a term is taken to mean an ele ment of terminology in the form of symbolic (logical) construction mapping (ascribing) in sign form of the equivalence relation to an object (image) and its sole meaning. If a word takes the part of an object then it is taken as a term and its sole meaning is mapped by an expression containing generally used words and other terms. The definition of definition is considered as a defi nition wherein the object to be defined is a sign (the sign of a sign, the sign of a real element, and/or a men tal sign). The sole meaning of a term means a meaning that is definitely perceived by most people set in (1) regu lating documents (laws, regulations, and/or interna tional and/or national standards), (2) a scientifically substantiated document, and/or (3) traditions. One should note that texts that are made of signs can have indeterminacy in perception; therefore, we will consider the concept of discourse. According to Tun Van Dijk [3], “Discourse is a communicative event occurring between a speaker and listener (observer, etc.) in communication in certain temporal, spatial, etc. contexts. The communication can be spo ken or written and have both verbal and nonverbal components.” In a general sense, discourse is a written or spoken verbal product of communicative activity. In our opin ion, discourse as the product of communicative activ ity is impossible without its definite understanding by the subjects who are exchanging messages; therefore, discourse is only the meaning of a message (a text) rather than just a message in a context. One more word—frame—is known [4] that can be used to designate a definitely identified unit of a real or existing situation. The frame is taken to mean the sole meaning of a sign mapping the context (surrounding) and a frame itself is considered as discourse as dis course is to a term. Therefore, one can unite term, dis
course, and frame in the triangle of sole meanings (Fig. 4). However, the meaning of a sign (data) is not its only feature. Its value is one more important characteristic of a sign. When a subject receives a sign it does not mean that he understands it, but even if he does it does not mean that the sign will be used for decision making to advance the subject to his goal. If a subject is able to obtain information from the data available and make a substantiated decision the data is considered as perti nent (of significance for the subject). Data that are understood by a subject but that are not used for deci sion making are also called relevant. Therefore, signif icance characterizes not only data but the subject’s goal as well. In addition, sometimes a subject needs data to show that the capability for new data generation is absent in the initial data. Such data is called detona tion data [5]. The detonation sign (data) characterizes not only data but also a subject’s ability (knowledge) to generation it. Here, a subject can generate not only new successful ideas (memes) but also new successful real elements as goods (noves) [6]. In this connection one can build the triangle of sign features consisting of meaning, value, and detonation (Fig. 5) as well as the triangle of data types that consist of relevant, perti nent, and detonation data (Fig. 6). Below, we will take the sign meaning as its proper meaning, its value, and/or its detonation feature. The science of the field of law is a specific sign environment. In the science of law, legitimate (legisla tive) definitions (saying definitely what terms used in laws mean in special defining articles), as well as jurid ical discourse (the definite meaning of articles them selves as word sets) are of significance. However, often defining articles of laws are called “notions and defini tions.” It is natural to pose the question: are there words or concepts that are to be defined in a law? In our opin ion, in legal texts the terms to be used are to be defined. Concepts are considered as mental objects; therefore the mental objects of one real element
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NERSTEROV detonation sign
pertinence
relevance
Fig. 6. Triangle of data types.
and/or existing sign can be as numerous as people. Moreover, a mental object, being ideal, can map an object of thought that is absent both in reality and in the sign form, e.g., such an abstract object as beauty. In laws (written law) terms under usage are to be defined for definite interpretation in specific law situations reflecting particular situations. One should note that some authors believe that for eign words should be used in scientific texts even if their Russian equivalents exist, since they correspond to the scientific style of thinking of the scientific com munity. In our opinion, the usage of foreign words in scientific texts does not work well. This is of interest when a foreign word is interpreted using two different words with a common root. For instance, kompeten tsia and kompetetntnost’ are used in the Russian lan guage, and some authors use just kompetentsia to interpret both meanings, which is also incorrect. If a foreign word is used its actual meaning must be cited immediately. Below we consider the features of terms. Com monly, terms are divided into legitimate, scientific, and general ones, among which community terms are identified. Legitimate terms are affixed in terminolog ical standards of laws and national regulations. Legal terms are obligatory for application and terms of national regulations are recommended. Scientific terms are presented in encyclopedias. General terms are divided into interdisciplinary, disciplinary, and thematic ones. As a rule, terminology is included in dictionaries, reference books, encyclopedias, hypertexts, and some other facilities, including glossaries, thesauri, and descriptive dictionaries (indices). The types of words can be divided into proper words (generally used words), definite words (terms), and retrieval words (descriptors or key words). If a term has one meaning then a set of terms can have several meanings. Therefore, when designing, interpreting, or retrieving texts, indefiniteness arises. To diminish it, descriptors and thesauri are used. The saurus comes from the Greek storehouse or treasury. Commonly, a thesaurus contains a list of descriptors
that can characterize the contents of a document, while stressing words that are recommended for index ation. An information retrieval thesaurus is a dictio nary of a descriptor information retrieval language with fixed paradigmatic relations between lexical units. A thesaurus is characterized by the availability of relations between descriptors that permit one to find relations between descriptor meanings. According to its thematic profile, a thesaurus can cover many fields, one field, or be thematic. Terms can be defined within a text. For example, in some books subject and alphabetic indices are found, as well as glossaries, by means of which the terms met in the book and their definitions are given. A glossary is taken to mean a thematic terminological dictionary that can exist outside a book. Among dictionaries we can mention defining and terminological dictionaries wherein the definitions of words or terms are given, namely, their meanings. In addition, terminological standards exist. Reference books can comprise not only texts but also other forms of information presentation. A definition should contain answers to the follow ing issues: what (who) is it (is it like), what is the dif ference, essential features, and where is it used, as well as its relations, field of mapping, etc.? Many authors support logical rules for definition building; however, their definitions do not satisfy them, which indicates the complexity found in observ ing particular rules. The most widespread mistake is, in our opinion, the use in a definition of words or met aphors by means of which the distinguishing and essential features of (image and/or concept) the map ping that is mapped by a term are described and/or elucidated. A definition should not contain any meta phors, as well, distinguishing and essential features should only be mapped by terms and specific generally used words. In a terminological dictionary often abbreviations are used to reduce the volume of the dictionary due to excluded repetitions. If one accepts that a word is the sign mapping of an object, the repeated part of the log ical construction of the equivalent relation between a term and its meaning designation can be designated as “:”. For example, the definition of the term object is a word by which a subjectively chosen set of objective features of the element of the World Universe is replaced by the following logical construction: “an object: a set of the objective features of the element of the World Universe subjectively chosen by a subject for study purposes.” Note that from this it follows that objects do not exist in the real world and they only exist in activities. In this connection, definition is a symbolic (logi cal) procedure that is generally applied to ascribe the sole meaning to a term by linguistic signs. By means of a term the sole meaning is mapped in sign form (value and detonation ability) of a sign of an
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element of the World Universe (real, sign, and/or mental world). The characteristics (features) of a real element, the proper element, and/or relations between real ele ments in the World Universe can take the part of a real object. The element always belongs to a universe (a finite set of the elements of the World). If an existing object (a sign and/or object of thought) is defined, then the definition ascribes the sole meaning of the features of the given object, the proper object (relation between a minimum of two fea tures), and/or the relationship between mutually related objects, and in necessary cases, the name itself is called a term. The term definition means not only ascribing the sole meaning to a word (a name) but also attributing term status to it; therefore, it should be included in a terminology, i.e., have a relationship to other terms of a given terminology or a terminological system. The definition of a term contains the definition of the distinctive and essential features of an object to be mapped. A term can be defined by describing domain features and/or structural features and explaining the functional characteristics and/or other features of the elements of the World Universe mapped by means of this term. A defining expression can be explicit, indirect, or conditional. An explicit expression can be strongly specifying (A is B). In this case auto reference is possi ble (A is B and B is A), which is inadmissible. There fore, such a form should have the type A is AI. The sec ond directing (mentioning) form is A is B. The third form is the relation that A is taken to mean AI. Axiom atic or recursive (convergent cycle) expressions are considered as indirect expressions. An expression con taining a condition is considered to be a conditional expression. Functional–structural definitions are known. The functional expression (concept) explains: (1) a func tion; (2) what produced it; and (3) the genesis of what is mapped by the term. The structural or domain expression (image) describes the structure or the com position of something mapped by the term. The struc ture of a thing mapped by the term can be hierarchic, network, or cyclic. In addition, an expression can be deductive, induc tive, or systemic. One should distinguish the following systemic features among the features of objects to be defined: temporal, spatial (geometric), and material– substantial. Since any element is a product, the concept that explains it should have three projections, in particular, those explaining the product as a result, production process, and the environment in which production occurs.
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Each term can define either a real element (4 Mor skya St.) or an ideal object (a house as a place to live), or as an abstract object (a house as a limitation in space). Finally, a term can describe a real element as a car rier or subject that is mapped on the carrier and/or a communicant (relations arising with the element in its surrounding). It is believed that a term should be neutral and independent of the context. The impossibility of using negative definitions is a classical requirement for defi nitions. It should be noted that the opinion exists that some terms cannot be defined in principle and should be defined via perception by means of examples of term application (showing something that is included in the term meaning) in the form of ostensive definition. CONCLUSIONS A definition is taken to mean a terminological ele ment in the form of symbolic (logical) construction that maps (attributes) in sign form the equivalence between an object (image) and its sole meaning. If a word takes the part of an object then it is called a term and its sole meaning is mapped by an expression con taining other terms or generally used words. The definition of definition is the definition wherein the object to be defined is a sign (the sign of a sign, the sign of a real element, and/or the sign of an object of thought). A term is taken to mean a sign (a word) having one meaning that is attributed to it by a definitely per ceived text by a set of individuals communicating within the framework of a terminology. A definition is considered as a generally applied symbolic (logical) procedure that is used to ascribe the sole meaning of an image (a sign) in sign form. REFERENCES 1. Vorob’eva, S.V., Filosofskii slovar’ (Philosophical Dic tionary), www.esopedia.ru. 2. Nesterov, A.V., On Semantic, Pragmatic, and Dialectic Triangle, NTI, Ser. 2, no. 5, pp. 9–14, 2009. [Aut. Doc.,(Engl. Transl.), vol. 43, no. 3, p. 132]. 3. Teum Van Dijk, Ideology: A Multidisciplinary Approach, London: Sage, 1998, www. psyberlink.flogis ton.ru/internet/bits/vandijk2.htm. 4. www.dmtsoft.ru/bn/471/as/oneaticleashablon. 5. Nesterov, A.V. and Ilovaiskii, I.V., Detonation as a Fea ture of Book Stock, Nauch. Tech.Bibl., 1992, no. 6, pp. 7–9. 6. Nesterov, A.V., Information Features of Business Medium, NTI, Ser. 2, 1998, no. 2, pp. 5–9.
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