Linguistic encyclopedic dictionary. Application in linguistics of logical and mathematical methods

The mathematical description of the language is based on the presentation of the language as a mechanism ascending to the well-known Swiss linguist for the beginning of the twentieth century Ferdinand de Sosurura.

The initial link of his concept is the theory of language as a system designed from three parts (actually language - langue, speech - parole., and speech activity - langage), in which each word (member of the system) is considered not in itself, but in connection with other members. As the other prominent linguist, Dane Louis Yelmslev, noted, Sosurur, "The first demanded a structural approach to the language, that is, the scientific description of the language by registering relations between units."

Understanding the language as a hierarchical structure, Sosurur first put the problem of value, the significance of language units. Separate phenomena and events (let's say, the history of the origin of individual Indo-European words) should be studied not by themselves, but in the system in which they are correlated with the same components.

The structural unit of the language of the Sosurur considered the word, "sign" in which the sound and meaning was connected. None of these elements exists without each other: therefore the native speaker is understood by various shades of the meaning of the meaningful word as separate element In the structural whole, in the language.

Thus, in the theory of F. de Sosurira, we can see the interaction of linguistics, on the one hand, with sociology and social psychology (it should be noted that at the same time the phenomenology of Husserl is developing, psychoanalysis of Freud, the theory of relativity Einstein, experiments on the shape and content in literature, music and visual art), on the other hand, with mathematics (the concept of systemics corresponds to the algebraic concept of the language). Such a concept has changed the concept of language interpretation as such: the phenomena began to be interpreted against the causes of their occurrence, but relative to the present and the future. Interpretation has ceased to be independent of human intentions (despite the fact that intentions can be impersonal, "unconscious" in the Freudian understanding of this word).

The functioning of the same language mechanism is manifested through the speech activity of the native speakers. The result of the speech is the so-called "right texts" - the sequence of speech units, subject to certain patterns, many of which allow a mathematical description. The study of the methods of the mathematical description of the correct texts (first of all, proposals) is engaged in the theory of how to describe the syntactic structure. In such a structure, the linguistic analogies are defined not by the help of the qualities initially inherent, but with the help of systemic ("structural") relations.

In the West, sacking ideas are developing the younger contemporaries of the Great Swiss Linguist: in Denmark - already mentioned by me L. Yelmslev, who gave the beginning of the algebraic language of the language in its work "Basics of Linguistic theory", in the USA - E. Sepir, L. Bloomfield, Ts. Harris, In the Czech Republic - the Russian scientist-emigrant N. Trubetskaya.

Statistical laws in learning a language began to do no one else, as the founder of Georgian Georg Mendel. Only in 1968 philologists found that, it turns out that in recent years of life, he was passionate about the study of linguistic phenomena with the help of mathematics methods. This method of Mendel will be brought to linguistics from biology; In the nineties of the nineteenth century, only the most bold linguists and biologists declared the feasibility of such an analysis. In the archive of the monastery of St. Tomasa in Brno, whose abbot was Mendel, were found leaflets with the names of the surnames ending with "Mann", "Bauer", "Mayer", and with some fractions and calculations. In an effort to detect formal laws of the origin of family names, Mendel produces complex calculations in which the number of vowels and consonants takes german language, the total number of words in question, the number of surnames, etc.

In our country, structural linguistics began to develop around at the same time as in the West - at the turn of the XIX-XX centuries. Simultaneously with F. de Sosyur, the concept of language as the system was developed in their works by Professor of Kazan University F.F. Fortunate and I.A. Boduen de Courtae. The latter for a long time corresponded to de Sosyur, respectively, the Geneva and Kazan schools of the Linguistics collaborated with each other. If the sausier can be called the ideologue of "accurate" methods in linguistics, then Boduen de Courta laid the practical foundations of their application. He first separated linguistics (as accurate Science using statistical methods and functional dependence) from philology (generality of humanitarian disciplines that study spiritual culture through language and speech). The scientist himself believed that "Linguistics may benefit in the near future, only free from the mandatory union with the philology and history of literature." The "test polygon" for the introduction of mathematical methods in linguistics has become phonology - sounds as "atoms" of the language system, which have a limited number of easily measurable properties, were the most convenient material for formal, strict description methods. Phonology denies the existence of the sound, so that the studies eliminated the "human" factor. In this sense, the phonam is similar to physical or biological objects.

Phone, as the smallest language elements, acceptable to perception, are a separate sphere, a separate "phenomenological reality". For example, in english language The sound "T" can be pronounced in different ways, but in all cases a person who owns English will perceive it as "t". The main thing is that the foundation will perform its main one - a senseless - function. Moreover, the differences between the languages \u200b\u200bare as follows that the varieties of one sound in one language can correspond to different phonemes in the other; For example, "L" and "P" in English are different, while in other languages \u200b\u200bthese are varieties of one phoneme (like English "T", spoken with or without). Extensive vocabulary Any natural language is a set of combinations a much smaller number of background. In English, for example, for pronouncing and writing about a million words, it is used only 40 phonemes.

Language sounds are a systemically organized set of features. In the 1920s -1930, followed by Sosyur, Jacobson and N.S. Trubetskaya allocated "distinctive features" to the phone. These features are based on the structure of speech organs - language, teeth, voice ligaments. For example, in English, the difference between "T" and "D" lies in the presence or absence of "voice" (voltage of voice ligaments) and in the level of voting, which distinguishes one background from another. Thus, the phonology can be considered an example of the overall language rule described by Sosyur: "There is only differences in the language." More importantly, not even this: the difference usually implies the exact conditions between which it is located; But in the language there are only differences without precise conditions. Whether we consider the "designation" or "denoted" - in the language there are neither concepts or sounds that would exist before the language system developed.

Thus, in Sosuraovsky linguistics, the phenomenon is understood as a set of comparisons and opposition to language. The language is the expression of the meaning of words, and the means of communication, and these two functions never coincide. We can notice alternation of form and content: Language contrasts define its structural units, and these units interact to create a certain meaningful content. Since the elements of the language random, neither the contrast nor the combination may be the basis. So, in the language, distinctive features form a phonetic contrast at another level of understanding, the phonemes are connected in morphemes, morphemes - in words, words - in suggestions, etc. In any case, a whole phoneme, word, proposal, etc. It is more than just the sum of the components.

Sosurur suggested the idea of \u200b\u200bthe new science of the twentieth century, separately from linguistics learning the role of signs in society. Sosurur called this science with semiology (from the Greek "SEMEION" - a sign). "Science" Semiotics, developed in Eastern Europe in 1920-1930 and in Paris in the 1950s - 1960, expanded the study of the language and linguistic structures to literary finds, drawn up (or formulated) with these structures. In addition, at the sunset of his career, parallel to the Council of General Linguistics, Sosuryur took up a "semiotic" analysis of late Roman poetry, trying to open intentionally compiled anagram names of their own. This method was largely opposite to rationalism in his linguistic analysis: he was an attempt to study the problem of "probabilities" in the system. Such a study helps to focus on the "real side" of the probability; The "keyword", whose anagram is looking for Sosuryur, according to Jean Starobinsky, "The poet's instrument, and not the source of the lifetime of the poem." The poem is used to swap the sounds of a key word. According to Stornobinsky, in this analysis, "Sosurur does not deepen the hidden meanings." On the contrary, in his works noticeably the desire to avoid issues related to consciousness: "Since poetry is expressed not only in words, but also that these words give rise to, it comes out from under the control of consciousness and depends only on the laws of the language" (CM . Attachment 1).

Susori's attempt to explore the names of their own in late Roman poetry emphasizes one of the components of its linguistic analysis - an arbitrary nature of signs, as well as the formal essence of Sosurah linguistics, which eliminates the possibility of analyzing the meaning. Todorov concludes that in our days, the work of the sausage looks on rarity consistent in reluctance to study the symbols of the phenomenon that have a clearly defined value [Appendix 1]. Exploring the anagram, the sausure only pays attention to the repetition, but not the previous options. . . . Studying "Song of Nibelunga", it defines characters only to assign them to erroneous reading: if they are unintentional, characters do not exist. In the end, in his writings in general linguistics, he makes an assumption about the existence of semiology describing not only linguistic signs; But this assumption is limited to the fact that seven-chickens can only describe random, arbitrary signs.

Once this is true, then only because I could not imagine "intention" without an object; He could not fully overcome the abyss between the form and content - it turned into a question in his works. Instead, he applied to the "linguistic law". Being between, on the one hand, the concepts of the nineteenth century, based on history and subjective guesses, and methods of accidental interpretation based on these concepts, and, on the other hand, structural concepts, eating confrontation between form and content (subject and object), meaning and origin in structuralism, psychoanalysis and even quantum mechanics - the works of Ferdinand de Sosurira in linguistics and semiotics denote a turning point in the study of meanings in language and culture.

Russian scientists have been presented at the First International Congress of Linguists in the Hague in 1928. S. Kartsevsky, R. Jacobson and N. Trubetskoy delivered a report in which was considered hierarchical structure Language - in the spirit of the most modern for the beginning of the last century of presentations. Jacobson in his writings developed the ideas of Sosury that the basic elements of the tongue should be studied, first of all, in connection with their functions, and not with the causes of their occurrence.

Unfortunately, after the arrival in 1924, the domestic linguistics, like many other sciences, throws back to power. Many talented scientists were forced to emigrate, were sent from the country or died in camps. Only from the mid-1950s, some theories pluralism became possible - about this in section 1.2.

There is no doubt that the use of mathematical and logical methods ("accurate methods" linguistics) was largely stimulated by the tasks of applied linguistics. If attempts are made to the application of these methods to solve problems directly related to the theoretical linguistics area, for example, to distinguish between language and speech phenomena *, then in perspective (although, maybe not always clear and close) were in mind still applied linguistics. By the way, this means that the assessment of the results of this kind of operations should be carried out with the obligatory taking into account the objectives of applied linguistics.

* (See: G. Nerdan, Language As Choice and Chance, Groningen, 1956.)

The success of using these methods in perfectly new region From a general point of view, it is largely due to the answer to the question, to what extent is the identification of a logically correct language with natural language, or, in another wording, is it possible to reduce the second to the first *. The answer to this question is usually given in practical form - by constructing statistical, theoretical information, theoretical, theoreticals of the co-multiple, theoretical and other mathematical models of the language, not always, however, focusing on specific tasks **. When building this kind of models, their authors often proceed from that assumption (apparent from their point of view) that any application of a formal logical or mathematical apparatus to linguistic description and research automatically contributes to improving them. On this occasion, Warren said well in his review of works on mathematical linguistics: "If we consider language models as abstract systems of discrete elements, you can use various mathematical concepts and methods, ranging from the elementary idea of \u200b\u200bthe number and ending with complex" logical, statistical and Theoretical and multiple operations. However, the idea that all attracting numbers and mathematical operations to describe such elements systems makes approval more "accurate" or more "scientific" is absolutely erroneous. First of all, it is necessary to show that the new system obtained in this way is a more satisfactory model "than the original system - either in the fact that it makes it possible to formulate simpler and more general theoretical statements about some aspects of the simulated area, or because The operations on the model shed light to the results of the corresponding operations in the simulated area. One of the main hazards associated with the construction of mathematical models of the language, especially quantitative, is that the inseparable use of the mathematical apparatus inevitably leads to meaningless and disorienting results. It is necessary to understand therefore that the premise of enrichment of linguistics with the help of mathematics is not only knowledge of the respective regions of mathematics, but also, in addition, a deep understanding of the essence linguistic problemsMathematical methods "*** should be sent to the permission of which.

* (Cf. Curney's comment: "The fact that there is a close connection between mathematics and logic, on the one hand, and the language - on the other, it became obvious for a long time ago, and now this fact turned out to be in the spotlight in a stricter miserable ..." ( N.V. Curry, Some Logical Aspects of Grammatical Structure, in the materials of the Symposium "Structure of Language and Its Mathematical Aspects", Providence, 1961, p. 57).)

** (A very timely in this regard is a remark of P. Garvin (made by him in the book. W. Vahar-Hillel, Language and Information: Selected Essays on Their Theory and Application, London, 1964): "Most of the work on information processing theory and applications For its purposes, computing machines are completely naive and, undoubtedly, it is not so useful as it would be desirable. " Referring to the negative position of the Bar Hillel relative to the effectiveness of logical and mathematical methods for automatic processing of speech information, P. Garvin believes that it still contains positive elements, since this position "will force at least some scientists treat less seriously to their theories" (Magazine "American Documentation", New York, "Vol. 16, N 2, 1965, p. 127).)

*** (W. PLATH, Mathematical Linguistics. In the book: "Trends in European and American Linguistics 1930-1960", Antwerp, 1961, PP. 22-2E.)

In order for, if possible, to avoid the danger specified by Warren, it is necessary not only to have purely empirical attempts to answer the question formulated above, but also to strive for its general theoretical understanding. In fact, the question of the redundancy of the natural language to one or another logical and mathematical model or interpretation is the main question of the theory of applied linguistics, the need to create which is still felt. When considering this issue, the nature of those phenomena, which make up the subject of study, on the one hand, logic and mathematics, and on the other, the natural language, and then the possibilities of those methods that each of these sciences works are also. Already from the comparative study of these moments it will be possible to make some common conclusions that may be unscrewed for all those who need to conduct their research on the intersection of listed sciences.

A symposium "Language structure and its mathematical aspects" serves to a certain extent of this goal, conducted by American mathematical society *. But all of them, as it appears from the very names of the symposium, affect only individual and in some cases there are very private aspects of the problems you are interested in. Although in their totality, they create enough argued prerequisites for the response to the question we distinguish themselves, but they still do not have a clear and unambiguous formulation of the necessary conclusions. In many ways, the Symposium participants continue to the line of empirical attempts to resolve the issue, by no means intrusive offering their experiments to the attention of linguists in the hope that they themselves will understand how their own hypothesis and solutions will be suitable for their purposes.

* ("STRUCTURE OF LANGUAGE AND ITS MATHEMATICAL ASPECTS". Proc. Of the Soc. Of Appl. Math., 12. Providence, 1961.)

More appropriate, therefore, as a starting point to understand the results of the work of linguists, logic and mathematicians in the plan we lose two articles placed in the collection "Natural Language and Computing Machine" *: M. Maeron "Point of view The logic for the processing of linguistic data" and . Garvin and V. Karasha "Linguistics, processing of linguistic data and mathematics". They outlines the working capabilities of logic and mathematics, their attitude to empirical sciences, ways to solve problems, etc. We turn to the consideration of problems raised by these articles from the point of view of the question that was formulated above.

* ("Natural Language and The Computer", ED. BV P. Garvin, New York, 1963.)

2

It would seem that we already have an absolutely unequivocal answer to our question. So, for example, N. D. Andreev and Ji. R. Zender write: "The mathematical representation (model) of languages \u200b\u200bis not identical to the very language" *. They followed the author of the book "Language Model" I. I. Revzin, which indicates that as a result of modeling, only "more or less close approximation of the data of a specific reality may be **. However, to say so - it means nothing to say anything, as it remains undisclosed why this is how it is necessary to still turn to the method of mathematical and logical modeling, and if so, in what limits and for what purpose.

* (H. D. Andreev, L. P. Zinder, the main problems of applied linguistics, "issues of linguistics"., 1959, No. 4, p. 18.)

** (I. I. Revzin, Language models, M., 1962, p. 8. By the way, the expression "close approximation" is a straight tautology: close approach.)

To resolve all these issues, it is initially established as an initial point, to which sciences - inductive or deductive - include linguistics, logic and mathematics. As for the last two sciences, their position is clear - they are undoubtedly belonging to the deductive sciences based on their research technique for conclusion. Linguistics are traditionally defined as empirical science, and this suggests that its main scientific goal is to describe the facts. This means, apparently, linguistics should be attributed to the field of inductive sciences. This also means that, seeking to use the formal apparatus of logic and mathematics in linguistics, try to apply deductive research methods in inductive science.

However, in recent years, the inductive nature of the science of language - linguistics has become indirectly or directly doubt. In the sharpest form it made L. Yelmslev. True, the terminology used by them is very shot and, in particular, is characterized by a peculiar and very personal understanding of the terms "deduction" and "induction" (in fact it interprets them completely inversely). However, the foundations of its linguistic theory outlined by them leave no doubt about its methodological essence. So he considers allowable use Any source operating definitions, which is characteristic of deductive sciences. And he himself in the following expressions characterizes his theory: "1. The theory in our sense by itself is independent of experience. By itself, it does not speak anything about the possibility of its application, no about the attitude to experienced data. It does not include the existence postulate . It represents what was called a purely deductive system in the sense that it can be used to calculate the possibilities arising from its prerequisites. 2. On the other hand, the theory includes a number of prerequisites that from previous experience know that They satisfy the conditions of application to some experienced data. These prerequisites are the most common and may therefore satisfy the conditions of application to a large number of experimental data "*.

* ( "Save to the theory of language". Sat "New in linguistics", vol. 1, M., 1960, p. 274-275.)

According to this statement, L. Yelmslev seeks to conduct an idea about the dual methodological nature of linguistic research objects, with a predominant focus on their deductive signs. He should attribute that pretty ambiguous way ("on the one hand ... But on the other hand ..."), which generally became characteristic of considering this issue (and which makes it possible to turn into any of the parties). The idea of \u200b\u200bthe methodical duality of linguistics has recently received wide walking and even served theoretical basis To formulate the principles and the most recent time for its occurrence of the direction in the science of language - Linguistics of universal (universalism). The "Memorandum relative to Linguistic Universals" speaks about this: "The study of linguistic universal leads to a whole series of empirical generalizations on language behavior - both still requiring experiment and already established. These generalizations are potential material to build a deductive structure of scientific laws. However Some and, perhaps, most of them are still posted only by the status of empirical generalizations, which, with the current state of our knowledge, it is not possible to relate with generalizations or deductively to derive more general significance from laws "*. With no less definiteness, J. Greenberg is expressed in his preface to the collection dedicated to linguistic universals. Pauluming with the famous words of L. Bloomford that "the only legitimate generalizations relative to the language are inductive generalizations," he writes: "Nevertheless, it seems to be considered to be generally accepted that the scientific method should be not only inductive, but also deductive. Formulation The generalizations obtained by inductive research leads to theoretical hypotheses, on the basis of which further generalizations can be derived by deuction. These latter must then be subjected to empirical check "**.

* ( "Memorandum Concerning Language Universals", "Universals of Language", ED. By J. Greenberg, Cambridge, Mass., 1963, p. 262-263.)

** ("Universals of Language", p. IX.)

The fact that the history of linguistics consists not only from the accumulation of the facts of the language and their classification, but also from the change of points of view to the language itself, which inevitably implies the difference in approaches to language facts and even different theoretical interpretation, forced some Soviet linguists to also come to Conclusions on the methodological duality of their science. S. K. Shaumyan prefers, however, on the method of hypothetical and deductive and as follows its features: "The hypothetical and deductive method is a cyclic procedure that begins with facts and ends with facts. In this procedure, four phases differ in this procedure:

1. fixing the facts requiring explanation;
2. nomination hypotheses to explain these facts;
3. predictions from the hypotheses of predictions on the facts lying outside the circle of facts, for the explanation of which hypothesis were put forward;
4. verification of facts that are predicted by hypotheses and determination of the probability of hypotheses.

The hypothetic and deductive method is fundamentally different from the inductive method used in such areas of knowledge, such as the descriptive botany or zoology. , for example, J. Greenberg talks about the combination of inductive and deductive methods, then S. K. Shaumyan refers to his hypothetical-deductive method: the designation is clearly inconsistent for the method that begins with the facts and ends with the facts.

* (S. K. Shaumyan, the problems of theoretical phonology, M., 1962, p. 18-19. Regarding the hypothetical and deductive method, see also Article V. S. Shrörerev "Some issues of the logical and methodological analysis of the relationship of theoretical and empirical levels of scientific knowledge" in the Sat. "Problems of logic of scientific knowledge" (M., 1964), p. 66-75 (3rd section of the article).)

The question of where the linguistics should be attributed, I. I. Rezzin is given. "By the very nature, he answers this question, - Languages \u200b\u200bshould first use inductive methods, it describes specific speech acts of specific languages \u200b\u200b...

On the other hand, the presence of an infinite multitude of speech acts studied by the linguist, hardly makes it possible to formulate the basic concepts of the science of language by generalizing induction.

It follows that linguists need not only inductive, but also in deductive research methods in order to obtain a system of general knowledge that help comprehend those data that is mined when analyzing specific languages \u200b\u200b...

In its deductive part, the lingopology, apparently, can be built as logic or mathematics are built, namely: some minimal amount Primary, non-defined terms, and all other terms are determined through primary. At the same time, some primary statements about the relationship of these terms among themselves (axioms) should be clearly formulated, and all other statements should be proved, that is, to come down to some other allegations "*.

* (I. I. Revzin, Language Models, M., 1962, p. 7-8.)

Here, the deduction method embodied in logic and mathematics is just as a means of ordering "a set of speech acts" for the creation of the system common concepts". In direct contradiction with this task, it is, however, the presentation of the deductive method recommended for use in the linguistics. It is completely intended from the acts and on the facts and for the initial moment of building a system of common linguistic concepts takes a set of non-defined and apparently , absolutely conditional primary terms, through which all subsequent terms are determined.

This contradiction is not by chance, it lies in the very nature of our sciences. It would seem that the conclusion that when studying linguistic objects, a combination of inductive and deductive methods is permissible, opens the doors for use in linguistics of logical and mathematical methods, and the specific implementation of this output is the creation of numerous formal-logical and mathematical models of the language. But, as it will be clear from further, such a simplified approach cannot give satisfactory results. It can be agreed that in a linguistic study, it is permissible and even it is necessary to combine the deductive and inductive techniques. In the end, as V. Krödal wrote, "the induction is nothing but disguised deduction, and for clean connections established between the observed phenomena, is completely inevitably assumed to be reality, a specific object of this science" *. But this does not mean that in linguistics should be unconditionally and mechanically transfer the formal apparatus of logic and mathematics without any accounting of the "specific object of this science." As the same I. I. Rezzin, "the evidence obtained by a deductive way, the evidence obtained by a deductive way, whenever they were imperative from a logical point of view, are not yet talking about the properties of the real language described by the model" **. And it recommends considerable to practice the effectiveness of models, which represents the machine translation and "other practical linguistics missions".

* (B. Breed, structural linguistics. Cited by book: V. A. 3Wegins, history of the XIX and XX centuries. In essays and extractions, h. II, M., 1965, p. 95.)

** ( I. I. Revzin, Language Models, M., 1962, p. 10.)

And the practice of applied linguistics testifies that the use of mathematical and logical methods in the study of language phenomena is superimposed by very strict limitations.

3

The logic gives an example of the most consistent use of the deductive method. Mathematics follows the logic in this regard, and therefore they can be considered jointly.

Of course, logic, and mathematics regarding their methods and interpretation of the goals are not homogeneous systems. For example, as applied to logic, we can talk about the logic of dialectical, formal, mathematical, and, in a narrower sense, about the subject, semantic, phenomenological, transcendental, or constructive, combinatorial, multivalued, modal, etc., if necessary, however, Assimate from all such units and speak only about the most common features inherent in logic and mathematics in general, and mainly about those that with the greatest discrimination demonstrate the deductive nature of these science methods.

Becoming to this position, we, therefore, will not refer to inductive logic. We only note that the conclusions in inductive logic are not determined by the prerequisites - thereby they are not tautologic. Conclusions in inductive logic are directly dependent on facts, and these latter are determined by the volume of our knowledge - thus, they are installed on a probabilistic basis. The probability is the main methodological instrument of inductive logic.

Detergent logic is most fully represented formal and mathematical logic that have a lot of common. Deaductive logic is a science that studies human thinking or thought acts from their structure or form, distracted by their specific content. Thus, deductive logic seeks to formulate laws and principles whose compliance is a prerequisite for achieving true results in the process of obtaining output knowledge. The main methodological instrument of deductive logic is implication. She gets output without directly appeal to experience or to practice, through only the application of logic laws. In the process of deduction, the prerequisite determines the conclusion: if the prerequisite is true, then the output must be true. Thus, the conclusion is already in the background, and the purpose of the deduction is to make an obvious thing that in the hidden state is concluded already in the background. It follows that any deduction obtained by deduction is tautologically, that is, logically is empty, although with other points of view, for example, in cases of applying a formal logical apparatus for the purposes of other sciences, it may be a new, unexpected and original.

A similar position occurs in mathematics - the validity of the arguments in it completely rests on the deduction. At the same time, in mathematics, as a rule, any initial point of view is acceptable, any approach to solving the problem - if only they satisfy the conditions of mathematical deduction. Mathematics has a rich set of this kind of "initial points of view" and "approaches", which researcher alternatively can use to solve its task. Mathematical issues are often translated into different equivalent forms, and each of them involves the use of various regions of mathematical theory in order to solve the problem. Thus, the mathematician has the actual unlimited freedom of selection of prerequisites - he chooses those of them that, from his point of view, make in themselves the most promising opportunities for the simplest, non-bank, elegant solution of the problem. His talent and experience manifest themselves in the successful choice of prerequisites, those "Suppose that ..." or "if ... then," mathematical works are fought. As in logic, mathematical prerequisites - axioms or postulates - determine the definitions of not yet certain units.

Freedom of choice of prerequisites in mathematics is directly depending on the fact that it operates intangible units, or objects, its attention is paid to relations between them. Mathematical objects serve as symbols expressing the structure of pure relationships. The mathematical system can thus be considered as a set of formal relations that exist only by virtue of the statement of these relations. Of course, in particular, in the applied purposes of the relationship of relations may seek to embody correspondence with external reality, but this does not affect the establishment of relationships themselves - rather, on the contrary. Mathematics examine not the "truth" of their axioms, although they require mutual consistency between them. The study inside the mathematical system is a study and establishment of links that allow us to prove that the fact of the theory A involves the fact of the theory of V. Consequently, the main issue in mathematics is not "What is and in?", But "assumes whether a (or whether) in ? ".

A completely different position in linguistics. It is mainly focused on the first of these issues, and this does not give her the opportunity to break away from reality; It, therefore, operates not abstract, but concrete units, although it seeks in some cases to create abstragated objects, such as the concept of a phonam or morpheme. This provision is characteristic not only for traditional linguistics, but equally, and the newest areas that united under the banner of structuralism. A number of statements have already been brought above, which, trying to use in science of language not only inductive, but also deductive methods (or mathematical and logical methods), could still have to circumvent the need to appeal to a real linguistic fact. In addition, it is possible to bring another one that makes a complete clarity in the question under review: "Linguistic analysis - writes in this connection P. Garvin, - mostly inductive process in the sense that he seeks to establish a list of elements or set of stations, based on Of the linguistic incentives of informants or from the study of text. It is based on the assumption that in both these sources of information it will be possible to recognize regularly encountered elements of various types and orders of complexity. Classification of these types and the statement of their distribution conditions obtained as a result of the analysis form an inductive description. Language "*.

* (P. Garvin, A Study of Inductive Method in Syntax, "Word", Vol. 18 (1962), p. 107,)

In linguistics, of course, you can also use the method of prerequisites, based on which private objects, facts or units are determined. But here we are confronted with two features that make substantial adjustments to the use of this method. In contrast to logic and mathematics in this case, the "truth" obtained by this method of definitions will be distinguished, that is, their compliance with the data of experience. Thus, the interdependence of the background and output knowledge is established: the premise determines the output (definition of a private linguistic object in the terms of the background), but if the output does not correspond to the experimental data, then the need for the rendering of the background itself. But this kind of prohibitory adjustments have nothing to do with that transfer to equivalent forms, which was indicated above, admissible in mathematics, as they are due to non-formal considerations, but data of experience. All of the above gives the ground to conclude that the concept of the prerequisite and freedom of its choice is in a linguistic analysis specificity with which it is impossible not to be considered when used in the linguistics of the deductive method.

Linguists can not use such a freedom by "if" or "permissible" as mathematics. Freedom of the premises of them are very strictly limited. The history of the science of language knows a lot of shifts of "points of view", or, in other words, the initial prerequisites, which were suggested by the discovery of new facts, the spread of general scientific ideas into linguistics or even the formation of original theories. But for a linguist in all such cases, the change of "if", or the source background, is the change of all scientific consideration. Therefore, Linguist says not "if", but he postulates his understanding of the prerequisite, that is, in fact, an understanding of the subject of its research, and, based on this understanding, gives the definition of private units of the language, checking the "truth" of these definitions of the experience. The last circumstance, by virtue of the interdependence of the prerequisite and withdrawal in linguistics, serves as a means of checking and the legitimacy of the prerequisite itself, standing at the beginning of the deductive form of a linguistic analysis. So, if we refer to specific examples, in the past, the language was interpreted as a natural organism (at the Schleiher), as individual psycho-physiological activity (in youngsters), etc. Research practice based on these concepts showed their insufficiency. Now the initial prerequisite for linguistic analysis is the postulate that the language is the system of signs *. It is subject to the same testing of experience and practice, like any other concept in the science of language.

* (See: Paul Garvin, The Definitional Model of Language. In the book: "Natural Language and The Computer", ED. By P. L. Garvin, New York, 1964.)

These preliminary and most general considerations show that deductive methods are not at all contraindicated by linguistics, but their use requires compliance with specific conditions. It is these specific conditions that impose certain restrictions on the mechanical transfer of methods of logic and mathematics to the linguistics area. However, if we confine ourselves to such a general statement, much will remain still unclear. That is why it is necessary to deepen our question and to reinforce potential conclusions to refer to the practice of applied linguistics, where the legality of the prerequisites and compliance with experimental data made on the basis of them are manifested.

4

The relationship between language and logic is very peculiar. Representatives of empirical sciences, which also include linguistics, study one or another subject or a phenomenon to describe or explain it. The results they obtained are formulated in the language, which is called the language-object. The logic wields evidence, conclusions, judgments, etc., but they are only available to him only in linguistic form. Thus, it turns out that the logic on one stage is further from real Mirathan representatives of empirical sciences. Its analysis is directed not directly to the real object studied by empirical sciences, but in their language *. In other words, he explores the language and formulates the results obtained in the language, which is called the methane language.

* ("The logical analysis of scientific knowledge - P. V. Tavanets and V. S. Shrosrev write in this regard, - there are primarily an analysis of the language in which this knowledge is expressed." See the article "Logic Scientific Cognition" in Sat. "Problems of logic of scientific knowledge", M., 1964, p. 161)

From a logical point of view, the main unit of the language is not a sign and an object not denoted by it, but a proposal, since only a logical process can unfold. That is why only the proposal may be true or false. And the words themselves cannot have these qualities. But before we can establish whether the proposal is true or not, we need to state that it matters.

The concepts of truth and values \u200b\u200bbelong to the field of semantics. Through these relationships, the truth or falsity of the sentence is determined: if the proposal describes objects correctly, it is true, and if incorrectly - no. But language expressions can enter into relations other than those that exist between the objects denoted. In addition, proposals can enter into relations with other offers. The task of logic is to find out the nature of the relationship between language expressions and suggestions and set the rules to determine whether the procedure prescribed in this case is maintained or not. When solving the last question, logic does not refer to the objects described by the proposal. It is interested in a linguistic form, and not its content, which, of course, does not interfere with its meaningful interpretation, resulting in a formalized language. A formalized language can be represented as an abstract system, such as predicate calculus.

So, logic can, depending on the tasks of the study, work at two levels - syntax (logical syntax) and semantic (logical semantics). Consider first the application of the first of these levels to the natural language.

If the logic occupied by learning the language forms and existing relations between them can remain within the syntax level, operating non-meaningful terms, then the linguist cannot do this. All levels of the natural language (except may be, phondatic) are meaningful and therefore outside the semantics are unthinkable. And moreover, the natural language does not exist outside the pragmatics, which cannot be easily derived from it because of the simple reason that in the speech act it is constantly transplanted into semantics. Therefore, the natural language is always an interpretation, and moreover a two-speed, since it is also connected with semantics and pragmatics *. And this interpretation does not succumb to no formalization.

* (Cf. Niles Bohr's comments about the mathematical language, where "the necessary definitions needed for an objective description is achieved when using mathematical symbols, it is due to the fact that this method is avoided by references to a conscious subject, which permeated daily language" (Nile Bor, Nuclear Physics and Human Cognition, M. , 1961, p. 96).)

We now turn to the second level when an interpretation is attributed to the second level when calculating through semantic rules. And in this case, we will get an education, in no way comparable to the natural language. True, here we are dealing with meaningful terms, but in a logical and natural language, they build their attitude towards "truth" in completely different foundations. As A. Tarsky writes, "True", "in any case, in his classical interpretation," is one to the extent that it "coincides with the reality" *. But this criterion "truth" is actually applicable only to natural languages, always-oriented on reality. This is different in logical semantics. Semantic analysis relies only on the logical interpretation of the system and implies the establishment of certain rules formulating the conditions of truth. He prescribes a consequence of these rules, not answering the question to what extent is the "coincidence with reality". In addition, the focal point for reality is carried out in a natural language not directly, but through a person that again makes it necessary to appeal to the third level - pragmatic. "The transition to the semantic level," P. V. Tavanan and V. S. Svrosrev, notifice, is in itself a return to a living language in its concreteness, as it may seem at first glance, due to the fact that the sense function of the language seems to The creature of the language, as "direct validity of thought". In fact, the original scheme of the semantics "language - reality" does not give another specific image of the language as the immediate reality of thought for the simple reason that the language is associated with the reality itself is not a certain mystical way, but Through a person, through his actions, his behavior. Therefore, in fact, a specific understanding of the language as a carrier of thought can be achieved only at the level of its pragmatic analysis according to the scheme "Language - actions of a person with a language and based on language" **.

* (A. Tarski, Grundlegung Der Wissenschaftlichen Semantik. "ACTES DU CONGRES INTERNATIONAL DE PHILOSOPHIE SCIENTIQUE", 1936.)

* (See the article "Logic Scientific Cognition" in Sat. "Problems of the logic of scientific knowledge" (M., 1964, p. 16).)

But that's not all. Touching the question under consideration, V. M. Glushkov writes: "A living human language can be considered as a formal language only after a strict rule system is formulated, allowing to distinguish expressions that are permissible in the language, from all other expressions, that is, meaningful sentences from meaningless sentences "*. Explaining the difficulties arising from the formalization of a natural language, it further indicates that "no fixed formalized language can be adequate to the living human language, since the latter unlike the first is continuously developing and improved. Therefore, any formalization of any living human language is only more or more or more or more. The less successful instant cast, losing the similarity with the original as the latter develops "**. If everything had come down only to this, then it would be more Polbie. In the applied linguistics, it is intersects from the moments of the development of the language, seek to consider it as a completely stable system and still fail to achieve the formalization of a natural language. It happens on a very simple reason. The formal system and natural language base their effectiveness on the polar opposite qualities. Any formal system is always identical to itself. It is this quality that makes it possible to fulfill its functions in all specific cases of its applications. And the natural language is in terms of its content, its semantics or, as in these cases it is customary to speak, in its informative plan - is never identical to himself. It is this ability that makes it possible to function in all specific cases of its application. Remaining the same language he in different situations Always other. At the same time, it does not have any explicit or formative rules, nor the rules of "truth" nor transformational rules to determine which of the potential values \u200b\u200bor shades of the values \u200b\u200bwill receive this word in a particular situation. Moreover, almost any word of the natural language can get a value that is not recorded by any language - it may occur, to gain a language in the language, but with the same success, like a runaway, flashed, get lost in linguistic "space" and go out. And with all these qualities, the natural language turns out to be an amazingly perfect tool that allows you to achieve complete understanding of the most complex concepts, and in any situations. Why does this happen?

* (V. M. Glushkov, Thinking and Cybernetics, "Issues of Philosophy", 1963, No. 1, p. 37-38.)

** ( V. M .. Glushkov, Thinking and Cybernetics, "Philosophy Questions", 1963, No. 1, p. 38.)

Apparently, the answer to this question is partially as follows in one thought of the founder of semiotics Ch. Pierce, which he persistently repeats in many of his works. It can be interpreted so. In modern linguistics, the language is customary to determine as a system of signs. This is the source background for the entire linguistic analysis. If so, then the language is not just a system of signs, but a system of mutually interpreting each other's signs that exist in the language in the Language, because they are interpreted in other signs. C. Pierce Formulates this as follows: "No sign can function as a sign, if it is not interpreted in another sign. Therefore, for the sign absolutely essential so that it affects another sign" *. And elsewhere: "All the purpose of the sign is that it will be interpreted in another sign" **. And perhaps, the most important thing: "The sign is not a sign, unless he translates himself into another sign in which he gets more complete development" ***.

* (Ch. Peirce, Collected Papers, Cambridge, Mass., Vol. eight, §. 225.)

** (TAM F E, §. 191.)

*** (Ch. Peirce, Collected Papers, Cambridge, Mass., Vol. 5, § 594.)

Consequently, the natural language is a system of signs that, through mutual interpretation, are able to respond to all the needs of a person in the meaningful expression. But here you need one substantial reservation. After all, all the needs of this kind are caused by the attitude of a person to the phenomena of the external world and the public environment in which his life takes place. By virtue of this circumstance, the transformational semantics, if it was possible to create, cannot be based only on the rules for the mutual interpretation of signs, to wear a closed and final nature. It turns out to be derived from a very large number of values, in every fat formalization *.

* ( P. Jacobson in this connection states: "We can build a purely linguistic semantics if we take the pier's position that the essential feature of each language sign is that it can be translated by another language sign, more detailed, more explicit or, opposite , more elliptical sign of the same or other language system. It is thanks to this translastivity that the semantic invariants that we are looking for in meaning are revealed. Thus, we get the opportunity to solve the semantic problems of the language also with the help of distributional analysis "(performance on the 1st international Symposium "Sign in the Language System", Erfurt, GDR, 1959). Cited by the book: V. A. 3Wegins, history of the Linguistics of the XIX - XX centuries in essays and extractions, part 2, M., 1965, p. 398.

In connection with this, it is important to consider the features of the procedure for solving problems and the very concept of determination in logic and mathematics, on the one hand, and in linguistics - on the other.

Before in mathematics, proceed to solving the problem, it must be formulated in exact terms - this formulation itself is a prerequisite for a successful solution to the problem. At the same time, as already mentioned, the mathematician can freely transform this formulation of the problem into an equivalent option - mathematics has for this and the corresponding means. Already at this primary stage of the research technique, linguistics differ significantly from mathematics. When formulating its problems, the linguist has a certain number of observed empirical data, which it can not always give an accurate wording, but that nevertheless, he must be the basis of his research, already in the process of this study itself. In order not to go far behind examples, it is possible to refer to a linguistic value that makes the basis of all work in the field of automatic processing of speech information, but at the same time it is determined very foggy and dissolve. It is this circumstance that makes researchers in this area constantly change their strategy.

But the study has begun and achieved some decision. What does this mean in relation to logic and mathematics and in relation to linguistics? The logic, as mentioned above, makes it possible to explicitly present the conclusions implicitly present in the premise, but it does not have the rules, the use of which can ensure that the desired decision will be mined, since it is not a means of achieving new conclusions, but only a technique Definitions of their correctness. She is not a magical key to all secrets. It is clear that if logic had similar rules, then there would be no unresolved problems. It would be enough to attach a certain set of logical rules, and we would automatically receive a ready-made answer to any question that torments us. In the light of the said specific importance acquires the concept of determination of the problem or task.

In logic and in mathematics, every end result is recognized as true if there was no formal rule in the process of evidence. Since it is possible to different ways of evidence, the existence of various solutions is permissible. But they can all be subject to verification in terms of logic or mathematics requirements. This is different in linguistics. It does not have an apparatus with which you can check or prove the correctness of the conclusions. Accordingly, the truth of the achieved solutions is determined with this - it is established not by formal rules, but by its compliance with the data of experience. Under these conditions, it would be theoretically to expect a single final solution. However, practically, as evidenced by the controversial linguistic definitions of even the main categories of the language, it does not have the place. The well-known subjectivism of estimates in this case is always present, and it is determined to a certain extent determined by the volume of facts (and, of course, their character), which are at the disposal of the researcher. It follows that the "truth" of solutions in linguistics is always given in some approximation and has a non-determinant character, but probabilistic.

Under these conditions, it is very important that the correctness of linguistic definitions and interpretations will be inspected on the basis of objective criteria. The possibility of such an inspection gives a wide area of \u200b\u200bapplied linguistics, where the machine is opposed to the machine representing the interests of logic and mathematics in this opposition.

5

To solve the practical tasks of applied linguistics, a digital computing machine is used. It is able to perceive, store, transmit, regroup and issue information. It interprets and performs a set of commands (command program), as well as modiculates them during the task execution. It is able to solve very complex problems, but the entire process of transition from the task to the solution must be exhaustively and consistently described in terms of the sequence of basic elementary operations. Information is entered into the machine using a double-digit (binary) code, or language. The machine operates with the words corresponding to the basic logical links or the functions of calculating statements or predicates in this way. The machine can solve complex mathematical tasks precisely due to the fact that complex mathematical operations are possible to reduce the sequence of arithmetic operations, and these latter, in turn, to logical operations. Consequently, the digital computing machine can be viewed as a logical machine.

Thus, whatever complexity is the task, the machine solves it with the help of a sequence of elementary operations, the program of which should be formulated absolutely unequivocally (consistently), for sure, in detail and comprehensively fully. In other words, it should not go beyond the limits that are set by the logical calculus of statements, and when we wonder whether the car can cope with the processing of information concluded in natural languages, we first need to find out to what extent the logical calculation of statements is Adequate model for natural language.

Considering the specifics of the digital computing machine described above, the first thing to be done so that the machine "understand" task and began processing speech information in accordance with this task is to reformulate the information contained in the natural language, to a logical language. The case, therefore, is about transferring a natural language into a language of logical statement. At the same time, as Bar Hillel shown *, it is necessary to deal with such difficulties that draw out the prospects for automatic processing in a very gloomy light, if all direction of searches for solving this problem will not be changed. At least have to be considered with the following obstacles, to overcome which we do not yet have the necessary means.

* ( Y. Var-Hillel, A Demonstration of the Nonfeasibility of Fully Automatic High Quality Translation, "Advances in Computers:", Vol. 1, NEW YORK, 1960, PP. 158-163.)

A. The logical calculation of statements is too poor so that it can even be possible to reformulate the natural language on it, incredibly complex in its semantic structure, which has a huge amount of excess elements and is the most important thing - often different such ambiguity and uncertainty in expression "Meaning" that no double-digit logic can cope with the creation of an artificial twin of the natural language *. True, logic, as indicated, is dealt with only with a linguistic form. But since it is a matter of automatic processing of information, it is necessary to be able to distinguish between and semantic information, and if this is impossible to achieve with the help of the logical tools that we have at our disposal, how can we learn confidence that our translation of the natural language on the logical is correct?

* ( In the article Ch. Hocket "Grammar for the listening" is given a lot of examples of this kind of difficulties in the "natural" understanding of the proposal, which are permitted by subsequent and far outgoing analysis steps (SH, HOCKETT, Grammar for the Hearer, "Structure of Language and Its Mathematical Aspects" , Providence, 1961, pp. 220-236).)

B. The machine cannot take into account that Bar Hillel calls "General Background of Information" (General Background of Information), which actually remain outside the natural language and therefore are not subject to translation to a logical language. Linguists in these cases talk about outside the language context (frame of reference), which is inconspicuous for us, but very strongly adjusts or even exposes full rethinking all our words. After all, even such a simple phrase, as "I will return to light up," for an accurate understanding and determining the temporary instructions contained in it, at a minimum, requires a preliminary knowledge when, where she was pronounced and at what time of year. Only this kind of preliminary information is often the only means for clarifying those intrafrase relations, with which no statement is able to cope with the calculation of predicates. So, taking for example two proposals flashed in newspapers:

Graduate student at the University of Kursk;

Honored rationalizer Siberia, -

we see that each of them can be interpreted in two ways. If you adhere to only formal-grammatical signs, then the first sentence with the same success can be understood as a "graduate student from the University of Kursk" and as "a graduate student of the University, living in the city of Kursk (or originating from the city of Kursk)." And the second proposal can be interpreted and as "the deserved rationalizer whose field of activity is Siberia" and as "Honored rationalizer, which is a resident of Siberia." And only the preliminary and not expressed in the proposals of knowledge (preliminary information), notifying that there is no university in the city of Kursk and that the "deserved rationalizer" is the honorary title, assigned in the Soviet Union with separate administrative districts, make it possible to properly understand these proposals. If you look closely, then almost every phrase spoken language It is very solid and branched preliminary information, of course, of course for a person, but underlying the "understanding" of a car that does not know any kind, no tribe.

B. The car can not do intratheral semantic conclusions that extend to several proposals (and sometimes even deliberately for a whole story to fully disclosure its character or storyline). Dutch linguist A. Reichling * drew attention to this circumstance, illustrating his idea by the following example. Suppose that we read a certain story that begins with a proposal: "I play with my brother." If we stop at this, then we will have no data at our disposal to find out how this phrase should be understood, what kind of game there is a question. After all, you can play for money (in the cards, etc.), on a musical instrument, in the theater or in the cinema, to toys, football, play for fun, to play a man and his fate, etc. But here we read on: " I said it when Wilhelm once met me in the bar. " Now with a greater probability, we can conclude that, apparently, we are talking about money for money. But still there are other possibilities. Then follows: "My brother approached the table, and the bones were thrown." Now it is clear about which game is we talking about, although nowhere in the text of the exact indication of the actual meaning of the word "game" was not given. We guessed about him for the aggregate of those external accepts, which are given in the text in different proposals. These signs are followed here alone after another, but they can in a written narrative and significantly defend each other. A person can choose them from a wide linked context (in this case we are dealing with it), compare and then make the appropriate conclusion. The machine is deprived of this possibility.

* (In Colloquium, organized in 1961. Stichting Studiecentrum Voor Administrative AutomatiSering. There is a German translation of the report: A. Ryyshling, Moglichkeiten und Grenzen der Mechanischen Ubersetzung, Aus der Sichtzung, "Beitrage Zur Sprachkunde und InformationEsveRBeitung", Heft 1, WiFCN, 1963.)

But maybe this does not need her? And indeed, with machine translation of these proposals for German or French special difficulties, it does not arise (but difficulties, of course, will arise when translating other offers). When translating to German, we can use Budalism: Ich Spile Mit Meinem Bruder. In the same way and in French, we can start: Je Joue Avec ... Already when transferring to English, there are difficulties of grammatical order, since there are no instructions on the text that the machine should be chosen: 1. I am Play Ing With My Brother, 2. I Play with My Brother or 3. I "LL Play with My Brother? And it's very very bad when transferring to Spanish, as the machine will have to choose at least between three verbs: Jugar, Tocar or Trabajar.

The logical language is helpless.

G. The car actually deals with speech (or, more precisely, with speech segments) - in its written and oral form. Each of these forms of speech has its own system of pragmatic elements capable of transition to the semantic (and the rules of such a transition and are not studied and largely arbitrarily). For example, oral speech It has such a supracemental superstructure as intonation. The intonation is now submitted to classify according to functional types and allocate questionative, narrative and other intonation. However, it is completely indisputable that intonation exists not autonomously from proposals; She, of course, interacts with the meaning concluded in them. In confirmation of this statement, it is enough to refer to the rhetorical question, which is an issue only on an external structure, but is not a matter of meaning: it does not require a response from the listeners. So a new form of difficulties arises, with which the logical language does not have the opportunity to cope.

D. Methods of automatic processing of speech information (and, in particular, machine translation) comes from the assumption that any sentence, and the language as a whole, "understands" to a certain number of elementary semantic units (words), of which then can be used by certain rules "Collect" asked proposals. The consequence of this assumption is another, according to which the sense of the proposal represents the arithmetic amount of the meanings of the components of his words. Here, math is taken for the sample, where the most difficult operations that the computing machine does, ultimately be reduced to extremely elementary. But in the language we are faced with an almost completely opposite picture. The point is not only that in different languages \u200b\u200bof the sentence in a sense, differently "dealt" on the part. For example:

Girl goes. Girl stands. Hat goes girl. Das Madchen Geht. Das Madchen Steht. Der Hut Steht Dem Madchen(Literally: Hat is worth a girl).

The case is also that even within one language, the arithmetic consistent relationship between the meaning of the proposal and the meanings (values) of the components of its words is most often not observed. On this occasion, E. Benvestist writes: "The proposal is implemented through words. But words are not just a segment of the sentence. The supply is a whole that does not reduce the amount of its parts inherent in a whole meaning is distributed to the entire set of components" *. In this case, it is not about idiomatic expressions (like: "do the sleeves after the sleeves," rub some glasses ", etc.), but about the most ordinary sentences. Take an elementary example:

Wait! - I'll go to the theater.

Is it possible to argue that the meaning of this proposal is an arithmetic amount of words of words: wait, go, theater, I, in? Based on such an arithmetic presentation, we would have to expect that any combination of these words, presented in grammatically correct proposal, will retain the same sense - after all, the terms of the terms do not change from the permutation of the location. But I will try only slightly modify this offer:

I will go to the theater - wait!

We see that in their sense this second offer is significantly different from the first.

* (E. Benveniste, Les Niveaux Deg Analyse Linguistique, "Preprints of Papers for the Ninth International Congress of Linguists", Cambridge, Mass., 1962, p. 497.)

This is from among the extremely elementary examples, and if we turn to more complex, the impotence of any transformation rules that such cases must be jumped, will become particularly obvious. Otherwise, it cannot be: after all, the proposal is a monosion sequence, and monosima (see the section "System of semantic studies"), as a syntactic configuration, more words. This circumstance leads to the fact that the proposal, as a monosion sequence, is a sequence of interconnected elements related to each other in the meaning in the inseparable chain, which is schematically and in a purely generalized form can be depicted as follows *:

* ( See "Appendix" at the end of the book.)

It is precisely because of these features of proposals between the last and words there is a qualitative difference. If words can be defined as signs, then suggestions are undoubtedly out of the limits of the iconic level.

The question of "decomposability" of the language and proposals rests in a more general. There are structures capable of performing their functions only in its complex composition. When trying to decompose them into smaller parts or to reduce to more elementary structures, they actually disintegrate, cease to exist as such, lose the qualities characteristic of them in their complex composition. Such is the language. It understood V. Humboldt (right away, however, this issue Several on the other side), when I wrote: "In order for a person to understand at least one, the only word is not just as a spiritual motivation (i.e. reflex and V.Z.), but as a self-consistent sound, denoting the concept, the whole The language is completely and in all its connections, it should already be laid in it. There is nothing single in the language, each individual item manifests itself only as a part of the whole "*. Transfering this judgment V. Humboldt into the language of modern science, we get the following wording belonging to M. Taube: "... It is not difficult to understand that the language as a system of meaningful characters, oral or written, is not a formal system and cannot be reduced to it Without the destruction of his true nature ... when the language is formalized, it ceases to be tongue and becomes the code "**.

* (V. Humboldt, on a comparative study of languages \u200b\u200bin relation to various epochs of their development. Quoted according to the book: V. A. Zveginsev, history of the Linguistics of the XIX - XX centuries in essays and extractions, h. I, M., 1964, p. 79.)

** (M. Taube, computing machines and common sense, M. * 1964, p. 18.)

But if it will even be possible to cope with the listed language difficulties, there are still obstacles of the actual logical order - in this case it is about the so-called "decision rules" (Decision Rules). After all, if we want to be confident that the car will act logically impeccably, we must provide it with a set of rules, following which it will be able to consistently go through the source information to the required conclusions. With regard to the logical statements, we have such rules, but for more complex logics there are no such rules, and moreover, there is reason to believe that such rules cannot be found. If you focus on those rules that are already available at our disposal, the use of them will make the permission process so complicated (even when applying advanced computing machines) that the game will not cost the candle *.

* (To show what work has to do with a computing machine, working using the method of consecutive steps, A. L. Samuel addresses the example of the game in the checkers. He writes: "To make the computer to play checkers, we first need to portray the position of the checkers on the board by the method that the computing machine could be remembered. Then the consequences of each of the existing moves must be analyzed by a look into the future, as this would do the person. , considering every initial move in turn, then all possible response moves of the enemy, then for each of them - all the cores, etc. Even if mentally moved to the future, to the most last possible machine subordinate only to such restrictions as the size of the Universe, Molecular nature of matter and the final speed of light, then many centuries would be required by such a computing machine, and maybe a longer period than even the age of the universe to make their first move "(A. L. Samuel, Artificial Mind: Progress and Problems. Annex to the book: M. Taube, computing machines and common sense, M., 1964 * p. 140-141).)

In this form, the problem of using logical and mathematical methods in the science of language on the basis of these applied linguistics is drawn. What are the conclusions? The conclusions have already been formulated above - a logical analysis allows a combination of inductive methods with deductive, but when we are talking about the use of deductive methods in linguistics, it should not all be reduced to the blind submission of a linguistic study of logical and mathematical methods. Natural language rebels against such violence. And the practice of applied linguistics confirms these conclusions, establishing that there are such differences between a formalized logical language and natural language that a fairly complete (in informative) is not possible to transfer the second to the first. Does this mean that in linguistics (and, in particular, applied), should the use of logical and mathematical methods? Of course not. But only one should not overestimate their capabilities. While they are rather modest. And in order not to be here with unfounded, turn to the testimony of mathematicians and logic, which in the practice of their work has to apply their knowledge of the study of natural language.

This is what mathematician says: "Mathematics assistance in learning a natural language is still far from obvious ... Before we can think about the use of mathematics for calculating, it is necessary to determine the boundaries and functions of linguistic units ... it is outside the mathematical task, it is part of inductive methods in linguistics.

It turned out that mathematics does not replace the empirical methodology, although some linguists tend to this. On the contrary, only after the units and ratio of the natural language will be established by an inductive method and are appropriately confirmed (verified), will be created the necessary conditions For the realistic application of mathematics to the natural language. At the same time, mathematicians will be found that they are dealing with a new manifestation of the fact that in their essence it is already familiar to them, or a stimulus for mathematical thinking of a new order "*.

* (P. Garvin and W. Karush, Linguistics - Data Processing and Mathematics, "Natural Language and The Computer", New York, 1963, PP. 368-369. See also in the same book Article: W. Ksrush, The Use of Mathematics in the Behavioral Sciencess, PP. 64-83.)

But what the logic says: "The prospects for automatic processing of speech information are very good, but the role of logic in this area is limited. However, as a weapon of linguistic analysis, not as a set of rules to derive conclusions, it gives real promises" *. And then it establishes which research strategy is more preferable: "Problems should be addressed not by means of an adequate following to the set of rules established by logic, but rather with the help of heuristic technology ** ... should be preferred with an empirical inductive approach to the automatic processing of speech information, which are searched for rough rules for solving information problems. Do not attempt to translate the usual language to the logical to follow it, but rather to look for the rules of the heuristic type that will allow you to cope with natural language. It should stop the search for absolute validity and refer to the approximate methods, which, with the accumulation of experience, will be clarified and improved. We prefer to consider the approximations in the same way as we consider the theory in science, where modifications and improvements are made on the basis of data obtained as a result of the experiment "***.

* (M. MARON, A LOGICIAN "S View of Language - Data Processing, this book, page 144.)

** (A fairly clear idea of \u200b\u200bthe heuristic technique gives A. L. Samuel. Opposing its formal methods of a logical procedure, he writes that instead you can apply the technique, "where a few more or less arbitrarily selected procedures are investigated quite incompletely and each gives some key to orientation, whether we are the right way * so far, finally, through the series we will not come to the wording of satisfactory evidence. In both cases, we can sometimes come to the right one or at least a very good answer for an amazingly short period of time, but at the same time there is no confidence that we ever get a decision, As with the confidence that the best solution is the best. This method of solving problems was called the "heuristic" procedure, in contrast to the use of the "algorithm" ... The heuristic solution of the tasks, when it is successful, must, of course, are to be regarded as higher mental activity than Solving tasks through more or less automatic procedure. " Cited by Russian translation: A. L. Samuel, Artificial Mind: Progress and problems. Appendix to the book: M. Taube, computing machines and common sense, M., 1964, p. 136-137.)

*** (M. MARON, Decree. Op., p. 143-144,)

These are common conclusions. They suggest that in working with logics and mathematicians linguists belongs a leading role. The obligation of linguists includes the preparation of language material in such a way as to make it an affordable processing of logical and mathematical methods. It is in this direction that the realistic combination in linguistics of inductive methods with deductive should be seen. And when when solving the tasks of applied linguistics, we are talking about the heuristic hypotheses, then they must first come from a linguist, as he is closer to the language and according to his position is obliged to better know and understand it.

mathematical discipline, the subject of which is the development of a formal apparatus for describing the structure of natural and some artificial languages. Originated in the 50s. 20 c.; One of the main incentives for the appearance of M. L. Served the need to clarify its basic concepts in linguistics. Methods M. l. They have a lot in common with the methods of mathematical logic - mathematical discipline engaged in the study of the structure of mathematical reasoning, and in particular its sections as the theory of algorithms and the theory of automata. Widely used in M. l. Also algebraic methods. M. l. Developed in close cooperation with linguistics. Sometimes the term "M. l. " It is also used to designate any linguistic studies that use any mathematical apparatus.

A mathematical description of the language is based on the ascending to F. de Sosyuru, the idea of \u200b\u200bthe language as a mechanism, the functioning of which is manifested in speech activity of its carriers; Its result is the "right texts" - a sequence of speech units, subject to certain patterns, many of which allow a mathematical description. Development and study of methods of mathematical description of the correct texts (first of all proposals) is the content of one of the sections of M. L. - theories of how to describe the syntactic structure. To describe the structure of the sentence - more precisely, its syntactic structure - you can either allocate in it compound - groups of words that function as whole syntactic units, or indicate for each word the words that are directly subordinated to it (if there are such). Thus, in the sentence, "the yamper sits on the irradiation" (A.S. Pushkin), when describing the 1st way, the components will be all proposal P, each of its separate word and group of words A \u003d sits on the irradiation and B \u003d on the irradiation (see Fig. 1; Arrows mean "direct attachment"); The description of the 2nd method gives a diagram shown in Fig. 2. The mathematical objects arising from this are called the component system (1st way) and tree of syntactic submission (2nd method).

More precisely, the system of components is a set of segments of a proposal, containing all the proposal as elements and all the entry of words into this proposal ("single-catching segments") and the property that every two segments of it are either not intersect, or one of them is contained. in a different; Tree of syntactic subordination, or just a subordination tree, there is a tree, a plurality of nodes of which is a lot of entries in the sentence. Tree In mathematics, the set is called between the elements of which they call them nodes - Installed binary attitude - it is called by way of submission and graphically depict the arrows going from subordinate knots to subordinates - such that: 1) among the nodes there is exactly one - it is called korean- not subordinate to any node; 2) each of the rest of the nodes is subordinate to exactly one node; 3) It is impossible, going from any node along the arrows, return to the same node. The nodes of the subordination tree are the entry of words in the sentence. With a graphic image, the component system (as in Fig. 1) also acquires the tree type ( tree components). Built for the offer of the submission tree or the component system often referred to him syntactic structure In the form of a subordination tree (system components). The components of the components are used mainly in the descriptions of languages \u200b\u200bwith the hard order of words, the trees of submission - in the descriptions of languages \u200b\u200bwith the free order of words (in particular, Russian), formally for each (not too short) proposals you can build many different syntactic structures of any of two types, but Among them are only one or several are correct. The root of the proper subordination tree is usually a lean. A proposal that has more than one correct syntactic structure (one species) is called syntactically homonymous; As a rule, different syntactic structures meet different senses of supply. For example, the proposal "Schoolchildren from Rzhev went to Torzhok" allows two right subordination tree (Fig. 3, a, b); The first of them meets the meaning of "Rzhevsky schoolchildren went (not necessarily from Rzhev) in Torzhok", the second - "Schoolchildren (not necessarily Rzhevsky) went from Rzhev to Torzhok."

In Russian and a number of other languages, the trees of subordination of proposals " business style»Submit, as a rule, law of projectivityIt is worthwhile that all arrows can be held over the straight line on which the proposal is recorded, so that no two of them will cross and the root will not lie under any arrow. In the language of artistic literature, especially in poetry, deviations from the law of projectivity are permissible and most often serve as a task of creating a certain artistic effect. Thus, in the sentence "Friends of the Blood Starny People's Cayali of War" (Pushkin), persistence leads to the emphatic allocation of the word "folk" and at the same time, as it should be speaking, creating this impression of famous rates, solemnity. There are other formal signs of subordination trees that can be used to characterize the style. For example, the maximum number of arrows attached to each other serves as a measure of "syntactic bulky" of the sentence (see Fig. 4).

For a more adequate description of the structure of the proposal, the components are usually marked with symbols of grammatical categories ("Personal Group", "A group of transition verb", etc.), and the arrow of the subordination tree - symbols of syntactic relations ("predicative", "determining", etc. .).

The apparatus of subordination trees and component systems is also used to represent the deep-syntactic structure of the sentence, which forms an intermediate level between the semantic and conventional syntactic structure (the latter is often called superficial syntactic).

A more advanced representation of the syntactic structure of the proposal (requiring, however, more complex mathematical apparatus) give systems of syntactic groupsIn which are included as phrases and syntactic connections, and not only between words, but also between phrases. Syntax group systems allow combining the rigidity of a formal description of the structure of a sentence with flexibility inherent in traditional, informal descriptions. The subordination trees and system of components are the utmost special cases of syntactic groups.

Another section M. L., which occupies a central place in it, - theory of formal grammatik, the beginning of which was found by the works of N. Khomsky. It is studying ways to describe the patterns characterizing no longer a separate text, but the entire set of the correct texts of a given language. These patterns are described using formal grammar - an abstract "mechanism", which allows using the uniform procedure to obtain the correct texts of this language together with the descriptions of their structure. The most widely used type of formal grammar - generate grammar, or Homsky's grammar, which is an ordered system r \u003d ⟨V, W, P, R⟩, where V and W - non-intersectable final sets, referred to basic, or terminal, I. auxiliary, or netterminal, alphabets (their elements are called main, or terminal, and auxiliary, or non-mining, symbols), P - element w, called initial symbol, and R - the final set rules The species φ → ψ, where φ and ψ are chains (final sequences) from the main and auxiliary characters. If φ → ψ is the grammar rule r and ω 1, ω 2 - chains from the main and auxiliary characters, they say that the chain ω 1 ψω 2 directly removed in r from ω 1 φω 2. If ξ 0, ξ 1, ..., ξ n is the chains and for each i \u003d 1, ..., n chain ξ i directly output from ξ i-1, they say that ξ n deprecated in r from ξ 0. Many of those chains from the basic characters that are displayed in G from its initial symbol is called language generated by grammar R, and denotes L (d). If all rules g have the form η 1 Aη 2 → η 1 ωη 2, then r is called grammar components (or directly components), abbreviated by NS grammar; if at the same time in each rule of the chain η 1 and η 2 ( right and left contexts) empty, then grammar is called bescontektova (or context-free), abbreviated grammar (or X- grammar). In the most common linguistic interpretation, the main symbols are words, auxiliary - symbols of grammatical categories, an initial character - a symbol of the category "Offer"; At the same time, the language generated by grammar is interpreted as many of all grammatically correct proposals for this natural language. In the HC-grammar, the withdrawal of the sentence gives it a tree of components in which each component consists of words "occurring" from one auxiliary symbol, so that its grammatical category is indicated for each component. So, if the grammar has, among others, the rules of P → S X, Y, im, V y → V IY O, O → S X, Y, Rasp, V IY → Sits, s Husband, un., Him → on , rocket, s husband, units, betrayed. → Olion, then the offer "the yamper sits on the irradiation" has the output shown in Fig. 5, where the arrows go from the left parts of the rules applied to the elements of the right parts. The system of components corresponding to this conclusion coincides with depicted in Fig. 1. Other interpretations are possible: for example, the main characters can be interpreted as morphids, auxiliary - as symbols of Morph types and permissible Morph chains, an initial symbol - as a symbol of the type "word form", and the language generated by grammar - as a set of correct words (morphological interpretation); Morrhocological and phonological interpretations are also consumed. In real descriptions of languages, typically "multi-level" grammar, which contain consistently working syntactic, morphological and morphological and phonological rules.

Another important type of formal grammar - dominational grammarwhich generates many chains interpreted usually as proposals along with their syntactic structures in the form of subordination trees. Grammar Syntax Group It generates many proposals together with their syntactic structures that have a type of syntactic groups. There are also various concepts transformational grammar (grammar Trees), an employee is not for the generation of proposals, but to transform trees, interpreted as subordination trees or the trees of components. An example is Δ- grammar - The system of rules for converting trees, interpreted as "clean" trees for subordination of proposals, i.e., subordination trees without a linear order of words.

Mansion cost grammar Montagusserving for the simultaneous description of the syntactic and semantic sentence structures; They use a complex mathematic and logical apparatus (the so-called intensional logic).

Formal grammar are used to describe not only natural, but also artificial languages, especially programming languages.

In M. l. Developed also analytical models Language in which, on the basis of certain data on speech, considered known, formal constructions are produced, the result of which is the description of some aspects of the structure of the language. In these models, a simple mathematical apparatus is usually used - simple concepts of the theory of sets and algebras; Therefore, analytical models of the tongue are sometimes called multiple theoretical. In analytical models, the most simple type of source data serve many correct proposals and system neighborhood - aggregates of "words" belonging to one lexeme (for example, (house, houses, house, house, house, houses, houses, houses, houses, houses)). The simplest derivative concept in such models is replacement: Word a. Replaceable for word b.if any right sentence containing the entry of the word a., remains correct when replacing this entry entering the word b.. If a but replaceable by b. and b. on the a., they say that a. and b. interchangeable. (For example, in Russian, the word "blue" is replaced by the word "blue"; the words "blue" and "blue" interchangeable.) The class of words, interchangeable among themselves, is called family. Based on the surroundings and families, you can get a number of other linguistically meaningful classifications words, one of which approximately corresponds to the traditional system of speech parts. In another type of analytical models, instead of a variety of correct proposals, the ratio of potential subordination between words, meaning the ability of one of them to subjugate another in proper proposals. In such models, it is possible to obtain, in particular, the formal definitions of a number of traditional grammatical categories - for example, a formal definition of a case of a noun, which is a procedure that allows you to restore the case of a language language, knowing only the ratio of potential subordination, a system of surroundings and many words that are forms of nouns.

In analytical models of the language, simple concepts of the theory of sets and algebra are used. The analytical models of the language are close decifing models - Procedures that allow by a fairly large case of texts on an unknown language without any preliminary information about it to obtain a number of data on its structure.

In its proposal M. L. It is primarily a tool for theoretical language. At the same time, its methods are widely used in applied linguistic studies - automatic text processing, automatic translation and development associated with the so-called communication between man and computer.

• KulaginO.S., On a method of determining grammatical concepts based on the theory of sets, in Sat.: Cybernetics problems, in. 1, M., 1958;
• HomskyN., Syntactic structures, in Sat: "New in Linguistics", in. 2, M., 1962;
• SmoothA.V., MelchukI. A., elements of mathematical linguistics, M., 1969 (lit.);
• their same, Grammar of trees, I, II, in Sat.: Information issues of semiotics, linguistics and automatic translation, in. 1, 4, M., 1971-74 (lit.);
• MarcusS., theoretical and multiple models of languages, trans. from English, M., 1970 (lit.);
• SmoothA.V., Formal grammar and languages, M., 1973 (lit.);
• its same, An attempt to formally determine the concepts of the case and kind of noun, in Sat.: Problems of grammatical modeling, M., 1973 (lit.);
• its same, Syntactic structures of the natural language in automated communication systems, M., 1985 (lit.);
• SuchkinB.V., optimization methods of language research. M., 1976 (lit.);
• SevbaI. P., Graphic representation of syntactic structures and stylistic diagnostics, K., 1981;
• ParticsB. H., Grammar Montague, mental views and reality, in the book: Semiotics, M., 1983;
• Montague.R., Formal Philosophy, New Haven - L., 1974 (lit.).

Table of contents
Introduction
Chapter 1. The history of the application of mathematical methods in linguistics
1.1. The formation of structural linguistics at the turn of the XIX - twentieth centuries
1.2. The use of mathematical methods in linguistics in the second half of the twentieth century
Conclusion
Literature
Introduction
In the twentieth century, there was an ongoing and understood by the tendency to interact and the interpenetration of various areas of knowledge. The convicts are erased between individual sciences; There are more and more branches of mental activity that are "at the junction" of humanitarian, technical and natural scientific knowledge.
Another obvious feature of modernity is the desire to study the structures and the components of their elements. Therefore, an increasing place in the scientific theory and in practice is given to mathematics. In contact with, on the one hand, with logic and philosophy, on the other hand, with statistics (and, consequently, with social sciences), mathematics penetrates deeper into those areas that have been considered purely "humanitarian" for a long time, expanding Their heuristic potential (the answer to the question "how much" will often peel into the questions "what" and "as). There was no exception to the linguistics. The number of my coursework is to briefly highlight the connection of mathematics with such a branch of linguistics as linguistics. Starting from the 50s of the last century, mathematics is used in linguistics when creating the theoretical apparatus to describe the structure of languages \u200b\u200b(both natural and artificial). However, it should be said that she did not immediately find a similar practical application. Initially mathematicheetters in linguistics began to be used to clarify the basic concepts of linguistics, however, with the development of computer equipment, such a theoretical package began to be used in practice. Resolution of tasks such as machine translation, machine search, automatic text processing required a fundamentally new approach to the language. The question in front of the linguists is the question: to compose to represent language patterns in the form in which they can be submitted directly to the technique. Popular in our time, the term "mathematical linguistics" is called any linguistic studies that apply exact methods (and the concept of accurate methods in science is always closely connected with mathematics). Some scientists of past years, believe that the expression itself cannot be erected by breakage of the term, as it denotes not some special "linguistics", but only a new direction focused on improving, improving the accuracy and reliability of language research methods. Linguistics are used both quantitative (algebraic) and non-quantitative methods, which brings it closer with mathematical logic, and, consequently, with philosophy, and even with psychology. I also remelmed the interaction of the language and consciousness, and the prominent linguist of the beginning of the twentieth century Ferdinand de Sosuryur (about his influence on the formation of mathematical methods in linguistics will tell later) connected the structure of the tongue with his belonging to the people. Modern researcher L. Perlovsky goes further, identifying the quantitative characteristics of the language (for example, the number of birth, cases) with the peculiarities of the national metality (about this in section 2. 2, "Statistical methods in linguistics").
The interaction of mathematics and linguistics is a multifaceted theme, and in its work I will not stop at all, but, first of all, on its applied aspects.
Chapter I. History of application of mathematical methods in linguistics
1.1 Formation of structural linguistics at the turn of the XIX - twentieth centuries
The mathematical description of the language is based on a resubmavance of the language as a mechanism ascending to the well-known Swiss linguist for the beginning of the twentieth century Ferdinand de Sosurura.
The initial link of his concept is the theory of language as a system designed from three parts (actually Langue - Langue, speech - Parole, and speech activities - LANGAGE), in which each word (member of the system) is not considered in itself, but in connection with others ...

& NBSP & NBSP & NBSP & NBSP & NBSP & NBSPS, when Boduen de Courtee, in 1904, first expressed an opinion on the need for applying mathematical methods in the linguistics ( Kondrashov N.A., 1979, 170), passed quite a long time while the first serious attempts to use them began. But gradually mathematical methods in linguistics found the most diverse use. Even the whole direction of linguistics - mathematical linguistics appeared ( Lesochin MM, 1982 TA Dr.). In phonetics and syntax, a large perspective has the use of the probability of Markov processes known in the theory of probability. In historical and comparative linguistics, which most of all we are interested in, the methods of glot-chronology are developing, one of which was proposed by Maurice summarized (Maurice Summer, 1960-1). He made that a certain part of the main dictionary of all languages \u200b\u200bforms a certain lexical core, which is relatively stable, because it changes with a constant, but very slow speed Approximately how the radioactive decay is coming. If we are known for the percentage of words that are preserved in the language for a certain time, then we can calculate the rate constant of the lexic composition of changes, which, although a constant value, but for different languages \u200b\u200band different periods of their development may differ somewhat. He compiled a list of the lexical core of words first in the amount of 100, and later, 200 words and, comparing the percentage of the words of this nucleus, which were preserved in pairs of close-related languages, tried to calculate the time passed from the moment when these languages \u200b\u200bseparated from each other. However, the pace of language changes in reality is very different for different languages \u200b\u200band eras. According to Vl. Georgiev, "with a primitive strict process of changes in public life and in the language, there are the slower, the further we penetrate into the depths of millennia: for the smallest changes were needed then no century, and the millennium" ( Georgiev Vl., 1958, 243). Therefore, probably, the results obtained by the summaries of the calculations contradicted the obvious facts, and the scientist tried to improve his method, but unsuccessfully ( Summer Morris, 1960-2). His idea was certainly very interesting, but its implementation was impossible due to the difficulty of determining the constant of the speed of changes in the lexical nucleus, and the principal impossibility of drawing up a list of words of this nucleus, which could be universal for everyone without exception of the world's languages. The impossibility of solving these problems was proved by Harry Hoyer ( Hoyer Harry., 1960) and V.A. Zvegintsev, who wrote:

& NBSP & NBSP & NBSP & NBSP & NBSP & NBSp When M. Svodash is trying to make a "experienced list", suitable for all languages, and formulate universal rules for its compilation, it sets himself a task that cannot actually be fulfilled "(Zvegents V.A., 1960, 13).

& NBSP & NBSP & NBSP & NBSP & NBSP & NBSpact NBSP & NBSP & NBSpacts An interesting attempt to determine the age of individual languages \u200b\u200bwas made by M.V.Arapov and M.M. Hertz. They set themselves the task "to build a mathematical model of changing dictionary and on the basis of this model to theoretically obtain the dependence between the time of the word occurrence and its rank in the frequency dictionary" ( Arapov M.V., Herz M.M., 1974, 3). Having received this model, they hoped to calculate the age of individual, related languages. For this, they proposed an empirical formula that describes the likelihood of the word to the chosen time. The key place in this formula has a certain constant, which itself may vary for different chronological sections and for different languages, but the rate of language development in different periods, as already noted, can be very different, and we can now not have the slightest on these features representation. The authors objectively appreciated their method, noting that they only wanted to demonstrate its capabilities, because for calculating the constant, it is necessary to have frequency dictionaries, compiled by a single technique, and historical lexicography would have to be developed so much that it could be given the opportunity to fix the moment of the new word with accuracy at least to a century. "Since both of these requirements are not fulfilled ... data on the speed of changes in individual languages \u200b\u200bof non-stakes" ( Arapov M.V., Herz M.M., 1974, 56). Consequently, the method still expects its implementation.

& NBSP & NBSP & NBSP & NBSP & NBSP & NBSPLAs A attempt to quantify the degree of kinship degree in 1927. Y. Chekhanovsky. He tried to use the mathematical criterion of independence to assess the similarity of two associations, introduced into the practice of anthropological studies by E. B.Teallor in 1888. Using this method, the Polish researcher showed the degree of kinship of Slavic languages, and later some Indo-European ( Czekanowski Jan., 1957, 71). The method was not perceived by most of the lingules due to an arbitrary choice of signs and the need for a double count of some of them ( Popowska-Taborska Hanna, 1991, 34). There are also other methods for assessing the similarity of associations, which take into account the presence of a specific feature in one of two objects missing in another object.

& NBSP & NBSP & NBSP & NBSP & NBSP & NBSPODO for the study of the kinship of languages \u200b\u200bby the method of comparing vocabulary they are unacceptable, because the lack of a sign can only mean its absence at our disposal, but in fact he could exist before or exists now, but not recorded by scientific researchers. In archeology and anthropology, such methods can be used, for there we are dealing with material objects, which sufficiently give an idea of \u200b\u200btheir original form, but in historical linguistics we can never be sure of the absence of some signs of the research object In the distant past. Therefore, in linguistics and there is a rule: "only positive facts have evidence power."

& NBSP & NBSP & NBSP & NBSP & NBSP & NBSP and the idea of \u200b\u200bChekanovsky in a certain sense continued another Polish explorer V.Mamek, who adheres to a fundamental concept: there is a certain connection between the relationship of languages \u200b\u200band their geographical location ( Mańczak Witold., 1981, 138). It makes a comparison of the number of general words of the Gothic, Starobolg and Lithuanian languages, using only the texts of the Bible written by these languages, allowing that they are very close to the German, Slavic and Baltic languages, based on the second principle: counting what can be found in grammar and dictionaries, may not once lead to false conclusions, while the counting of what is contained in the texts allows you to open the truth. Consider its linguistic principles here is not a place, especially since it has already done Popovskaya Tuborsk ( Popowska-Taborska Hanna, 1991, 35-35, 94-97), but the mathematical side of studies needs certain comments. To bind the geographical location of the Pranodina of Slavs based on the obtained data of the three languages \u200b\u200bis impossible in general, for, figuratively expressing, here in one equation is more than one unknown. After receiving even the true scheme of the location of three languages \u200b\u200bon the plane, we need to know exactly the place of formation at least one of these languages \u200b\u200band be sure that the area of \u200b\u200bone of the remaining languages \u200b\u200blies in a certain direction from him. In addition, it is also necessary to somehow decide on time, for the carriers of all three languages \u200b\u200bcould change the places of their settlements during the course of time and to be placed in different provisions on others. Acquisition to research on the relationships of these languages \u200b\u200bwith Latin, as does the Manchac makes it, it also changes little, for allowing the Priori that the German, Slavic and Baltic language was formed during the existence of the Roman Empire, there are also no foundations.