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 1950s. 20th century; one of the main stimuli for the appearance of M. l. served as a mature need in linguistics to clarify its basic concepts. Methods M. l. have much in common with the methods of mathematical logic - a mathematical discipline that studies the structure of mathematical reasoning - and in particular such sections of it as the theory of algorithms and the theory of automata. Are widely used in M. l. also algebraic methods. M. l. develops in close interaction with linguistics. Sometimes the term "M. l." is also used to refer to any linguistic research that uses some kind of mathematical apparatus.

The mathematical description of the language is based on F. de Saussure's idea of ​​language as a mechanism, the functioning of which is manifested in the speech activity of its speakers; its result is "correct texts" - sequences of speech unitssubject to certain patterns, many of which allow mathematical description. The development and study of methods for the mathematical description of correct texts (primarily sentences) is the content of one of the sections of M. l. - theory of ways to describe the syntactic structure. To describe the structure of a sentence - more precisely, its syntactic structure - one can either single out in it constituents- groups of words that function as integral syntactic units, or indicate for each word those words that are directly subordinate to it (if any). So, in the sentence “The coachman sits on the irradiation” (A. S. Pushkin), when described according to the 1st method, the components will be the entire sentence P, each of its individual words and groups of words A = sits on the irradiation and B = on the irradiation (see. Fig. 1, arrows mean "immediate nesting"); the description according to the 2nd method gives the circuit shown in fig. 2. The resulting mathematical objects are called system of components(1st method) and syntactic subordination tree(2nd method).

More precisely, the system of components is a set of segments of a sentence, containing as elements the entire sentence and all occurrences of words in this sentence (“single-word segments”) and having the property that every two segments included in it either do not intersect, or one of them is contained in a different; a syntactic subordination tree, or simply a subordination tree, is a tree whose node set is the set of occurrences of words in a sentence. tree in mathematics, a set is called, between the elements of which - they are called knots- a binary relation is established - it is called subordination and graphically depicted by arrows going from subordinate nodes to subordinate ones - such that: 1) among the nodes there is exactly one - it is called root, - not subordinate to any node; 2) each of the other nodes is subordinate to exactly one node; 3) it is impossible, having started from any node along the arrows, to return to the same node. The nodes of the subordination tree are the occurrences of words in sentences. With a graphical representation, the system of components (as in Fig. 1) also takes the form of a tree ( component tree). A subordination tree or a system of components built for a sentence is often called it syntactic structure in the form of a subordination tree (system of components). Component systems are used mainly in descriptions of languages ​​with a rigid word order, subordination trees are used in descriptions of languages ​​with a free word order (in particular, Russian), formally for each (not too short) sentence, many different syntactic structures of any of the two types can be built, but among them, only one or a few are correct. The root of the correct subordination tree is usually the predicate. A sentence that has more than one correct syntactic structure (of the same kind) is called syntactically homonymous; as a rule, different syntactic structures correspond to different meanings of the sentence. For example, the sentence "Schoolchildren from Rzhev went to Torzhok" allows two regular subordination trees (Fig. 3, a, b); the first of them corresponds to the meaning “Rzhev schoolchildren went (not necessarily from Rzhev) to Torzhok”, the second - “Schoolchildren (not necessarily Rzhev) went from Rzhev to Torzhok”.

In Russian and a number of other languages, the subordination trees of "business style" sentences, as a rule, obey the law of projectivity, which consists in the fact that all the arrows can be drawn over the line on which the sentence is written, in such a way that no two of them intersect and the root does not lie under any arrow. In the language of fiction, especially in poetry, deviations from the law of projectivity are permissible and most often serve the task of creating a certain artistic effect. So, in the sentence “Friends of the bloody antiquity of the people looked forward to war” (Pushkin), non-projectivity leads to an emphatic emphasis on the word “folk” and at the same time, as it were, slows down speech, thus creating the impression of a certain elation and solemnity. There are other formal signs of subordination trees that can be used to characterize style. For example, the maximum number of nested arrows serves as a measure of the “syntactic bulkiness” of a sentence (see Fig. 4).

For a more adequate description of the structure of the sentence, the components are usually marked with symbols of grammatical categories (“nominal group”, “transitive verb group”, etc.), and the arrows of the subordination tree - with symbols of syntactic relations (“predicative”, “attributive”, etc. .).

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

A more perfect representation of the syntactic structure of a sentence (requiring, however, a more complex mathematical apparatus) is given by syntactical group systems, which include both phrases and syntactic links, and not only between words, but also between phrases. Syntactic group systems allow you to combine the rigor of a formal description of the structure of a sentence with the flexibility inherent in traditional, informal descriptions. Subordination trees and component systems are extreme special cases of syntactic group systems.

Another section of M. l., which occupies a central place in it, is theory of formal grammars, the beginning of which was laid by the works of N. Chomsky. It studies ways of describing patterns that no longer characterize a single text, but the entire set of correct texts of a particular language. These patterns are described using formal grammar- an abstract "mechanism" that allows, using a uniform procedure, to obtain the correct texts of a given language along with descriptions of their structure. The most widely used type of formal grammar is generative grammar, or the Chomsky grammar, which is an ordered system Г = ⟨ V, W, P, R ⟩, where V and W are disjoint finite sets, called respectively main, or terminal, and auxiliary, or non-terminal, alphabets(their elements are called, respectively, the main, or terminal, and auxiliary, or non-terminal, symbols), P is an element of W, called initial symbol, and R is a finite set rules of the form φ → ψ, where φ and ψ are chains (finite sequences) of main and auxiliary symbols. If φ → ψ is a grammar rule G and ω 1 , ω 2 are chains of basic and auxiliary symbols, they say that the chain ω 1 ψω 2 directly derivable into Г from ω 1 φω 2 . If ξ 0 , ξ 1 , ..., ξ n are chains and for each i = 1, ..., n the chain ξ i is directly derivable from ξ i−1 , we say that ξ n derivable to Г from ξ 0 . The set of those chains of basic symbols that are deducible in Г from its initial symbol is called language generated by grammarГ, and is denoted by L(Г). If all rules Г have the form η 1 Aη 2 → η 1 ωη 2 , then Г is called the grammar of the constituents(or directly components), abbreviated as NS- grammar; if, in addition, in each rule the chains η 1 and η 2 ( right and left contexts) are empty, then the grammar is called context-free(or context-free), abbreviated B- grammar(or KS- grammar). In the most common linguistic interpretation, the main symbols are words, the auxiliary symbols are symbols of grammatical categories, the initial symbol is the symbol of the “sentence” category; the language generated by the grammar is interpreted as the set of all grammatically correct sentences of the given natural language. In an NN grammar, the derivation of a sentence gives a tree of constituents for it, in which each constituent consists of words "derived" from one auxiliary symbol, so that for each constituent its grammatical category is indicated. So, if the grammar has, among others, the rules P → S x, y, im, V y → V i y O, O → S x, y, preposition, V i y → sits, S husband, singular, im → on , coachman, S husband, sing., proposition. → irradiation, then the sentence "The coachman is sitting on the irradiation" has the output shown in Fig. 5, where the arrows go from the left parts of the applied rules to the elements of the right parts. The system of components corresponding to this conclusion coincides with that shown in Fig. 1. Other interpretations are also possible: for example, the main symbols can be interpreted as morphs, auxiliary - as symbols of types of morphs and acceptable chains of morphs, the initial symbol - as a symbol of the type "word form", and the language generated by the grammar - as a set of regular word forms (morphological interpretation); morphonological and phonological interpretations are also common. Real descriptions of languages ​​usually use "multilevel" grammars that contain sequentially working syntactic, morphological and morphonological-phonological rules.

Another important type of formal grammar is dominance grammar, which generates a set of chains, usually interpreted as sentences, together with their syntactic structures in the form of subordination trees. Grammar of syntactic groups generates a set of sentences together with their syntactic structures, which have the form of systems of syntactic groups. There are also various concepts transformational grammar (tree grammars), which serves not to generate sentences, but to transform trees interpreted as trees of subordination or trees of constituents. An example would be Δ- grammar- a system of tree transformation rules interpreted as "pure" sentence subordination trees, i.e. subordination trees without a linear word order.

stand apart Montague grammars, which serve to simultaneously describe the syntactic and semantic structures of the sentence; they use a complex mathematical and logical apparatus (the so-called intensional logic).

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

In M. l. also developed analytical models language, in which, on the basis of certain data about speech that are considered known, formal constructions are made, the result of which is a description of some aspects of the structure of the language. These models usually use a simple mathematical apparatus - simple concepts of set theory and algebra; therefore analytical models of language are sometimes called set-theoretic. In analytical models of the simplest type, the initial data are the set of correct sentences and the system surroundings- sets of "words" belonging to one lexeme (for example, (house, house, house, house, house, house, house, house, house, house)). The simplest derived concept in such models is substitutability: word a replaced by a word b, if every correct sentence containing an occurrence of the word a, remains valid when this occurrence is replaced by an occurrence of the word b. If a a 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" are interchangeable.) The class of words that are interchangeable with each other is called family. From neighborhoods and families, a number of other linguistically meaningful word classifications can be derived, one of which roughly corresponds to the traditional system of parts of speech. In another type of analytical models, instead of a set of correct sentences, a potential subordination relationship between words is used, meaning the ability of one of them to subordinate another in correct sentences. In such models, one can obtain, in particular, formal definitions of a number of traditional grammatical categories - for example, the formal definition of the noun case, which is a procedure that allows you to restore the case system of the language, knowing only the relation of potential subordination, the system of neighborhoods and the set of words that are forms of nouns.

The analytical models of the language use simple concepts of set theory and algebra. Close to analytical models of language decryption models- procedures that allow obtaining a number of data on its structure from a sufficiently large corpus of texts in an unknown language without any preliminary information about it.

According to its purpose, M. l. is primarily a tool of theoretical linguistics. At the same time, its methods are widely used in applied linguistic research - automatic text processing, automatic translation and developments related to the so-called communication between a person and a computer.

• Kulagina O. S., On one way of defining grammatical concepts based on set theory, in: Problems of Cybernetics, c. 1, Moscow, 1958;
• Chomsky N., Syntactic structures, in collection: "New in linguistics", v. 2, M., 1962;
• Smooth A. V., Melchuk I. A., Elements of mathematical linguistics, M., 1969 (lit.);
• their own, Grammars of Trees, I, II, in: Informational Issues of Semiotics, Linguistics and Automatic Translation, c. 1, 4, M., 1971-74 (lit.);
• Marcus S., Set-theoretic models of languages, trans. from English, M., 1970 (lit.);
• Smooth A. V., Formal grammars and languages, M., 1973 (lit.);
• his own, An attempt to formally define the concepts of case and gender of a noun, in Sat: Problems of grammatical modeling, M., 1973 (lit.);
• his own, Syntactic structures of natural language in automated communication systems, M., 1985 (lit.);
• Sukhotin BV, Optimization methods for language research. M., 1976 (lit.);
• Sevbo I. P., Graphic representation of syntactic structures and stylistic diagnostics, K., 1981;
• Party B. Kh., Grammar Montagu, mental representations and reality, in the book: Semiotics, M., 1983;
• Montague R., Formal philosophy, New Haven - L., 1974(lit.).

There is no doubt that the use of mathematical and logical methods ("exact methods") in linguistics was largely stimulated by the tasks of applied linguistics. If attempts were made to apply these methods to solve problems directly related to the field of theoretical linguistics, for example, to distinguish between the phenomena of language and speech * , then in the future (although, perhaps, not always clear and close), they still had in mind the needs of applied linguistics. By the way, this means that the evaluation of the results of such operations should be carried out with the obligatory consideration of the goals of applied linguistics.

* (See: G. Herdan, Language as Choice and Chance, Groningen, 1956.)

The success of using these methods in a completely new field, from a general point of view, is largely determined by the answer to the question of the extent to which it is permissible to identify a logically correct language with a natural language, or, in another formulation, is it possible to reduce the second to the first * . The answer to this question is usually given in a practical form - by constructing statistical, information-theoretic, set-theoretic, probabilistic and other mathematical models of the language, which, however, are not always focused on specific tasks ** . When constructing models of this kind, their authors often proceed from the assumption (obvious from their point of view) that any application of a formal-logical or mathematical apparatus to linguistic description and research automatically contributes to their improvement. On this occasion, Warren Plyat said well in his review of works on mathematical linguistics: “If we consider language models as abstract systems of discrete elements, then various mathematical concepts and methods can be applied to them, ranging from the elementary idea of ​​a number to complex “logical, statistical and set-theoretic operations. However, the notion that any use of numbers and mathematical operations to describe such systems of elements makes statements more "exact" or more "scientific" is completely erroneous. First of all, it must be shown that the new system thus obtained is a more satisfactory model than the original system, either in the sense that it makes it possible to formulate simpler and more general theoretical statements about certain aspects of the modeled area, or because operations on the model shed light on the results of corresponding operations in the domain being modeled.One of the main dangers associated with the construction of mathematical models of the language, especially quantitative ones, is that the indiscriminate use of the mathematical apparatus inevitably leads to meaningless and misleading results.It is necessary to clearly understand therefore that a prerequisite for the enrichment of linguistics with the help of mathematics is not only knowledge of the relevant areas of mathematics, but, in addition, a deep understanding of the essence of linguistic problems, the solution of which should be aimed at mathematical methods" *** .

* (Wed G. Curry's remark: "The fact that there is a close connection between mathematics and logic, on the one hand, and language, on the other, has become obvious for a long time, and now this fact has become the focus of attention in a more rigorous thought ..." ( N. V. Curry, Some Logical Aspects of Grammatical Structure, in Proceedings of the Symposium "Structure of Language and its Mathematical Aspects", Providence, 1961, p. 57).)

** (In this regard, P. Garvin's remark (made by him in a review of W. Bar-Hillel, Language and Information: Selected Essays on Their Theory and Application, London, 1964) seems to be very timely: "Most of the works on the theory of information processing and applications for its purposes of computing machines, it is completely naive and, undoubtedly, not as useful as it would be desirable. Regarding the negative position of Bar-Hillel regarding the effectiveness of logical-mathematical methods for automatic processing of speech information, P. Garvin believes that it still contains positive elements, since this position "will make at least some scientists take their theories less seriously" (American Documentation, New York, Vol. 16, No. 2, 1965, p. 127).)

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

In order to, if possible, avoid the danger indicated by Warren Plat, 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 reducibility of a natural language to one or another logical-mathematical model or interpretation of it is the main issue of the theory of applied linguistics, the need for which is felt more and more urgently. When considering this issue, first of all, the nature of those phenomena that constitute the subject of study, on the one hand, logic and mathematics, and on the other hand, natural language, and then also the possibilities of the methods by which each of these sciences works, should be considered. Already from a comparative study of these points, it will be possible to draw some general conclusions, which may be of some use to all those who, of necessity, have to carry out their research at the intersection of the listed sciences.

To a certain extent this goal is served by the symposium "The Structure of Language and Its Mathematical Aspects" held by the American Mathematical Society*. But all of them, as it is clear from the very title of the symposium, affect only individual and in some cases very particular aspects of the problem of interest to us. Although in their totality they create sufficiently reasoned prerequisites for answering the question we are considering, they still lack a clear and unambiguous formulation of the necessary conclusions. In many ways, the participants of the symposium continue the line of empirical attempts to resolve the issue, by no means obsessively offering their experiments to the attention of linguists in the hope that they themselves will figure out how the hypotheses and solutions presented by them will turn out to be suitable for their purposes.

* ("Structure of Language and its Mathematical Aspects". Proc. of the Soc. of Appl. Math., 12. Providence, 1961.)

More suitable, therefore, as a starting point for understanding the results of the work of linguists, logicians and mathematicians in the plan we are analyzing are two articles placed in the collection "Natural Language and the Computing Machine" *: M. Meron "The point of view of the logician on the processing of linguistic data" and P Garvin and V. Karash "Linguistics, linguistic data processing and mathematics". They outline the working possibilities of logic and mathematics, their relation to the empirical sciences, methods of solving problems, etc. Let us turn to the consideration of the 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 unambiguous answer to our question. So, for example, N. D. Andreev and JI. R. Zinder write: "The mathematical representation (model) of languages ​​is by no means identical to the language itself" * . They are also followed by the author of the book "Models of Language" II Revzin, who points out that as a result of modeling, only "a more or less close approximation of the data of concrete reality" ** can appear. However, to say so means to say nothing yet, since it remains undisclosed why this is so and whether one should still resort to the method of mathematical and logical modeling, and if so, to what extent and for what purpose.

* (N. D. Andreev, L. R. Zinder, Basic problems of applied linguistics, "Problems of Linguistics", 1959, No. 4, p. 18.)

** (I. I. Revzin, Models of language, M., 1962, p. 8. By the way, the expression "close approximation" is a direct tautology: close approximation.)

To resolve all these issues, it is initially established as a starting point which sciences - inductive or deductive - include linguistics, logic and mathematics. As for the last two sciences, their position is clear - they undoubtedly belong to the deductive sciences, based in their research methodology on inference. Linguistics is traditionally defined as an empirical science, which implies that its main scientific goal is to describe facts. This means, apparently, that linguistics should be assigned to the field of inductive sciences. This also means that, in an effort to use the formal apparatus of logic and mathematics in linguistics, they are trying to apply deductive methods of research in inductive science.

However, in recent years, the inductive nature of the science of language - linguistics has come under direct or indirect doubt. L. Elmslev did this in the sharpest form. True, the terminology he uses is very inconsistent and, in particular, is characterized by a peculiar and very personal understanding of the terms "deduction" and "induction" (in fact, he interprets them in a completely opposite way). However, the foundations of his linguistic theory he expounds leave no doubt about its methodological essence. Thus, he considers it acceptable to use any initial operational definitions, which is typical for deductive sciences. And he himself characterizes his theory in the following terms: “1. A theory in our sense is in itself independent of experience. It is what has been called a purely deductive system in the sense that it alone can be used to calculate the possibilities arising from its premises 2. On the other hand, the theory includes a number of premises, of which it is known from previous experience that they satisfy the conditions of application to certain experimental data. These premises are the most general and may therefore satisfy the conditions of application to a large number of experimental data" * .

* ("Prolegomena to the Theory of Language". Sat. "New in Linguistics", vol. 1, M., 1960, pp. 274-275.)

As is clear from this statement, L. Hjelmslev seeks to carry out the idea of ​​the dual methodological nature of the objects of linguistic research, with a predominant emphasis on their deductive features. He should also be credited with that rather ambiguous way (“on the one hand ... but on the other hand ...”), which has generally become characteristic of the consideration of this issue (and which makes it possible to turn in either direction). The idea of ​​the methodical duality of linguistics has recently received wide circulation and even served as a theoretical basis for formulating the principles and the most recent direction in the science of language - the linguistics of universals (universalism). The "Memorandum on Linguistic Universals" says in this regard: "The study of linguistic universals leads to a whole series of empirical generalizations about linguistic behavior - both still requiring experiment and already established. These generalizations are potential material for constructing a deductive structure of scientific laws. However , some and perhaps most of them still have only the status of empirical generalizations, which, in the present state of our knowledge, cannot be correlated with generalizations or deductively derived from laws of more general validity" * . J. Greenberg expresses himself with no less definiteness in his preface to the collection devoted to linguistic universals. Arguing with the well-known words of L. Bloomfield that "the only legitimate generalizations about language are inductive generalizations," he writes: "Nevertheless, it seems to be generally accepted that the scientific method should be not only inductive, but also deductive. Formulation generalizations obtained by inductive investigation leads to theoretical hypotheses, on the basis of which, by deduction, further generalizations can in turn be deduced. These latter must then be subjected to empirical verification" ** .

* ("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 of the accumulation of the facts of a language and their classification, but also of a change in points of view on the language itself, which inevitably implies a difference in approaches to linguistic facts and even their different theoretical interpretations, made some Soviet linguists also come to the conclusion conclusions about the methodological duality of their science. S. K. Shaumyan prefers, however, to speak of the hypothetical-deductive method and outlines its features as follows: “The hypothetical-deductive method is a cyclic procedure that begins with facts and ends with facts. Four phases are distinguished in this procedure:

1. fixing facts that require explanation;
2. putting forward hypotheses to explain these facts;
3. derivation from hypotheses of predictions about facts lying outside the range of facts for the explanation of which hypotheses were put forward;
4. checking the facts that are predicted by hypotheses, and determining the likelihood of hypotheses.

The hypothetical-deductive method is fundamentally different from the inductive method used in such fields of knowledge as, for example, descriptive botany or zoology "*. The method of S.K. Shaumyan actually completely repeats the method of linguistics of universals by J. Greenberg. The only difference is in the name. If , for example, J. Greenberg speaks of a combination of inductive and deductive methods, then S. K. Shaumyan calls his method hypothetical-deductive: the designation is clearly inconsistent for a method that "begins with facts and ends with facts."

* (S. K. Shaumyan, Problems of Theoretical Phonology, Moscow, 1962, pp. 18-19. Regarding the hypothetical-deductive method, see also the article by V. S. Shvyrev "Some questions of the logical and methodological analysis of the relationship between the theoretical and empirical levels of scientific knowledge" in Sat. "Problems of the logic of scientific knowledge" (M., 1964), pp. 66-75 (3rd section of the article).)

The question of where linguistics should be attributed is also asked by I. I. Revzin. “By its very nature,” he answers this question, “linguistics must first of all use inductive methods, it describes specific speech acts of specific languages ​​...

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

It follows that linguists need not only inductive but also deductive methods of research in order to obtain a system of general knowledge that helps to comprehend the data that is obtained in the analysis of specific languages ​​...

In its deductive part, linguistics, apparently, can be built in the same way as logic or mathematics is built, namely: a certain minimum number of primary, undefined terms is singled out, and all other terms are defined through primary ones. At the same time, some primary assertions about the connection of these terms with each other (axioms) must be clearly formulated, and all other assertions must be proved, i.e., reduced to some other assertions" * .

* (I. I. Revzin, Models of language, M., 1962, pp. 7-8.)

Here the method of deduction, embodied in logic and mathematics, acts only as a means of ordering the "set of speech acts" for the purpose of creating a "system of general concepts." In direct contradiction to this task, however, stands the presentation of the deductive method itself, recommended for use in linguistics. It is completely thought out both from acts and from facts, and for the initial moment of constructing a system of general linguistic concepts, it takes a set of undefined and, apparently, absolutely conditional primary terms, through which all subsequent terms are defined.

This contradiction is not accidental, it lies in the very nature of the sciences we are considering. It would seem that the conclusion that a combination of inductive and deductive methods is acceptable in the study of linguistic objects opens the door for the use of logical and mathematical methods in linguistics, and the specific implementation of this conclusion is the creation of numerous formal-logical and mathematical models of the language. But, as will be clear from what follows, such a simplified approach cannot give satisfactory results. We can agree that in linguistic research it is permissible and even necessary to combine deductive and inductive methods. In the end, as W. Bröndal wrote, "induction is nothing but a disguised deduction, and behind the pure connections established between the observed phenomena, reality, the specific object of this science, is absolutely inevitably assumed" * . But this does not mean that the formal apparatus of logic and mathematics should be unconditionally and mechanically transferred to linguistics without any consideration of the "specific object of this science." As the same I. I. Revzin rightly notes, “the evidence obtained by deductive means, no matter how irreproachable they may be from a logical point of view, still does not say anything about the properties of the real language described by the model” ** . And to determine the effectiveness of the models, he recommends turning to the practice, which is machine translation and "other practical applications of linguistics."

* (B. Bröndal, Structural Linguistics. Quoted from the book: V. A. Zvegintsev, History of linguistics in the 19th and 20th centuries. in essays and extracts, part II, Moscow, 1965, p. 95.)

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

And the practice of applied linguistics shows that very strict restrictions are imposed on the use of mathematical and logical methods in the study of linguistic phenomena.

3

Logic provides an example of the most consistent use of the deductive method. Mathematics largely follows logic in this regard, and so they can be considered together.

Of course, both logic and mathematics do not represent homogeneous systems in terms of their methods and interpretation of goals. So, for example, in relation to logic, we can talk about dialectical, formal, mathematical logic, and, in a narrower sense, about objective, semantic, phenomenological, transcendental, or constructive, combinatorial, many-valued, modal, etc. Of necessity, however, it will be necessary think of all such subdivisions and speak only of the most general features characteristic of logic and mathematics as a whole, and mainly of those that most clearly demonstrate the deductive nature of the methods of these sciences.

Having taken this position, we, therefore, will not turn to inductive logic. We only note that conclusions in inductive logic are not determined by premises - thus they are not tautological. The conclusions in inductive logic are directly dependent on the facts, and these latter are determined by the amount of our knowledge - thus, they are established on a probabilistic basis. Probability is the main methodological tool of inductive logic.

Deductive logic is most fully represented by formal and mathematical logics, which have much in common. Deductive logic is a science that studies human thinking or mental acts from the point of view of their structure or form, abstracting from their specific content. Thus, deductive logic seeks to formulate laws and principles, the observance of which is a prerequisite for achieving true results in the process of obtaining inferential knowledge. The main methodological tool of deductive logic is implication. It obtains inferential knowledge without direct appeal to experience or practice, by merely applying the laws of logic. In the process of deduction, the premise conditions the conclusion: if the premise is true, then the conclusion must be true. Thus, the conclusion is already in the premise, and the purpose of the deduction is to make evident what in the latent state is already contained in the premise. It follows from this that any conclusion obtained by means of deduction is tautological, i.e., logically empty, although from other points of view, for example, in cases where the formal logical apparatus is used for the purposes of other sciences, it can be new, unexpected and original.

A similar situation takes place in mathematics - the validity of the arguments in it rests entirely on deduction. Moreover, in mathematics, as a rule, any initial point of view, any approach to solving a problem is acceptable - as long as they satisfy the conditions of mathematical deduction. Mathematics has a rich set of such "initial points of view" and "approaches" that the researcher can alternatively use to solve his problem. Mathematical problems are often translated into different equivalent forms, and each of them involves the use of different areas of mathematical theory in order to solve the problem. Thus, a mathematician has virtually unlimited freedom to choose premises - he chooses those that, from his point of view, contain the most promising possibilities for the most simple, unbanal, elegant solution of the problem. His talent and experience are manifested precisely in the successful choice of prerequisites, those "let's say that ..." or "if ... then" that are full of mathematical works. Just as in logic, mathematical premises - axioms or postulates - determine the definitions of yet undefined units.

The freedom to choose premises in mathematics is directly dependent on the fact that it operates with non-material units, or objects - its attention is directed to the relationships between them. Mathematical objects serve as symbols expressing the structure of pure relations. A mathematical system can thus be regarded as a set of formal relations that exist only by virtue of the statements of these relations. Of course, in particular, for applied purposes, statements of relations may tend to embody correspondences with external reality, but this does not affect the statements of relations themselves in any way - rather, on the contrary. Mathematicians do not investigate the "truth" of their axioms, although they require mutual agreement between them. Investigation within a mathematical system is the investigation and establishment of connections that make it possible to prove that the fact of theory A implies the fact of theory B. Therefore, the main question in mathematics is not "what are A and B?", but "Does A presuppose (or determines) B ?".

Completely different situation in linguistics. She mainly focuses on the first of these questions, and this does not give her the opportunity to break away from reality; therefore, it operates not with abstract, but with concrete units, although in a number of cases it tends to create abstract objects, such as the concept of a phoneme or a morpheme. This situation is characteristic not only of traditional linguistics, but is equally characteristic of its latest trends, united under the banner of structuralism. A number of statements have already been cited above, which, while trying to use not only inductive but also deductive methods (or mathematical and logical methods) in the science of language, could not bypass the need to refer to a real linguistic fact. In addition to them, one more thing can be cited, which brings complete clarity to the issue under consideration: “Linguistic analysis,” writes P. Garvin in this connection, “is basically an inductive process in the sense that it seeks to establish a list of elements or a set of statements, based on from the linguistic stimuli of the informants or from the study of the text.It is based on the assumption that in both these sources of information it will be possible to recognize regularly occurring elements of various types and orders of complexity.The classification of these types and the statement of their conditions of distribution, 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, one can also use the method of presuppositions, on the basis of which particular objects, facts, or units of language are then determined. But here we are faced with two features that make significant adjustments to the use of this method. In contrast to logic and mathematics, in this case the "truth" of the definitions obtained in this way will be sought, i.e., their correspondence to the experimental data. Thus, the interdependence of the premise and inferential knowledge is established: the premise determines the conclusion (the definition of a particular linguistic object in terms of the premise), but if the conclusion does not correspond to the data of experience, then the premise itself needs to be corrected. But adjustments of the presupposition of this kind have nothing in common with the translatability into equivalent forms, which, as noted above, is permissible in mathematics, since they are determined not by formal considerations, but by the data of experience. All of the above gives reason to conclude that the very concept of a premise and the freedom to choose it have a specificity in linguistic analysis, which cannot be ignored when using the deductive method in linguistics.

Linguists cannot use the "if" or "let's" method with such freedom as mathematicians. Their freedom of premises is very strictly limited. The history of the science of language knows many changes in "points of view", or, in other words, in the initial premises, which were prompted by the discovery of new facts, the spread of general scientific ideas to linguistics, or even the formation of original theories. But for the linguist, in all such cases, the change of "if", or the initial premise, is the change of the whole scientific concept. Therefore, the linguist does not say "if", but postulates his understanding of the premise, i.e., in fact, the understanding of the subject of his research, and, based on this understanding, he gives a definition of private units of the language, checking the "truth" of these definitions with the data of experience. The latter circumstance, due to the interdependence of the premise and the conclusion in linguistics, serves as a means of verifying the legitimacy of the premise itself, which is at the beginning of a linguistic analysis that is deductive in form. So, if we turn to specific examples, in the past language was interpreted as a natural organism (by Schleicher), as an individual psychophysiological activity (by neogrammarists), etc. Research practice based on these concepts has shown their insufficiency. Today, the initial premise of linguistic analysis is the postulate that language is a system of signs*. It is subject to the same test of experience and practice as any other concept in the science of language.

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

Already these preliminary and most general considerations show that deductive methods are by no means contraindicated in linguistics, but their application requires compliance with specific conditions. It is these specific conditions that impose certain restrictions on the mechanical transfer of the methods of logic and mathematics to the field of linguistics. However, if we confine ourselves to such a general statement, much remains still unclear. That is why it is necessary to deepen the issue we are considering and, in order to reinforce potential conclusions, turn to the practice of applied linguistics, where the legitimacy of the premises and the correspondence to the experimental data of the conclusions made on their basis are most clearly manifested.

4

The relationship between language and logic is very peculiar. Representatives of the empirical sciences, which include linguistics, study a particular object or phenomenon in order to describe or explain it. They formulate their results in a language called the object language. The logician wields proofs, inferences, judgments, etc., but they are available to him only in linguistic form. Thus, it turns out that the logician is one step further from the real world than the representatives of the empirical sciences. His analysis is directed not directly at the real object studied by the empirical sciences, but at their language*. In other words, he investigates the language and formulates the results obtained in a language that is called a metalanguage.

* ("The logical analysis of scientific knowledge," P. V. Tavanets and V. S. Shvyrev write in this connection, "is primarily and directly an analysis of the language in which this knowledge is expressed." See the article "The logic of scientific knowledge" in Sat. "Problems of the logic of scientific knowledge", M., 1964, p. 161)

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

The concepts of truth and meaning belong to the realm of semantics. Through these relations, the truth or falsity of a sentence is determined: if the sentence describes objects correctly, it is true, and if it is wrong, it is not. But linguistic expressions can enter into relations other than those that exist between the objects they designate. In addition, offers may enter into relationships with other offers. The task of the logician is to find out the nature of the relationship between linguistic expressions and sentences and to lay down rules for determining whether the procedure prescribed in a given case is followed or not. When solving the last question, the logician does not refer to the objects described by the sentence. He is interested in the linguistic form, not its content, which, of course, does not prevent its meaningful interpretation, resulting in a formalized language. A formalized language can be represented as an abstract system, such as a predicate calculus.

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

If a logician, occupied with the study of linguistic forms and the relations existing between them, can remain within the syntactic level, operating with terms that are not meaningful, then the linguist cannot do this. All levels of natural language (with the possible exception of the phonemic one) are meaningful and therefore unthinkable outside of semantics. Moreover, natural language does not exist outside of pragmatics, which cannot be easily detached from it for the simple reason that in the speech act it is constantly transpolated into semantics. Therefore, a natural language is always an interpretation, and, moreover, a two-stage one, since it is connected with both semantics and pragmatics * . And this interpretation does not yet lend itself to any formalization.

* (Wed Niels Bohr's remarks on mathematical language, where "the unambiguity of definitions necessary for an objective description is achieved by using mathematical symbols precisely because in this way the references to the conscious subject that permeate everyday language are avoided" (Nieles Bohr, Atomic Physics and Human Cognition, M. , 1961, p. 96).)

Let us now pass to the second level, when an interpretation is attributed to the calculus by means of semantic rules. And in this case, we will get an education that is in no way comparable to natural language. True, here we are dealing with meaningful terms, but in logical and natural language they build their relationship to "truth" on completely different grounds. As A. Tarsky writes, "true", "in any case in its classical interpretation", is such insofar as it "coincides with reality" * . But this criterion of "truth" actually applies only to natural languages, which are always oriented towards reality. The situation is different in logical semantics. Semantic analysis relies only on the logical interpretation of the system and involves the establishment of certain rules that formulate the truth conditions. He prescribes a consequence of these rules, without answering the question to what extent "coincidence with reality" takes place here. In addition, the focus on reality itself is carried out in natural language not directly, but through a person, which again makes it necessary to turn to the third level - the pragmatic one. “The transition to the semantic level,” P. V. Tavanets and V. S. Shvyrev state, “is not in itself a return to the living language in its concreteness, as it might seem at first glance, due to the the essence of language as the “immediate reality of thought.” In fact, the original scheme of semantics “language-reality” does not yet give a concrete image of language as the immediate reality of thought, for the simple reason that language is connected with reality not by itself in some mystical way, but through a person, through his actions, his behavior.Therefore, in fact, a concrete idea of ​​language as a carrier of thought can be achieved only at the level of its pragmatic analysis according to the scheme "language - human actions with language and on the basis of language - reality" **.

* (A. Tarski, Grundlegung der Wissenschaftlichen Semantik. "Actes du Congres International de Philosophie Scientique", 1936.)

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

But that's not all. Concerning the issue under consideration, V. M. Glushkov writes: “A living human language can be considered as a formal language only after a strict system of rules has been formulated that makes it possible to distinguish expressions that are permissible in the language from all other expressions, that is, meaningful sentences from meaningless " * . Explaining the difficulties that arise in the formalization of a natural language, he further points out that "no fixed formalized language can be adequate to a living human language, since the latter, unlike the first, is constantly developing and improving. Therefore, any formalization of any living human language is only more or a less successful instant cast of it, losing its resemblance to the original as the latter develops" ** . If it all boiled down to just this, then it would be half the trouble. Applied linguistics thinks out from the moments of the development of the language, tends to consider it as a completely stable system, and yet it is not possible to achieve the formalization of a natural language. This happens for a very simple reason. The formal system and natural language base their effectiveness on polar opposite qualities. Any formal system is always identical to itself. It is this quality that makes it possible for it to perform its functions in all specific cases of its application. And natural language - in terms of its content, its semantics, or, as it is customary to say in these cases, in its informative terms - is never identical to itself. It is this ability that makes it possible to function in all specific cases of its application. Remaining the same language, it is always different in different situations. At the same time, he has neither explicit nor formative rules, nor the rules of "truth", nor transformational rules for determining which of the potential meanings or shades of meanings a given word will receive in a given situation. Moreover, almost any word of a natural language can acquire a meaning that is not fixed in any language - it can, having arisen, gain a foothold in the language, but with the same success, like a quick flame, flashing, get lost in the linguistic "space" and go out. And with all these qualities, natural language turns out to be an amazingly perfect tool that allows you to achieve complete mutual understanding regarding the most complex concepts, and in any situation. Why is this happening?

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

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

Apparently, the answer to this question should be partially sought in one thought of the founder of semiotics Ch. Pierce, which he persistently repeats in many of his works. It can be interpreted like this. In modern linguistics, language is usually defined as a system of signs. This is the basic premise for all linguistic analysis. If this is so, then language is not just a system of signs, but a system of mutually interpreting signs that exist in the language insofar as they are interpreted in other signs. C. Peirce formulates it as follows: "No sign can function as a sign if it is not interpreted in another sign. Therefore, it is absolutely essential for a sign that it acts on another sign" * . And elsewhere: "The whole purpose of a sign is that it will be interpreted in another sign" ** . And perhaps the most important: "A sign is not a sign, unless it translates itself into another sign, in which it receives a more complete development" ***.

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

** (Ibid e, §. 191.)

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

Consequently, natural language is a system of signs that, through mutual interpretation, are able to respond to all human needs in semantic expression. But one important caveat is needed here. After all, all the needs of this kind are determined by the attitude of a person to the phenomena of the external world and the social environment in which his life takes place. Due to this circumstance, transformational semantics, if it could be created, cannot be based only on the rules of mutual interpretation of signs, be of a closed and finite nature. It turns out to be a derivative of a very large number of quantities that in every possible way oppose formalization * .

* (P. Jacobson states in this connection: "We can build a purely linguistic semantics if we accept Peirce's position that the essential feature of each linguistic sign is that it can be translated by another linguistic sign, more developed, more explicit, or, on the contrary , a more elliptical sign of the same or another language system. It is thanks to this translatability that the semantic invariants that we are looking for in the signifier are revealed. Thus, we get the opportunity to solve the semantic problems of the language also with the help of distributive analysis "(speech at the 1st International Symposium "Sign in the system of language", Erfurt, GDR, 1959). Quoted from the book: V. A. Zvegintsev, History of linguistics of the XIX - XX centuries in essays and extracts, part 2, M., 1965, p. 398.

In connection with the foregoing, 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 a problem can be solved in mathematics, it must be formulated in precise terms - this very formulation is a prerequisite for a successful solution of the problem. In this case, as already mentioned, a mathematician can freely transform a given formulation of the problem into an equivalent version - mathematics has the appropriate means for this. Already at this primary stage of the research methodology, linguistics differs significantly from mathematics. When formulating his problems, the linguist has at his disposal a certain amount of observed empirical data, to which he cannot always give an exact formulation, but which, willy-nilly, he must, willy-nilly, make the basis of his research, already in the process of this research itself. In order not to go far beyond examples, we can refer to the linguistic meaning, which forms the basis of all work in the field of automatic processing of speech information, but at the same time is defined very vaguely and contradictorily. It is this circumstance that forces researchers in this field to constantly change their strategy.

But now the research has begun and some solution has been reached. What does this mean in relation to logic and mathematics and in relation to linguistics? Logic, as mentioned above, makes it possible to explicitly represent the conclusions implicitly present in the premise, but it does not have rules, the use of which can guarantee that the desired solution will be obtained, since it is not a means of reaching new conclusions, but only a technique. determining their correctness. She is not the magic key to all mysteries. It is quite obvious that if logic had such rules, then there would be no unsolved problems. It would be enough to apply a certain set of logical rules, and we would automatically receive a ready answer to any question that torments us. In the light of what has been said, the concept of the determination of a problem or task also acquires a specific meaning.

In logic and mathematics, any final result is recognized as true if no formal rule has been violated in the process of proof. Since different ways of proof are possible in this case, the existence of different solutions is admissible. But all of them can be subject to verification from the point of view of the requirement of logic or mathematics. The situation is different in linguistics. It does not have an apparatus with which to verify or prove the correctness of the conclusions drawn. Accordingly, the truth of the decisions reached is also determined - it is established not by formal rules, but by its correspondence to the data of experience. Under these conditions, one would theoretically expect a single final solution. However, in practice, as contradictory linguistic definitions of even the main categories of language testify, this is not the case. A certain subjectivity of assessments is always present in this case, and to a certain extent it is determined by the amount of facts (and, of course, their nature) at the disposal of the researcher. It follows that the "truth" of a solution in linguistics is always given in some approximation and is not deterministic, but probabilistic.

Under these conditions, it is very important to test the correctness of linguistic definitions and interpretations on the basis of objective criteria. The possibility of such verification is provided by a wide area of ​​applied linguistics, where natural language is opposed by a machine, representing the interests of logic and mathematics in this opposition.

5

A digital computer is used to solve practical problems of applied linguistics. It is able to perceive, store, transmit, regroup and issue information. It interprets and executes a set of commands (command program), and also modifies them in the process of executing a task. It is able to solve very complex problems, but the entire process of transition from task to solution must be exhaustively and consistently described in terms of a sequence of basic elementary operations. Information is entered into the machine using a two-digit (binary) code, or language. The machine operates on words encoded in this way, corresponding to the basic logical connections or functions of the propositional or predicate calculus. A machine can solve complex mathematical problems precisely because it is possible to reduce complex mathematical operations to a sequence of arithmetic operations, and these latter, in turn, to logical operations. Therefore, a digital computer can be considered as a logical machine.

Thus, whatever the complexity of the task, the machine solves it with the help of a sequence of elementary operations, the program of which must be formulated absolutely unambiguously (consistently), accurately, in detail and exhaustively. In other words, it should not go beyond the limits set by the logical propositional calculus, and when we ask ourselves whether a machine can cope with the processing of information contained in natural languages, we first need to find out to what extent the logical propositional calculus is adequate model for natural language.

Given the specifics of the digital computer described above, the first thing to do in order for the machine to "understand" the task and start processing speech information in accordance with this task is to reformulate the information contained in natural language into logical language. The point, therefore, is the translation of natural language into the language of the logical propositional calculus. At the same time, as Bar-Hillel has shown, one has to face such difficulties that paint the prospects for automatic processing in a very gloomy light, unless the whole direction of the search for a solution to this problem is changed. At the very least, we will have to reckon with the following obstacles, for which we do not yet have the necessary means to overcome.

* (Y. Bar-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 propositional calculus is too poor to be able even with a distant approximation to reformulate a natural language, which is incredibly complex in its semantic structure, has a huge amount of redundant elements and, most importantly, is often characterized by such vagueness and indefiniteness in expression. "meaning" that no two-valued logic can cope with the creation of an artificial counterpart of a natural language * . True, logic, as pointed out, deals only with linguistic form. But since it is a matter of automatic processing of information, it is necessary to be able to distinguish between semantic information, and if this cannot be achieved using the logical means at our disposal, then how can we get confidence that our translation of natural language into logical is correct?

* (Ch. Hockett's article "Grammar for the Hearer" gives many examples of such difficulties in the "natural" understanding of a sentence, which are resolved by subsequent and far-reaching steps of analysis (Ch, Hockett, Grammar for the Hearer, "Structure of Language and its Mathematical Aspects" , Providence, 1961, pp. 220-236).)

B. The machine cannot take into account what Bar-Hillel calls "general background of information", which in fact remain outside the boundaries of natural language and therefore cannot be translated into logical language. Linguists in these cases speak of an extra linguistic context (frame of reference), which inconspicuously for us, but in a very decisive way, corrects or even completely rethinks all our words. After all, even such a simple phrase as "I will return before dark", for its accurate understanding and determination of the temporary indication contained in it, at least requires prior knowledge of when, where it was uttered and at what time of the year. Preliminary information of this kind alone is often the only means for elucidating those intra-phrasal relations that neither the propositional calculus nor the predicate calculus is able to cope with. So, taking for example two sentences that flashed in the newspapers:

Postgraduate student of the university from the city of Kursk;

Honored innovator of Siberia, -

we see that each of them can be interpreted in two ways. If we adhere only to formal grammatical features, then the first sentence can be equally well understood as "A graduate student from a university located in the city of Kursk" and as "A graduate student of a university living in the city of Kursk (or originating from the city of Kursk)". And the second sentence can be interpreted both as "Honored innovator, whose field of activity is Siberia" and as "Honored innovator, who is a resident of Siberia." And only preliminary knowledge (preliminary information) that is not expressed in any way in the sentences, stating that there is no university in the city of Kursk and that "honored innovator" is an honorary title awarded in the Soviet Union by individual administrative districts, makes it possible to correctly understand these proposals. If you look closely, then almost every phrase of the spoken language is very solid and ramified preliminary information, which is self-evident for a person, but lies beyond the "understanding" of a machine that knows neither clan nor tribe.

B. The machine cannot make intratextual semantic conclusions that extend over several sentences (and sometimes even intentionally for a whole story, so as not to completely reveal its character or plot move). The Dutch linguist A. Reichling drew attention to this circumstance, illustrating his idea with the following example. Suppose we are reading a story that begins with the sentence "I am playing with my brother." If we stop there, then we will not have any data at our disposal to clarify how this phrase should be understood, what kind of game we are talking about here. After all, you can play for money (cards, etc.), on a musical instrument, in a theater or cinema, with toys, football, play for fun, play with a person and his fate, etc. But here we read further: " I said this when Wilhelm met me one day in a bar." Now we can more likely conclude that, apparently, we are talking about a game for money. But still there are other possibilities. It follows: "My brother came to the table, and the dice were thrown." It is now clear which game is being referred to, although nowhere in the text is an exact indication of the actual meaning of the word "game" given. We guessed about him by the totality of those external signs that are given in the text in different sentences. These signs follow here one after the other, but in the written narrative they can be significantly separated from each other. A person can choose them from a broad linguistic context (in this case, we are dealing with it), compare and then make an appropriate conclusion. The machine is deprived of this possibility.

* (At a colloquium organized in 1961 by the Stichting Studiecentrum voor Administrative Automatisering. There is also a German translation of the report: A. Reichling, Moglichkeiten und Grenzen der mechanischen Ubersetzung, aus der Sicht des Linguisten, "Beitrage zur Sprachkunde und Informationsverarbeitung", Heft 1, Wifcn, 1963.)

But maybe she doesn't need it? Indeed, when translating these sentences into German or French by machine, there are no particular difficulties (but, of course, difficulties will arise when translating other sentences). When translating into German, we can use literalism: Ich spile mit meinem Bruder. Similarly, in French, we can start: Je joue avec... Even when translating into English, difficulties of grammatical order arise, since in the text given there is no indication of which form the machine should choose: 1. I am playing with my brother, 2. I play with my brother or 3. I "ll play with my brother? And it's really bad when translated into Spanish, since the machine will have to choose between at least three verbs: jugar, tocar or trabajar.

Here logical language is helpless.

D. The machine 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, which are also capable of transforming into semantic ones (and the rules for such a transition have not been studied and are largely arbitrary). So, for example, oral speech has such a suprasegmental superstructure as intonation. It is now possible to classify intonation according to functional types and distinguish between interrogative, narrative and other intonations. However, it is absolutely indisputable that intonation does not exist independently of sentences; it certainly interacts with the meaning contained in them. In support of this statement, it suffices to refer to a rhetorical question, which is a question only in its external structure, but is not a question in meaning: it does not require an answer from the hearers. Thus a new kind of difficulty arises, which the logical language has no way of coping with.

E. The method of automatic processing of speech information (and, in particular, machine translation) is based on the assumption that any sentence, and the language as a whole, is "disassembled" into a certain number of elementary semantic units (words), from which it can then be, according to certain rules, "collect" given sentences. A consequence of this assumption is another one, according to which the meaning of a sentence is the arithmetic sum of the meanings of its constituent words. Here, mathematics is taken as a model, where the most complex operations that a computer performs are ultimately reduced to extremely elementary ones. But in language we are faced with an almost completely opposite picture. The point is not only that in different languages ​​sentences are semantically "understood" into parts in different ways. For example:

The girl is walking. The girl is standing. The hat suits the girl. Das Madchen geht. Das Madchen steht. Der Hut steht dem Madchen(literally: The hat is worth the girl).

The point is also that even within the same language, most often there is no arithmetically correct relationship between the meaning of a sentence and the meanings (meanings) of its constituent words. On this occasion, E. Benveniste writes: "A sentence is realized through words. But words are not just segments of a sentence. A sentence is a whole, not reducible to the sum of its parts, the meaning inherent in the whole is distributed to the entire set of components" *. This is not about idiomatic expressions (such as: "to do carelessly", "rub someone's glasses", etc.), but about the most common sentences. Let's take an elementary example:

Wait! - I'm going to the theatre.

Can it be argued that the meaning of this sentence is the arithmetic sum of the meanings of the words: wait, go, theater, I, in? Based on such an arithmetic representation, we should expect that any combination of these words, presented in a grammatically correct sentence, will retain the same meaning - after all, the sum of the terms does not change from a rearrangement of the place of the terms. But let's try to slightly modify this proposal:

I'm going to the theater - wait!

We see that in its meaning this second sentence differs significantly from the first.

* (E. Benveniste, Les niveaux de G analyse linguistique, "Preprints of Papers for the Ninth International Congress of Linguists", Cambridge, Mass., 1962, p. 497)

This is one of the most elementary examples, and if we turn to more complex ones, then the impotence of any transformational rules that should govern such cases becomes especially obvious. It cannot be otherwise: after all, a sentence is a sequence of monosemes, and a monoseme (see the section "System of Semantic Research"), as a syntactic configuration, is more than a word. This circumstance leads to the fact that the sentence, as a sequence of monosemes, is a sequence of mutually determined elements, connected with each other in a semantic relation into an inextricable chain, which can be schematically and in a highly generalized form as follows *:

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

It is precisely because of these features of the sentences that there is a qualitative difference between the last and the words. If words can be defined as signs, then sentences undoubtedly go beyond the sign level.

The question of the "decomposability" of language and sentences rests on a more general one. There are structures capable of performing their functions only in their complex composition. When you try to decompose them into smaller parts or reduce them to more elementary structures, they actually disintegrate, cease to exist as such, lose the qualities inherent in their complex composition. Such is the language. W. Humboldt understood this (approaching this issue, however, from a slightly different angle), when he wrote: “In order for a person to understand at least one single word, not just as a spiritual impulse (i.e., reflexively. - V. Z.), but as an articulate sound denoting a concept, the entire language and in all its connections must already be embedded in it. There is nothing singular in the language, each of its individual elements manifests itself only as part of the whole "*. Translating this judgment of W. Humboldt into the language of modern science, we get the following formulation belonging to M. Taube: "... it is easy to understand that language as a system of meaningful symbols, oral or written, is not a formal system and cannot be reduced to it without destroying its true nature... When a language is formalized, it ceases to be a language and becomes a code" ** .

* (W. Humboldt, On the comparative study of languages ​​in relation to different epochs of their development. Quoted from the book: V. A. Zvegintsev, History of linguistics of the XIX - XX centuries in essays and extracts, part I, M., 1964, p. 79.)

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

But even if it is possible to cope with the listed linguistic difficulties, there are still obstacles of a proper logical order - in this case we are talking about the so-called "resolution rules" (decision rules). After all, if we want to be sure that the machine will act logically flawlessly, we must provide it with a set of rules, following which it can consistently go from the source information to the required conclusions. As applied to propositional logical calculi, we have such rules, but for more complex logics there are no such rules, and, moreover, there are reasons to believe that such rules cannot be found. If we focus on the rules that we already have at our disposal, then using them will make the process of resolution so complicated (even with the use of improved computers) that the game will not be worth the candle * .

* (To show what work a step-by-step computer has to do, A. L. Samuel turns to the example of a game of checkers. He writes: “In order to make a computer play checkers, we must first of all depict the position of the checkers on the board in a way that the computer could remember. Then the consequences of each of the available moves must be analyzed by looking into the future, as a person would generally do. , considering each initial move in turn, then all the opponent's possible retaliatory moves, then for each of them all counter-answers, and so on. the molecular nature of matter and the finite speed of light, then it would take such a computer many centuries, and perhaps longer than even the age of the universe, to make its first move" (A. L. Samuel, Artificial Intelligence: Progress and problems. Appendix to the book: M. Taube, Computing machines and common sense, Moscow, 1964* pp. 140-141).)

In this form, the problem of applying logical and mathematical methods in the science of language is drawn based on the data of applied linguistics. What are the conclusions? The conclusions have already been formulated above - logical analysis allows a combination of inductive methods with deductive ones, but when we talk about the use of deductive methods in linguistics, everything should not be reduced to the blind subordination of linguistic research to logical-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 a natural language that a sufficiently complete (in informative terms) translation of the second into the first is impossible. Does this mean that in linguistics (and, in particular, applied) the use of logico-mathematical methods should be abandoned? Of course not. But one should not overestimate their capabilities. While they are quite modest. And in order not to be unfounded here, let's turn to the testimony of mathematicians and logicians, who in the practice of their work have to apply their knowledge to the study of natural language.

Here is what the mathematician says: “The help of mathematics in the study of natural language is still far from obvious ... Before we can think about using mathematics for calculus, it is necessary to determine the boundaries and functions of linguistic units ... This is a non-mathematical problem, it is part of inductive methods in linguistics.

It turned out that mathematics does not replace empirical methodology, although some linguists strive to do so. On the contrary, only after the units and relations of natural language have been established by the inductive method and appropriately confirmed (verified), will the necessary conditions be created for a realistic application of mathematics to natural language. At the same time, mathematicians will either find that they are dealing with a new manifestation of what is essentially already familiar to them, or they will receive 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 the article in the same book: W. Ksrush, The Use of Mathematics in the Behavioral Sciences, pp. 64-83.)

And here is what the logician 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 tool for linguistic analysis, not as a set of rules for deriving conclusions, it makes real promises" * . And he further establishes which research strategy is more preferable: “Problems should not be solved by rigorously following a set of rules established by a logician, but rather by using heuristic techniques ** ... An empirical inductive approach to automatic processing of speech information should be preferred, with in which rough rules are sought for solving information problems.One should not try to translate ordinary language into logical language for the purpose of further processing it, but rather look for heuristic-type rules that will allow one to master natural language.One should stop looking for absolute certainty and turn to approximate methods, which, with the accumulation of experience, will be refined and improved. We prefer to consider approximations in the same way that theory is considered in science, where modifications and improvements are made on the basis of data obtained as a result of experiment "***.

* (M. Maron, A Logician's View of Language - data Processing, cited book, p. 144.)

** (A fairly clear idea of ​​the heuristic technique is given by A. L. Samuel. Contrasting it with the formal technique of the logical procedure, he writes that one could instead apply a technique "where a number of more or less arbitrarily chosen procedures are examined in a rather incomplete guesswork, we will not arrive at a satisfactory proof.In both of these cases, we can sometimes come up with a correct or even a very good answer in an amazingly short period of time, but at the same time there is no certainty that we will ever get a solution, as well as the confidence that the solution presented to us is the best.This method of problem solving has been called a "heuristic" procedure in contrast to the application of an "algorithm" ... Heuristic problem solving, when it is successful, must, of course, be regarded as a higher mental activity than problem solving by means of a more or less automatic procedure. Quoted from the Russian translation: A. L. Samuel, Artificial Intelligence: Progress and Problems. Appendix to the book: M. Taube, Computing machines and common sense, M., 1964, pp. 136-137.)

*** (M. Maron, op. cit., pp. 143-144,)

These are the general conclusions. They say that linguists play a leading role in joint work with logicians and mathematicians. It is the duty of linguists to prepare language material in such a way as to make it accessible to processing by logical and mathematical methods. It is in this direction that one should look for a realistic combination of inductive and deductive methods in linguistics. And when, when solving problems of applied linguistics, we are talking about heuristic hypotheses, then they should first of all come from a linguist, since he is closer to the language and, according to his position, is obliged to know and understand it better.

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 19th – 20th Centuries
1.2. Application of mathematical methods in linguistics in the second half of the twentieth century
Conclusion
Literature
Introduction
In the 20th century, there has been a continuing trend towards the interaction and interpenetration of various fields of knowledge. The boundaries between individual sciences are gradually blurring; there are more and more branches of mental activity that are "at the junction" of humanitarian, technical and natural science knowledge.
Another obvious feature of modernity is the desire to study structures and their constituent elements. Therefore, an increasing place, both in scientific theory and in practice, is given to mathematics. Coming into contact, on the one hand, with logic and philosophy, on the other hand, with statistics (and, consequently, with the social sciences), mathematics penetrates deeper and deeper into those areas that for a long time were considered to be purely "humanitarian", expanding their heuristic potential (the answer to the question "how much" will often help answer the questions "what" and "how"). Linguistics was no exception. The purpose of my course work is to briefly highlight the connection between mathematics and such a branch of linguistics as linguistics. Since the 50s of the last century, mathematics has been used in linguistics to create a theoretical apparatus for describing the structure of languages ​​(both natural and artificial). However, it should be said that it did not immediately find such a practical application for itself. Initially, mathematical methods in linguistics began to be used in order to clarify the basic concepts of linguistics, however, with the development of computer technology, such a theoretical premise began to be applied in practice. The resolution of such tasks as machine translation, machine information retrieval, automatic text processing required a fundamentally new approach to the language. A question has arisen before linguists: how to learn to represent linguistic patterns in the form in which they can be applied directly to technology. The term “mathematical linguistics”, which is popular in our time, refers to any linguistic research that uses exact methods (and the concept of exact methods in science is always closely related to mathematics). Some scientists of past years believe that the expression itself cannot be elevated to the rank of a term, since it does not mean any special “linguistics”, but only a new direction focused on improving, increasing the accuracy and reliability of language research methods. Linguistics uses both quantitative (algebraic) and non-quantitative methods, which brings it closer to mathematical logic, and, consequently, to philosophy, and even to psychology. Even Schlegel noted the interaction of language and consciousness, and the prominent linguist of the early twentieth century, Ferdinand de Saussure (I will tell about his influence on the development of mathematical methods in linguistics later), connected the structure of the language with its belonging to the people. The modern researcher L. Perlovsky goes further, identifying the quantitative characteristics of the language (for example, the number of genders, cases) with the peculiarities of the national mentality (more on this in Section 2. 2, "Statistical Methods in Linguistics").
The interaction of mathematics and linguistics is a multifaceted topic, and in my work I will not dwell on all, but, first of all, on its applied aspects.
Chapter I. History of the Application of Mathematical Methods in Linguistics
1.1 The formation of structural linguistics at the turn of the XIX - XX centuries
The mathematical description of the language is based on the idea of ​​language as a mechanism, which goes back to the famous Swiss linguist of the early twentieth century, Ferdinand de Saussure.
The initial link of his concept is the theory of language as a system consisting of three parts (language itself - langue, speech - parole, and speech activity - langage), in which each word (member of the system) is considered not in itself, but in connection with others. ...

I MATHEMATICAL ASPECTS OF LANGUAGE STRUCTURE

AT.Zvegintsev APPLICATION OF LOGICAL AND MATHEMATICAL METHODS IN LINGUISTICS

].

There is no doubt that the use of mathematical and logical methods in linguistics was largely stimulated by the tasks of applied linguistics. If attempts were made to apply these methods to solving problems directly related to the field of theoretical linguistics, for example, to distinguish between the phenomena of language and speech, 1 then in the future (although, perhaps, not always clear and close), they still had in mind the needs of applied linguistics.

The success of using these methods in a completely new field, from a general point of view, is largely determined by the answer to the question of the extent to which it is permissible to identify a logically correct language with a natural language, or, in another formulation, is it possible to reduce the second to the first 2 . The answer to this question is usually given in practical form. - by constructing statistical, information-theoretic, set-theoretic, probabilistic and other models of the language, which, however, are not always focused on specific tasks. When constructing models of this kind, their authors often proceed from the assumption (obvious from their point of view) that any application of a formal logical or mathematical apparatus to linguistic description and research automatically contributes to their improvement. By this is good

1 See . G. Herdan, Language as Choice and Chance, Gronigen, 1956.

2 Wed G. Curry’s remark: “The fact that there is a close connection between mathematics and logic, on the one hand, and language - on the other hand, it became obvious quite a long time ago, and now this fact has become the focus of attention in a stricter sense...” (see below, p. 98).

said Warren Plath in his review of the work of mathematical linguistics: “If we consider language models as abstract systems of discrete elements, then various mathematical concepts and methods can be applied to them, ranging from the elementary idea of ​​number to complex logical, statistical and set-theoretic operations. However, the notion that any use of numbers and mathematical operations to describe such systems of elements makes statements more "exact" or more "scientific" is completely erroneous. First of all, it must be shown that the new system thus obtained is a more satisfactory model than the original system, either in the sense that it makes it possible to formulate simpler and more general theoretical statements about some aspects of the modeled area, or because operations on the model shed light on the results of the corresponding operations in the modeled area. One of the biggest dangers associated with building mathematical models of a language, especially quantitative ones, is that indiscriminate use of the mathematical apparatus inevitably leads to meaningless and disorienting results. Therefore, it is necessary to clearly understand that a prerequisite for the enrichment of linguistics with the help of mathematics is not only knowledge of the relevant areas of mathematics, but, in addition, a deep understanding of the essence of linguistic problems, the solution of which should be directed to mathematical methods.

In order to avoid as far as possible the danger indicated by Warren Plath, it is necessary to have not only purely empirical attempts to answer the question formulated above, but also to strive for its general theoretical understanding. In fact, the question of the reducibility of a natural language to one or another of its logical-mathematical models or interpretations is the main issue of the theory of applied linguistics, the need to create which is felt more and more urgently. To resolve this issue, first of all, the nature of those phenomena that constitute the subject of study, on the one hand, logic and mathematics, should be considered.

3 See the article Fee in this collection, p. 202.

and on the other, natural language, and then also the possibilities of those methods that each of these sciences uses. Already from a comparative study of these points it will be possible to draw some general conclusions. The latter may not be useless for all those who, by necessity, have to carry out their research at the intersection of these sciences.

To a certain extent, this goal was also pursued by the symposium "The Structure of Language and Its Mathematical Aspects" held by the American Mathematical Society. Selected papers from this symposium constitute the following section. But all of them, as it is clear from the very title of the symposium, affect only individual and in some cases very particular aspects of the problem of interest to us. Although in their totality they create sufficiently reasoned prerequisites for answering our question, they still lack a clear and unambiguous formulation of the necessary conclusions. In many ways, the participants of the symposium continue the line of empirical attempts to resolve this issue, by no means obsessively offering their experiments to the attention of linguists in the hope that the latter will themselves figure out how suitable the hypotheses and solutions put at their disposal will turn out to be suitable for the purposes of linguistics.

2.

It seems that we already have an unambiguous answer to our question. Thus, N. D. Andreev and L. R. Zinder write: “The mathematical representation (model) of languages ​​is by no means identical to the language itself” 4 . This idea is also developed by the author of the book "Models of Language" II Revzin, who points out that the result of modeling can only be "a more or less close approximation of the data of concrete reality" 5 . However, to say so means to say nothing yet, since it remains

4 N. D. Andreev, L. R. Zinder, The main problems of applied linguistics, "Problems of Linguistics", 1959, No. 4, p. 18

5 I. I. Revzin, Models of language, Moscow, 1962, p. 8. By the way, the expression “close approximation” is a direct tautology: close approximation.

not disclosed why this is so, and whether one should still resort to the method of mathematical and logical modeling, and if so, to what extent and for what purpose.

Before proceeding to address these issues, it is first necessary to establish which sciences - inductive or deductive - include linguistics, logic and mathematics. As for the last two sciences, their position is clear - they undoubtedly belong to the deductive sciences, which rely on inference in their research methodology. Linguistics is traditionally defined as an empirical science, since it is believed that its main scientific goal is the description of facts. This means, apparently, that linguistics should be assigned to the field of inductive sciences. This also means that, in an effort to use the formal apparatus of logic and mathematics in linguistics, they are trying to apply deductive methods of research in inductive science.

In recent years, however, the inductive nature of the science of language has come into question either directly or indirectly. L. Elmslev did this in the sharpest form. True, the terminology he uses is very inconsistent and, in particular, is characterized by a peculiar and very personal understanding of the terms deduction and induction (in fact, he interprets them in the opposite sense). However, the foundations of his linguistic theory leave no doubt about its methodological essence. Thus, he considers it acceptable to use any initial operational definitions, which is typical for deductive sciences. And he himself characterizes his theory in the following terms: “1. Theory in our sense is itself independent of experience. By itself, it does not say anything about the possibility of its application, or about the attitude to experimental data. It does not include the postulate of existence. It is what has been called a purely deductive system, in the sense that it alone can be used to calculate the possibilities that follow from its premises. 2. On the other hand, the theory includes a number of premises which are known from previous experience to satisfy the conditions of application to certain experimental data. These assumptions are the most general and may therefore satisfy the conditions of application to a large number of experimental data” 6 .

As is clear from this statement, L. Hjelmslev seeks to carry out the idea of ​​the dual methodological nature of the objects of linguistic research with a predominant emphasis on their deductive features. He should also be credited with that rather ambiguous way ("on the one hand .., but on the other hand ..."), which has generally become characteristic of the consideration of this issue (and which makes it possible to turn in either direction). The idea of ​​methodological duality of linguistics has recently become widespread and even served as a theoretical basis for formulating the principles of the most recent trend in the science of language. - linguistics of universals (universalism). The "Memorandum on Linguistic Universals" says in this regard: "The study of linguistic universals leads to a whole series of empirical generalizations about linguistic behavior - both still requiring experimentation and those already established. These generalizations are potential material for constructing the deductive structure of scientific laws. However, some and perhaps most of them still have only the status of empirical generalizations, which, in the current state of our knowledge, cannot be correlated with generalizations or deduced deductively from laws of more general significance” 7 . J. Gryanberg expresses himself with no less definiteness in his preface to the collection devoted to linguistic universals. Arguing with the well-known words of L. Bloomfield that “the only legitimate generalizations about language are inductive generalizations,” he writes: “Nevertheless, it seems to be generally accepted that the scientific method should be not only inductive, but also deductive. The formulation of generalizations obtained by inductive research leads to theoretical hypotheses based on

6 L. Elmslev, Prolegomena to the Theory of Language, Sat. "New-in Linguistics", vol. I, M., 1960, pp. 274-275.

7 Memorandum Concerning Language Universals, in Universals of Language, ed. by J. Greenberg, Cambridge, Mass., 1963, pp. 262 - 263.

which, by deduction, further generalizations can in turn be deduced. These latter must then be subjected to empirical verification.

The fact that the history of linguistics consists not only of the accumulation of the facts of a language and their classification, but also of a change in points of view on the language itself, which inevitably implies a difference in approaches to linguistic facts and even their different theoretical interpretations, made some Soviet linguists also come to the conclusion conclusions about the methodological duality of their science. S. K. Shaumyan prefers, however, to speak of the hypothetical-deductive method, and describes its features as follows: “The hypothetical-deductive method is a cyclic procedure that begins with facts and ends with facts. This procedure has four phases:

1) fixing facts that require explanation;

2) putting forward hypotheses to explain these facts;

3) derivation from hypotheses of predictions about facts lying outside the range of facts for the explanation of which hypotheses were put forward;

4) checking the facts that are predicted by hypotheses, and determining the likelihood of hypotheses.

The hypothetical-deductive method is fundamentally different from the inductive method used in such fields of knowledge as, for example, descriptive botany or zoology” 9 . The method of S. K. Shaumyan completely repeats the method of linguistics of universals and J. Greenberg. The only difference is in the name. If, for example, J. Greenberg speaks of a combination of the inductive and deductive method, then S. K. Shaumyan calls his method hypothetical-deductive - the designation is clearly inconsistent for a method that "begins with facts and ends with facts".

The question of where linguistics should be attributed is also asked by I. I. Revzin. "By its very nature,

8 Universals of Languages ​​p. IX.

9 S. K-Shaumyan, Problems of theoretical phonology, M., 1962, cf. 18-19. Regarding the hypothetical-deductive method, see also the article by V. S. Shvyreva, Some questions of the logical and methodological analysis of the relationship between theoretical and empirical levels of scientific knowledge, in the collection “Problems of the logic of scientific knowledge”, M., “ The science", 1964, pp. 66-75 (3rd section of the article).

He answers this question - linguistics must first of all use inductive methods, it describes specific speech acts of specific languages ​​...

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

It follows from this that linguists need not only inductive but also deductive methods of research in order to obtain a system of general knowledge that helps to comprehend the data that is obtained in the analysis of specific languages ​​...

In its deductive part, linguistics, apparently, can be built in the same way as logic or mathematics is built, namely: a certain minimum number of primary, undefined terms is singled out, and all other terms are defined through primary ones. At the same time, some primary statements about the connection of these terms with each other (axioms) must be clearly formulated, and all other statements must be proved, that is, reduced to some other statements” 10 .

Here the method of deduction, embodied in logic and mathematics, acts only as a means of streamlining the "set of speech acts", for the purpose of creating a "system of general concepts". In direct contradiction to this task, however, stands the presentation of the deductive method itself, recommended for use in linguistics. It is completely thought out both from acts and from facts, and for the initial moment of constructing a system of general linguistic concepts, it takes a set of undefined and, apparently, absolutely conditional primary terms, through which all subsequent terms are defined.

This contradiction is not accidental, it lies in the very nature of the sciences we are considering. It would seem that the conclusion that a combination of inductive and deductive methods is permissible in the study of linguistic objects opens the door for the use of logical and mathematical methods in linguistics, and the specific implementation of this conclusion is the creation of numerous

10 I. I. Revzin, Models of language, M., 1962, pp. 7-8.

formal-logical and mathematical models of the language. But, as will be shown below, such a simplified approach cannot give satisfactory results. We can agree that in linguistic research it is permissible and even necessary to combine deductive and inductive methods. In the end, as W. Bröndal wrote, “induction is nothing but a disguised deduction, and behind the pure connections established between the observed phenomena, reality, the specific object of this science, is absolutely inevitably assumed” 11 . But this does not mean that the formal apparatus of logic and mathematics should be unconditionally and mechanically transferred to linguistics without any consideration of the “specific object of this science”. As the same I. I. Revzin rightly notes, “the evidence obtained by deductive means, no matter how irreproachable they may be from a logical point of view, still does not say anything about the properties of the real language described by the model” 12 . And to determine the effectiveness of the models, he recommends turning to the practice, which is machine translation and "other practical applications, linguistics."

And the practice of applied linguistics shows that very strict restrictions are imposed on the use of mathematical and logical methods in the study of linguistic phenomena.

Logic provides an example of the most consistent use of the deductive method. Mathematics largely follows logic in this respect, and so they can be considered together.

Of course, both logic and mathematics do not represent homogeneous systems in terms of their methods and interpretation of goals. So, for example, in relation to logic, we can talk about dialectical, formal, mathematical logic, and in a narrower sense - about subject, semantic, phenomenological, transcendental, or constructive, combinatorial, many-valued,

11 W. Bröndal, Structural linguistics. Cit. on
V. A. Zvegintsev’s book “The History of Linguistics in the 19th and 20th Centuries. in the outline
kah and extracts, part II, M., Uchpedgiz, 1960, pp. 41-42.

12 I. I. Revzin, Models of language, M., 1962, p. 10.

distant, etc. Of necessity, however, we will have to think of all such divisions and talk only about the most general features inherent in logic and mathematics as a whole, and mainly about those that most clearly demonstrate the deductive nature of the methods of these sciences.

Having taken this position, we, therefore, will not turn to inductive logic. We only note that conclusions in inductive logic are not determined by premises - thus they are not tautological. The conclusions in inductive logic are directly dependent on the facts, and these latter are determined by the amount of our knowledge - thus, they are established on a probabilistic basis. Probability is the main methodological tool of inductive logic.

Deductive logic is most fully represented by formal and mathematical logics, which have much in common. Deductive logic is a science that studies human thinking or mental acts from the point of view of their structure or form, abstracting from their specific content. Thus, deductive logic seeks to formulate laws and principles, the observance of which is a prerequisite for achieving true results in the process of obtaining inferential knowledge. The main methodological tool of deductive logic is implication. It receives derivational knowledge without direct appeal to experience or practice, only through the application of the laws of logic. In the process of deduction, the premise conditions the conclusion: if the premise is true, then the conclusion it should be true. Thus, the conclusion is already in the premise, and the purpose of the deduction is to make evident what in the latent state is already contained in the premise. It follows from this that any conclusion obtained by means of deduction is tautological, that is, it is logically empty, although from other points of view, for example, in cases where the formal logical apparatus is used for the purposes of other sciences, it can be new, unexpected and original.

A similar situation takes place in mathematics - the validity of the arguments in it rests entirely on deduction. Moreover, in mathematics, as a rule, any initial point of view, any approach to solving a problem is acceptable - as long as they satisfy the conditions of mathematical deduction. Mathematics has a rich set of such "initial points of view" and "approaches" that the researcher can alternatively use to solve his problem. Mathematical problems are often translated into different equivalent forms, and each of them involves the use of different areas of mathematical theory in order to solve the problem. Thus, a mathematician has virtually unlimited freedom to choose premises - he chooses those that, from his point of view, contain the most promising possibilities for the most simple, unbanal, elegant solution of the problem. His talent and experience are manifested precisely in the successful choice of prerequisites, those “let's say that ...” or “if ..., then”, which are full of mathematical works. Just as in logic, mathematical premises - axioms or postulates - determine the definitions of yet undefined units.

The freedom of choice of premises in mathematics is directly dependent on those non-material units or objects with which it operates - its attention is directed to the relationship between them. Mathematical objects act as symbols expressing the structure of pure relations. A mathematical system can thus be regarded as a set of formal relations that exist only by virtue of the statement of these relations. Of course, in particular for applied purposes, statements of relations can be aimed at embodying in them a correspondence with external reality, which will not have any effect on these statements themselves, rather, on the contrary. Mathematicians do not investigate the "truth" of their axioms, although they require mutual agreement between them. Research within a mathematical system is research and the establishment of connections that make it possible to prove that the fact of theory A implies the fact of theory B. Therefore, the main question in mathematics is not “what are A and B”, but “does A presuppose (or conditions) B? »

The situation in linguistics is completely different - it mainly focuses on the first of these questions, and this does not give it the opportunity to break away from reality; therefore, it operates not with abstract, but with concrete units, although in a number of cases it tends to create abstract objects like the concept of a phoneme or a morpheme. This situation is characteristic not only of traditional linguistics, but is equally characteristic of its latest trends, united under the banner of structuralism. A number of statements have already been cited above, the authors of which, trying to use not only inductive, but also deductive methods (or mathematical and logical methods) in the science of language, could not avoid the need to refer to a real linguistic fact. In addition to them, one more thing can be cited, which brings complete clarity to the issue under consideration. "Linguistic Analysis,- P. Garvin writes in this connection,- basically an inductive process in the sense that it seeks to establish a list of elements or a set of statements from the linguistic stimuli of the informants or from the study of a text. It is based on the assumption that in both of these sources of information it will be possible to recognize regularly occurring elements of various types and orders of complexity. The classification of these types and the statement of their conditions of distribution, obtained as a result of the analysis, form an inductive description of the language” 13 .

In linguistics, of course, one can also use the method of presuppositions, on the basis of which particular objects, facts, or units of language are then determined. But here we are faced with two features that make significant adjustments to the use of this method. In contrast to logic and mathematics, in this case, the “truth” of the definitions obtained in this way will be sought, that is, their correspondence to the data of experience. Thus, the interdependence of the premise and inferential knowledge is established: the premise determines the conclusion (the definition of a particular linguistic object in terms of the premise), but if the conclusion does not correspond to the data of experience, then the premise itself needs to be corrected. But adjustments of the presupposition of this kind have nothing in common with the translatability into equivalent forms which, as noted above, is permissible in mathematics, since they are not conditioned by

13 P. Garvin, A Study of Inductive Method in Syntax, "Word", vol. 18, 1962, p. 107.

formal considerations, but the data of experience. All of the above gives reason to conclude that the very concept of a premise and the freedom to choose it have a specificity in linguistic analysis, which cannot be ignored when using the deductive method in linguistics.

Linguists cannot use the “if” or “let’s” method with such freedom as mathematicians. Their freedom of premises is very strictly limited. The history of the science of language knows many changes in "points of view" or, in other words, initial premises, which were prompted by the discovery of new facts, the spread of general scientific ideas to linguistics, or even the formation of original theories. But for the linguist, in all such cases, the change of "if", or the initial premise, is the change of the whole scientific concept. Therefore, the linguist does not say “if”, but postulates his understanding of the prerequisite, that is, in fact, an understanding of the subject of his research, and, based on this understanding, gives a definition of private units of the language, checking these definitions with experience data. The latter circumstance, due to the interdependence of the premise and the conclusion in linguistics, serves as a means of verifying the legitimacy of the premise itself, which is at the beginning of a linguistic analysis that is deductive in form. Thus, if we turn to specific examples,inIn the past, language was interpreted as an expression of the spiritual essence of a people (by Humboldt), as a natural organism (by Schleicher), as an individual psycho-physiological activity (by neogrammarists), etc. Research practice based on these concepts showed their insufficiency. Today, the initial premise of linguistic analysis is the postulate that language is a system of signs. It is subject to the same test of experience and practice as any other concept in the science of language.

Already these preliminary and most general considerations show that deductive methods are by no means contraindicated in linguistics, but their application requires compliance with specific conditions. It is these specific conditions that impose certain restrictions on the mechanical transfer of the methods of logic and mathematics to the field of linguistics. However, if we confine ourselves to such a general statement, much remains still unclear. That is why it is necessary to deepen the issue under consideration by us and, in order to reinforce potential conclusions, turn to the practice of applied linguistics, where the legitimacy of the premises and the correspondence to the experimental data of the conclusions made on their basis are most clearly manifested.

The relationship between language and logic is very peculiar. Representatives of the empirical sciences, which include linguistics, study a particular object or phenomenon in order to describe or explain it. They formulate their results in a language called the object language. The logician wields proofs, inferences, judgments, etc., but they are available to him only in linguistic form. Thus, it turns out that the logician is one step further from the real world than the representatives of the empirical sciences. His analysis is directed not directly to the real object studied by the empirical sciences, but to their language 14 . In other words, he investigates the language and formulates the results obtained in a language that is called a metalanguage.

From a logical point of view, the basic unit of the language is not a sign and not the object denoted by it, but a sentence, since only in it can a logical process unfold. That is why only a sentence can be true or false. And words by themselves cannot have these qualities. But before we can establish whether a sentence is true or not, we must state that it has a meaning.

The concepts of truth and meaning belong to the field of semantics, which studies the relationship between language and the objects it denotes. Through these relations, the truth or falsity of a sentence is determined: if the sentence describes objects correctly, it is true, and if it is wrong, it is not. But linguistic expressions may enter into relations other than those which

14 “The logical analysis of scientific knowledge,” P. V. Tavanets and V. S. Shvyrev write in this connection, “is first and foremost an analysis of the language in which this knowledge is expressed.” See the article "The Logic of Scientific Cognition" in the collection "Problems of the Logic of Scientific Cognition", M., "Nauka", 1964, p. 161.

exist between the objects they denote. In addition, offers may enter into relationships with other offers. The task of the logician is to find out the nature of the relationship between linguistic expressions and sentences and to lay down rules for determining whether the procedure prescribed in a given case is followed or not. In solving this last question, the logician does not refer to the objects described by the sentence. He is interested in the linguistic form, not its content, which, of course, does not prevent the interpretation of its content, resulting in a formalized language. A formalized language can be represented as an abstract system, such as a predicate calculus.

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

If a logician, occupied with the study of linguistic forms and the relations existing between them, can remain within the syntactic level, operating with meaningless terms, then the linguist cannot do this. All levels of natural language (with the possible exception of the phonemic one) are meaningful and therefore unthinkable outside of semantics. Moreover, natural language does not exist outside of pragmatics, which cannot be easily detached from it for the simple reason that in the speech act it is constantly transpolated into semantics. Therefore, natural language is always an interpretation and, moreover, a two-stage one, since it is connected with both semantics and pragmatics 15 . And this interpretation does not yet lend itself to any formalization.

Let us now pass to the second level, when an interpretation is attributed to the calculus by means of semantic rules. And in this case, we will get an education that is in no way comparable to natural language. Truth,

15 Wed Niels Bohr's remarks on mathematical language, where "the unambiguity of definitions necessary for an objective description is achieved by using mathematical symbols precisely because in this way the references to the conscious subject that permeate everyday language are avoided." (Nile Bor, Atomic physics and human knowledge, M., IL, 1961, p. 96.)here we are dealing with meaningful terms, but in logical and natural language they build their relationship to "truth" on completely different grounds. As A. Tarsky writes, "true", "in any case, in its classical interpretation" is true to the extent that it "coincides with reality" 16 . But this criterion of truth actually applies only to natural languages, which are always oriented towards reality. The situation is different in logical semantics. Semantic analysis relies only on the logical interpretation of the system and involves the establishment on- icertain rules that formulate truth conditions,iHe prescribes adherence to these rules, without answering the question of the extent to which "coincidence" takes place here.irelationship with reality. In addition, the focus on reality itself is carried out in natural language not directly, but through a person, which again makes it necessary to turn to the third level,- pragmatic. “... The transition to the semantic level,- ascertained by P. V. Tavanets and V. S. Shvyrev,- is not in itself a return to a living language in its concreteness, as it may seem at first glance due to the fact that the semantic function of language is, as it were, the essence of language as the “immediate reality of thought”. In fact, the original scheme of the semantics "language - reality” does not yet give a concrete image of language as the immediate reality of thought for the simple reason that language is connected with reality not in itself in some mystical way, but through a person, through his actions, his behavior. Therefore, in fact, a concrete idea of ​​language as a carrier of thought can only be achieved at the level of its pragmatic analysis according to the “language - human actions with and based on language - reality" 17 .

But that's not all. Regarding this issue, M. | Glushkov writes: “A living human language can be considered as a formal language only after a strict system of rules has been formulated that allows

16 A . T a g s k i, Grundlegung der Wissenschaftlichen Semantik
(Actes du Congrès International de Philosophie Scientifique, 1936).

17 See the article "The logic of scientific knowledge" in the collection "Pro-
problems of the logic of scientific knowledge”, M., “Nauka”, 1964, page 16.

to distinguish expressions allowed in the language from all other expressions, that is, meaningful sentencesFromsenseless" 18 . Explaining the difficulties that arise in the formalization of a natural language, he further points out that “... no fixed formalized language can be adequate to a living human language, since the latter, unlike the former, is continuously developing and improving. Therefore, any formalization of any living human language is only a more or less successful instant copy of it, which loses its resemblance to the original as the latter develops. If everything boiled down to just this, then it would be half the trouble. In applied linguistics, they think of the moments of the development of the language, they strive to consider it as a completely stable system, and yet they still fail to achieve the formalization of a natural language. This happens for a very simple reason. The formal system and natural language base their effectiveness on polar opposite qualities. Any formal system is always identical to itself. It is this quality that makes it possible for it to perform its functions in all specific cases of its application. And natural language - in terms of its content, its semantics, or, as it is customary to say in these cases, in its informative terms - is never identical to itself. It is this ability of his that makes it possible for him to function in all specific cases of his application. Remaining the same language, it is always different in different situations. At the same time, it has neither explicit nor formative rules, nor rules of truth, nor transformational rules for determining which of the potential meanings or shades of meanings a given word will receive in a given situation. Moreover, almost any word of a natural language can acquire a meaning that is not fixed in any language - it can, having arisen, be fixed in the language, but with the same success, like a quick flame, flashing, get lost in the linguistic space and go out.

18 V. M. Glushkov, Thinking and cybernetics, “Issues of fi-
losophy”, 1963, No. 1, pp. 37-38

19 Ibid., p. 38.

And with all these qualities, natural language turns out to be an amazingly perfect tool that allows you to achieve complete mutual understanding regarding the most complex concepts and in any situations. Why is this happening?

Apparently, the answer to this question should be partially sought in one of the thoughts of the founder of semiotics Ch. Pierce, which he persistently repeats in many of his works. It boils down to the following. In modern linguistics, language is usually defined as a system of signs. This is the basic premise for all linguistic analysis. If this is so, then language is not just a system of signs, but a system of mutually interpreting signs that exist in it insofar as they are interpreted in other signs. C. Pierce formulates it as follows: “No sign can function as a sign if it is not interpreted in another sign. Therefore, it is absolutely essential for a sign that it acts on another sign. And elsewhere: "The whole purpose of a sign is that it will be interpreted in another sign" 21 . And, finally, perhaps the most important: "A sign is not a sign, unless it translates itself into another sign, in which it receives a more complete development" 22 .

Consequently, natural language is a system of signs that, through mutual interpretation, are able to respond to all human needs in semantic expression. But one important caveat is needed here. After all, all the needs of this kind are determined by the attitude of a person to the phenomena of the external world and the social environment in which his life takes place. Due to this circumstance, transformational semantics, if it could be created, cannot rely only on the rules of mutual interpretation of signs, that is, be of a closed and finite nature. It turns out to be a derivative of a very large number of quantities that in every possible way oppose formalization.

20 Ch. R e i g c e , Collected Papers, Cambridge, Mass., vol. eight,
p. 225.

21 Ibid., vol. 8, p. 191.

22 Ibid., vol. 5, p. 594.

In connection with what has been said, it is important to consider the features of the procedure for solving problems and the very concept of solvability in logic and mathematics, on the one hand, and in linguistics, on the other.

Before solving a problem in mathematics, the problem must be formulated in precise terms. This formulation itself is a prerequisite for a successful solution of the problem. At the same time, as has already been pointed out, a mathematician can freely transform a given formulation of a problem into an equivalent variant; she also has the appropriate means for this. Already at this first stage of the research methodology, linguistics differs significantly from mathematics. When formulating his problems, the linguist has a certain amount of observed empirical data, which he cannot always give an exact formulation, but which, nevertheless, he willy-nilly must put as the basis of his research - already in the process of this research itself, formulations are clarified, which are often the goal of the research itself. research. In order not to go far beyond examples, we can refer to linguistic meaning, which underlies research in the field of automatic processing of speech information, but at the same time is defined very vaguely and contradictorily. It is this circumstance that forces researchers in this field to constantly change their strategy.

But now the research has begun and some solution has been reached. What does this mean in relation to logic and mathematics and in relation to linguistics? Logic, as stated above, makes it possible to explicitly represent the conclusions that are implicit in the premise. However, logic has no rules, the use of which can guarantee that the desired solution will be obtained in this case, since it is not a means of reaching new conclusions, but only a method for determining their correctness. She is not the magic key to all mysteries. It is quite obvious that if logic had such rules, then there would be no unsolved problems. It would be enough to apply a certain set of logical rules, and we would automatically receive a ready answer to any question that torments us. In the light of what has been said, the concept of the solvability of a problem or task also acquires a specific meaning.

In logic and mathematics, any final result is recognized as true if no formal rule has been violated in the process of proof. Since different ways of proof are possible in this case, the existence of different solutions is admissible. But all of them can be subject to verification from the point of view of the requirement of logic or mathematics. The situation is different in linguistics. It does not have an apparatus with which to verify or prove the correctness of the conclusions drawn. Accordingly, the truth of the decisions reached is also determined - it is established not by formal rules, but by its correspondence to the data of experience. Under these conditions, one would theoretically expect a single final solution. However, in practice, as contradictory linguistic definitions of even the main categories of language testify, this is not the case. In this case, there is always a certain subjectivity of assessments, which is largely determined by the amount of facts at the disposal of the researcher. It follows from this that the truth of a decision in linguistics is always given in some approximation and is not deterministic, but probabilistic.

Under these conditions, it is very important to test the correctness of linguistic definitions and interpretations on the basis of objective criteria. The possibility of such verification is provided by a wide field of applied linguistics, where natural language is opposed by a machine that represents the interests of logic and mathematics.

A digital computer is used to solve practical problems of applied linguistics. It is able to perceive, store, transmit, regroup and issue information. It interprets and executes a set of commands (command program) and also modifies them during the execution of a task. It is able to solve very complex problems, but the entire process of transition from task to solution must be exhaustively and consistently described in terms of a sequence of basic elementary operations. Information is entered into the machine using a two-digit (binary) code or language. The machine operates with words encoded in this way, corresponding to the main logical connections . or functions of the propositional or predicate calculus. A machine can solve complex mathematical problems precisely because it is possible to reduce complex mathematical operations to a sequence of arithmetic operations, and these latter, in turn, to logical operations. Therefore, a digital computer can be considered in the same way as a logical machine.

Thus, whatever the complexity of the task, the machine solves it with the help of a sequence of elementary operations, the program of which must be formulated absolutely unambiguously (consistently), accurately, in detail and exhaustively. In other words, it must not go beyond the limits set by the logical calculus of propositions; and when we ask ourselves whether a machine can cope with the processing of information contained in natural languages, we first need to find out to what extent the logical propositional calculus is an adequate model for natural language.

Given the specifics of the digital computer described above, the first thing to do in order for the machine to “understand” the task and start processing speech information in accordance with this task is to reformulate the information contained in natural language into logical language. We are talking about the translation of natural language into the language of logical propositional calculus.

In this case, as Bar-Hillel 23 has shown, one has to face such difficulties that paint the prospects for automatic information processing in a very gloomy light, unless the whole direction of the search for a solution to this problem is changed. At the very least, we will have to reckon with the obstacles listed below, for which we do not yet have the necessary means to overcome.

A. The logical calculus of propositions is too poor to be able, even remotely

23 Y. V a g - H i 1 1 f 1, A Demonstration of the Non-feasibility of Fully Automatic High Quality Translation, "Advances in Computers", ed. by F. Alt., vol. I, N . Y., 1960, pp. 158-163.

approximation, to reformulate a natural language that is incredibly complex in its semantic structure, has a huge amount of redundant elements and, most importantly, is often characterized by such vagueness and indefiniteness in the expression of “meaning” that no two-valued logic is able to cope with the creation of an artificial twin of a natural language 24 . True, logic, as pointed out, deals only with linguistic form. But since it is a matter of automatic information processing, it is necessary to be able to distinguish between semantic information, and if this cannot be achieved using the logical means at our disposal, then how can we get "certainty that our translation of natural language into logical is correct?

B. The machine cannot take into account what Bar-Hillel calls "common prior data of information"(gênerai background of information),which actually remain outside the natural language and therefore cannot be translated into a logical language. Linguists in these cases speak of an extralinguistic context.(frame of reference), which, in a subtle but very decisive way, corrects or even completely rethinks all our words. After all, even such a simple phrase as “I will return before dark” requires at least prior knowledge of where it was uttered and at what time of the day and year to accurately understand it and determine the time indication contained in it. Preliminary information of this kind alone is often the only means for elucidating those intra-phase relations that neither the propositional calculus nor the predicate calculus is able to cope with. So, using as an example two sentences that flashed in the newspapers:

Postgraduate student of the university from the city of Kursk. Honored innovator of Siberia,

we see that each of them can be interpreted in two ways. If only formally

24 C. Hockett's article "Grammar for the Listener" included in this section gives many examples of such difficulties in the "natural" understanding of the sentence, which are resolved by subsequent and far-reaching steps of analysis.

grammatical features, then the first sentence can equally well be understood as "A graduate student from a university located in the city of Kursk" and as "A graduate student of a university living in the city of Kursk (or originating from the city of Kursk)". And the second sentence can be interpreted both as "Honored innovator, whose field of activity is Siberia" and as "Honored innovator, who is a resident of Siberia." And only preliminary and not expressed in sentences knowledge (preliminary information), stating that there is no university in the city of Kursk and that well-deserved rationalist congestion there is an honorary title conferred in the Soviet Union by individual administrative districts, make it possible to correctly understand these proposals. If you look closely, then almost every phrase of the spoken language is very solid and ramified preliminary information, which is self-evident for a person, but lies beyond the “understanding” of a machine that knows neither clan nor tribe.

B. The machine cannot make intratextual semantic conclusions that extend over several sentences (and sometimes even intentionally for a whole story, so as not to completely reveal its character or plot move). The Dutch linguist A. Reichling 25 drew attention to this circumstance, illustrating his idea with the following example. Suppose we are reading a story that begins with the sentence: "I am playing with my brother." If we stop there, then we will not have any data at our disposal to clarify how this phrase should be understood, what kind of game we are talking about here. After all, you can play for money (cards, etc.), on a musical instrument, in the theater or in the cinema, with toys, football, play for fun, play with a person and his fate, etc. But here we read further: “ I said it when Wilhelm met me one day

25 At the colloquium Stichting Studiecentrum voor Administrative Automation,organized in 1961. There is also a German translation of the report: A. R e i c h 1 i n g, Möglichkeiten und Grenzen der mechanischen Obersetzung, aus der Sicht des Linguisten, "Beiträge zur Sprachkunde und Informationsverarbeitung", Heft I., Wien, 1963.

in the bar". Now we can more likely conclude that, apparently, we are talking about a game for money. But still there are other possibilities. It follows: "My brother came to the table and the dice were thrown." It is now clear which game is being referred to, although nowhere in the text is an exact indication of the actual meaning of the word "game" given. We guessed about him by the totality of those external signs that are given in the text in different sentences. These signs follow here one after another, but in a written narrative they can be significantly separated from each other. A person can select them from a broad linguistic context, compare them and then draw the appropriate conclusion. The machine is deprived of this possibility.

But maybe it's not so important? Indeed, when translating these sentences into German or French by machine, there are no particular difficulties (but, of course, difficulties may arise when translating other sentences). When translating into German, we can use literalism:Ich spiele mit meinem Bruder.Similarly, in French we can start: Je joue avec... When translating into English, however, grammatical difficulties arise, because in the text given there is no indication of which form the machine should choose: 1. I am playing with my brother, 2. I play with my brother, or 3. I'll play with my brother. And it will be really bad when translating into Spanish, since the machine will have to choose between at least three verbs: jugar, tocar or trabajar.

Here logical language is helpless.

D. The machine actually deals with speech (or, more precisely, with speech segments) - in her written and oral form. Each of these forms of speech has its own system of pragmatic elements, which are also capable of transforming into semantic ones (and the rules for such a transition have not been studied and are largely arbitrary). So, for example, oral speech has such a suprasegmental superstructure as intonation. It seems now possible to classify intonation according to functional types, highlighting interrogative, narrative, etc. intonations. However, it is quite clear that intonation does not exist in isolation from sentences. She, of course, interacts with the meaning contained in them. In support of this, it suffices to refer to a rhetorical question, which is a question only in its external structure, but not in its meaning. - it does not require a response from the hearers. These are the new difficulties with which the logical language is unable to cope.

E. But even if it is possible to cope with the listed linguistic difficulties, there are still obstacles of a proper logical order. - in this case we are talking about the so-called "rules of inference decision"(decision rules). After all, if we want to be sure that the machine will act logically flawlessly, we must provide it with a set of rules, following which it can consistently go from the initial information to the necessary conclusions. We have such rules for logical propositional calculi, but for more complex logics there are no such rules, and, moreover, there is reason to believe that such rules cannot be found. If we focus on the rules that we already have at our disposal, then using them will make the resolution process so complicated (even with advanced computers) that the game will not be worth the candle.

In this form, the problem of applying logical and mathematical methods in the science of language is drawn based on the data of applied linguistics. What are the conclusions? The conclusions have already been formulated above. - linguistic analysis allows a combination of inductive and deductive methods, but when we talk about the use of deductive methods in linguistics, one should not reduce everything to the blind subordination of linguistic research to logical-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 a natural language that a fairly complete (in informative terms), the translation of the second into the first is impossible. Does this mean that in linguistics, and in applied linguistics in particular, the use of logico-mathematical methods should be abandoned? Of course not. But you should not rely entirely on them, but combine them with others. And in order not to be unfounded, let's turn to the testimony of mathematicians and logicians, who in practice have to apply their knowledge to the study of natural language.

Here is what the mathematician says: “The help of mathematics in the study of natural language is still far from obvious ... Before we can think about using mathematics for calculus, it is necessary to define the boundaries and functions of linguistic units ... This - non-mathematical problem, it is part of the inductive methods in linguistics.

It turned out that mathematics does not replace empirical methodology, although some linguists strive to do so. On the contrary, only after the units and relations of natural language have been established by the inductive method and appropriately confirmed (verified), will the necessary conditions be created for a realistic application of mathematics to natural language. At the same time, mathematicians will either find that they are dealing with a new manifestation of what is essentially already familiar to them, or they will receive a stimulus for mathematical thinking of a new order.

And here is what the logician 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 tool of linguistic analysis, not as a set of rules for deriving conclusions, it makes real promises” 27 . And then he establishes which research strategy is more preferable in this case: “Problems should be solved not by steadfastly following a set of rules established by a logician, but rather by using heuristic techniques ... For automatic processing of speech information, an empirical, inductive approach is preferable, in which rough rules for solving information problems. One should not try to translate ordinary language into logical language for the purpose of further processing it, but rather look for heuristic-type rules that will allow one to cope with natural language. Necessary stop looking

26 P. Garvin and W. C a g u s h, Linguistics, Data Processes-
sing and Mathematics, "Natural language and the computer", N. Y.,
1963, pp. 368-369. Cm . also in the same book article W. K a g u s h,
The use of mathematics in the behavioral sciences, pp. 64-83.

27 M. M a g o n, A Logician's View of Language-data Processes-
sing, said book, p. 144.

absolute certainty and turn to approximate methods, which, with the accumulation of experience, will be refined and improved. We prefer to treat approximations in the same way that theory is treated in science, where modifications and improvements are made on the basis of experimental data.

These are the general conclusions. They say that linguists play a leading role in joint work with logicians and mathematicians. It is the duty of linguists to prepare language material in such a way as to make it accessible to processing by logical and mathematical methods. It is in this direction that one should look for a realistic combination in linguistics of inductive methods with deductive ones. And when, when solving problems of applied linguistics, we are talking about heuristic hypotheses, then they should first of all come from a linguist, since he is closer to the language and, according to his position, is obliged to know and understand it better.

It is with these considerations in mind that the articles included in this section should be approached. As already mentioned, they are taken from the collection of materials of the symposium on applied mathematics "The Structure of Language and Its Mathematical Aspects" (the symposium was held in New York in April 1960, the materials of the symposium were published in 1961).

The symposium was attended by mathematicians, logicians and linguists, that is, just representatives of those sciences whose joint work was mentioned above. The theme of the symposium, formulated quite freely, gave its participants the opportunity to talk both about very particular and special issues, and about fairly general ones, without binding themselves either to a common understanding of the tasks of the issues under consideration, or to an assessment of their share in the whole problem as a whole. Perhaps the only theoretical beginning that united the participants of the symposium was the thesis cited by R. Jacobson in the "Preface" to the materials, according to which linguistics should

28 Ibid., pp. 143-144.

should be considered as a bridge between the mathematical and humanities disciplines. Otherwise, each author of the communication acted in accordance with his individual interests and in accordance with the direction of his research work.

Due to a certain page limit of this collection, it was not possible to use all the articles included in the symposium materials. Some selection of papers had to be made, however, in such a way that it would give the Soviet reader the opportunity to form a fairly complete picture of the general trends in the study of the problem that stands in the title of the symposium. In their information quality, all articles of this section are of undeniable interest both for the theory of linguistics and for the research practice of applied linguistics.

AT.Zvegintsev

The Formation of Structural Linguistics at the Turn of the 19th – 20th Centuries. Statistical methods in language learning. Application of mathematical methods in linguistics in the second half of the twentieth century. Learning the language by methods of formal logic. Features of machine translation.

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 19th - 20th Centuries

1.2. Application of mathematical methods in linguistics in the second half of the twentieth century

Chapter 2. Selected examples of the use of mathematics in linguistics

2.1. Machine translate

2.2.Statistical methods in language learning

2.3. Learning a language by methods of formal logic

2.4. Prospects for the application of mathematical methods in linguistics

Conclusion

Literature

Appendix 1. Ronald Schleifer. Ferdinand de Saussure

Appendix 2. Ferdinand de Saussure (translation)

INTRODUCTION

In the 20th century, there has been a continuing trend towards the interaction and interpenetration of various fields of knowledge. The boundaries between the individual sciences are gradually blurred; there are more and more branches of mental activity that are "at the junction" of humanitarian, technical and natural science knowledge.

Another obvious feature of modernity is the desire to study structures and their constituent elements. Therefore, an increasing place, both in scientific theory and in practice, is given to mathematics. Coming into contact, on the one hand, with logic and philosophy, on the other hand, with statistics (and, consequently, with the social sciences), mathematics penetrates deeper and deeper into those areas that for a long time were considered to be purely “humanitarian”, expanding their heuristic potential (the answer to the question "how much" will often help answer the questions "what" and "how"). Linguistics was no exception.

The purpose of my course work is to briefly highlight the connection between mathematics and such a branch of linguistics as linguistics. Since the 50s of the last century, mathematics has been used in linguistics to create a theoretical apparatus for describing the structure of languages ​​(both natural and artificial). At the same time, it should be said that it did not immediately find such a practical application for itself. Initially, mathematical methods in linguistics began to be used in order to clarify the basic concepts of linguistics, however, with the development of computer technology, such a theoretical premise began to find application in practice. The resolution of such tasks as machine translation, machine information retrieval, automatic text processing required a fundamentally new approach to the language. A question has arisen before linguists: how to learn to represent linguistic patterns in the form in which they can be applied directly to technology. The term “mathematical linguistics”, which is popular in our time, refers to any linguistic research that uses exact methods (and the concept of exact methods in science is always closely related to mathematics). Some scientists of the past believe that the expression itself cannot be elevated to the rank of a term, since it does not mean any special “linguistics”, but only a new direction focused on improving, increasing the accuracy and reliability of language research methods. Linguistics uses both quantitative (algebraic) and non-quantitative methods, which brings it closer to mathematical logic, and, consequently, to philosophy, and even to psychology. Even Schlegel noted the interaction of language and consciousness, and Ferdinand de Saussure, a prominent linguist of the early twentieth century (I will tell about his influence on the development of mathematical methods in linguistics later), connected the structure of the language with its belonging to the people. The modern researcher L. Perlovsky goes further, identifying the quantitative characteristics of the language (for example, the number of genders, cases) with the peculiarities of the national mentality (more on this in Section 2.2, "Statistical Methods in Linguistics").

The interaction of mathematics and linguistics is a multifaceted topic, and in my work I will not dwell on all, but, first of all, on its applied aspects.

Chapter IHistory of application of mathematical methods in linguistics

1.1 Formation of structural linguisticsat the turn of the XIX - XX centuries

The mathematical description of the language is based on the idea of ​​language as a mechanism, which goes back to the famous Swiss linguist of the early twentieth century, Ferdinand de Saussure.

The initial link of his concept is the theory of language as a system consisting of three parts (the language itself is language, speech - password, and speech activity - language), in which each word (member of the system) is considered not in itself, but in connection with other members. As another prominent linguist, the Dane Louis Hjelmslev, later noted, Saussure "was the first to demand a structural approach to language, that is, a scientific description of the language by recording the relationships between units."

Understanding language as a hierarchical structure, Saussure was the first to pose the problem of the value and significance of linguistic units. Separate phenomena and events (say, the history of the origin of individual Indo-European words) should be studied not by themselves, but in a system in which they are correlated with similar components.

The structural unit of the language of Saussure considered the word, "sign", in which sound and meaning were combined. None of these elements exist without each other: therefore, the native speaker understands the various shades of the meaning of a polysemantic word as a separate element in the structural whole, in the language.

Thus, in the theory of F. de Saussure one can see the interaction of linguistics, on the one hand, with sociology and social psychology (it should be noted that at the same time, Husserl's phenomenology, Freud's psychoanalysis, Einstein's theory of relativity were developing, experiments were taking place on form and content in literature, music and fine arts), on the other hand, with mathematics (the concept of systemicity corresponds to the algebraic concept of language). Such a concept changed the concept of linguistic interpretation as such: Phenomena began to be interpreted not in relation to the causes of their occurrence, but in relation to the present and future. Interpretation ceased to be independent of a person's intentions (despite the fact that intentions may be impersonal, "unconscious" in the Freudian sense of the word).

The functioning of the linguistic mechanism is manifested through the speech activity of native speakers. The result of speech is the so-called "correct texts" - sequences of speech units that obey certain patterns, many of which allow a mathematical description. The theory of ways to describe the syntactic structure deals with the study of methods for mathematical description of correct texts (primarily sentences). In such a structure, linguistic analogies are defined not with the help of their inherent qualities, but with the help of system (“structural”) relations.

In the West, Saussure's ideas are developed by the younger contemporaries of the great Swiss linguist: in Denmark - L. Hjelmslev, already mentioned by me, who gave rise to the algebraic theory of language in his work "Fundamentals of Linguistic Theory", in the USA - E. Sapir, L. Bloomfield, C. Harris, in the Czech Republic - the Russian émigré scientist N. Trubetskoy.

Statistical regularities in the study of language began to be dealt with by none other than the founder of genetics, Georg Mendel. It was only in 1968 that philologists discovered that, in the last years of his life, he was fascinated by the study of linguistic phenomena using the methods of mathematics. Mendel brought this method to linguistics from biology; in the 1990s, only the most daring linguists and biologists claimed the feasibility of such an analysis. In the archives of the monastery of St. Tomasz in Brno, whose abbot was Mendel, sheets were found with columns of surnames ending in "mann", "bauer", "mayer", and with some fractions and calculations. In an effort to discover the formal laws of the origin of family names, Mendel makes complex calculations, in which he takes into account the number of vowels and consonants in the German language, the total number of words he considers, the number of surnames, etc.

In our country, structural linguistics began to develop at about the same time as in the West - at the turn of the 19th-20th centuries. Simultaneously with F. de Saussure, the concept of language as a system was developed in their works by professors of Kazan University F.F. Fortunatov and I.A. Baudouin de Courtenay. The latter corresponded for a long time with de Saussure, respectively, the Geneva and Kazan schools of linguistics collaborated with each other. If Saussure can be called the ideologist of "exact" methods in linguistics, then Baudouin de Courtenay laid the practical foundations for their application. He was the first to separate linguistics (as accurate a science using statistical methods and functional dependence) from philology (a community of humanitarian disciplines that study spiritual culture through language and speech). The scientist himself believed that "linguistics can be useful in the near future, only freed from the mandatory union with philology and literary history" . Phonology became the "testing ground" for the introduction of mathematical methods into linguistics - sounds as "atoms" of the language system, having a limited number of easily measurable properties, were the most convenient material for formal, rigorous methods of description. Phonology denies the existence of meaning in sound, so the "human" factor was eliminated in the studies. In this sense, phonemes are like physical or biological objects.

Phonemes, as the smallest linguistic elements acceptable for perception, represent a separate sphere, a separate "phenomenological reality". For example, in English, the sound "t" can be pronounced differently, but in all cases, a person who speaks English will perceive it as "t". The main thing is that the phoneme will perform its main - meaningful - function. Moreover, the differences between languages ​​are such that varieties of one sound in one language can correspond to different phonemes in another; for example, "l" and "r" in English are different, while in other languages ​​they are varieties of the same phoneme (like the English "t", pronounced with or without aspiration). The vast vocabulary of any natural language is a set of combinations of a much smaller number of phonemes. In English, for example, only 40 phonemes are used to pronounce and write about a million words.

The sounds of a language are a systematically organized set of features. In the 1920s -1930s, following Saussure, Jacobson and N.S. Trubetskoy singled out the "distinctive features" of phonemes. These features are based on the structure of the speech organs - tongue, teeth, vocal cords. For example, in English the difference between "t" and "d" is the presence or absence of a "voice" (the tension of the vocal cords) and the level of voice that distinguishes one phoneme from another. Thus, phonology can be considered an example of the general language rule described by Saussure: "There are only differences in language". Even more important is not this: the difference usually implies the exact conditions between which it is located; but in language there are only differences without precise conditions. Whether we are considering "designation" or "signified" - in the language there are neither concepts nor sounds that would have existed before the development of the language system.

Thus, in Saussurean linguistics, the studied phenomenon is understood as a set of comparisons and oppositions of language. Language is both an expression of the meaning of words and a means of communication, and these two functions never coincide. We can notice the alternation of form and content: linguistic contrasts define its structural units, and these units interact to create a certain meaningful content. Since the elements of language are random, neither contrast nor combination can be the basis. This means that in a language, distinctive features form a phonetic contrast at a different level of understanding, phonemes are combined into morphemes, morphemes - into words, words - into sentences, etc. In any case, an entire phoneme, word, sentence, etc. is more than just the sum of its parts.

Saussure proposed the idea of ​​a new science of the twentieth century, separate from linguistics, studying the role of signs in society. Saussure called this science semiology (from the Greek "semeion" - a sign). The "science" of semiotics, which developed in Eastern Europe in the 1920s and 1930s and in Paris in the 1950s and 1960s, extended the study of language and linguistic structures into literary findings composed (or articulated) in terms of these structures. In addition, in the twilight of his career, in parallel with his course in general linguistics, Saussure engaged in a "semiotic" analysis of late Roman poetry, trying to discover deliberately composed anagrams of proper names. This method was in many ways the opposite of rationalism in its linguistic analysis: it was an attempt to study in a system the problem of "probability" in language. Such research helps to focus on the "real side" of probability; the "key word" for which Saussure is looking for an anagram is, according to Jean Starobinsky, "a tool for the poet, not the source of the life of the poem." The poem serves to swap the sounds of the keyword. According to Starobinsky, in this analysis, "Saussure does not delve into the search for hidden meanings." On the contrary, in his works, a desire to avoid questions related to consciousness is noticeable: “since poetry is expressed not only in words, but also in what these words give rise to, it goes beyond the control of consciousness and depends only on the laws of language” (see . Attachment 1).

Saussure's attempt to study proper names in late Roman poetry emphasizes one of the components of his linguistic analysis - the arbitrary nature of signs, as well as the formal essence of Saussure's linguistics, which excludes the possibility of analyzing meaning. Todorov concludes that today the works of Saussure seem to be extremely consistent in their reluctance to study the symbols of a phenomenon that have a clearly defined meaning [Appendix 1]. Exploring anagrams, Saussure pays attention only to repetition, but not to previous options. . . . Studying the Nibelungenlied, he defines the symbols only to assign them to erroneous readings: if they are unintentional, the symbols do not exist. After all, in his writings on general linguistics, he makes the assumption of the existence of a semiology that describes not only linguistic signs; but this assumption is limited by the fact that semiology can only describe random, arbitrary signs.

If this is really so, it is only because he could not imagine "intention" without an object; he could not completely bridge the gap between form and content - in his writings this turned into a question. Instead, he turned to "linguistic legitimacy". Between, on the one hand, nineteenth-century concepts based on history and subjective conjectures, and methods of random interpretation based on these concepts, and, on the other hand, structuralist concepts that erase the opposition between form and content (subject and object), meaning and origins in structuralism, psychoanalysis, and even quantum mechanics - the writings of Ferdinand de Saussure on linguistics and semiotics mark a turning point in the study of meanings in language and culture.

Russian scientists were also represented at the First International Congress of Linguists in The Hague in 1928. S. Kartsevsky, R. Yakobson and N. Trubetskoy made a report that examined the hierarchical structure of the language - in the spirit of the most modern ideas for the beginning of the last century. Jakobson in his writings developed Saussure's ideas that the basic elements of a language should be studied, first of all, in connection with their functions, and not with the reasons for their occurrence.

Unfortunately, after Stalin came to power in 1924, Russian linguistics, like many other sciences, is thrown back. Many talented scientists were forced to emigrate, were expelled from the country or died in camps. Only since the mid-1950s has a certain pluralism of theories become possible - more on this in Section 1.2.

1.2 Application of mathematical methods in linguistics in the second half of the twentieth century

By the middle of the twentieth century, four world linguistic schools had formed, each of which turned out to be the ancestor of a certain “exact” method. Leningrad Phonological School(its ancestor was a student of Baudouin de Courtenay L.V. Shcherba) used a psycholinguistic experiment based on the analysis of the speech of native speakers as the main criterion for generalizing sound in the form of a phoneme.

Scientists Prague Linguistic Circle, in particular - its founder N.S. Trubetskoy, who emigrated from Russia, developed the theory of oppositions - the semantic structure of the language was described by them as a set of oppositionally constructed semantic units - Sem. This theory was applied in the study of not only language, but also artistic culture.

Ideologists American descriptivism were linguists L. Bloomfield and E. Sapir. Language was presented to descriptivists as a set of speech statements, which were the main object of their study. Their focus was on the rules of scientific description (hence the name) of texts: the study of organization, arrangement and classification of their elements. Formalization of analytical procedures in the field of phonology and morphology (development of principles for the study of language at different levels, distributive analysis, the method of direct constituents, etc.) led to the formulation of general questions of linguistic modeling. Inattention to the plan of the content of the language, as well as the paradigmatic side of the language, did not allow descriptivists to interpret the language as a system fully enough.

In the 1960s, the theory of formal grammars developed, which arose mainly due to the work of the American philosopher and linguist N. Chomsky. He is rightfully considered one of the most famous modern scientists and public figures, many articles, monographs and even a full-length documentary are devoted to him. By the name of a fundamentally new way of describing the syntactic structure invented by Chomsky - generative (generative) grammar - the corresponding trend in linguistics was called generativism.

Chomsky, a descendant of immigrants from Russia, studied linguistics, mathematics and philosophy at the University of Pennsylvania since 1945, being strongly influenced by his teacher Zelig Harris - like Harris, Chomsky considered and still considers his political views close to anarchism (he is still known as critic of the existing US political system and as one of the spiritual leaders of anti-globalism).

Chomsky's first major scientific work, master's thesis "Morphology of Modern Hebrew » (1951) has remained unpublished. Chomsky received his doctorate from the University of Pennsylvania in 1955, but much of the research underlying his dissertation (published in full only in 1975 under the title The Logical Structure of Linguistic Theory) and his first monograph, Syntactic Structures (1957, Rus. trans. 1962), was performed at Harvard University in 1951-1955. In the same 1955, the scientist moved to the Massachusetts Institute of Technology, where he became a professor in 1962.

Chomsky's theory has gone through several stages in its development.

In the first monograph "Syntactic Structures", the scientist presented the language as a mechanism for generating an infinite set of sentences using a finite set of grammatical means. To describe linguistic properties, he proposed the concepts of deep (hidden from direct perception and generated by a system of recursive, i.e., can be applied repeatedly, rules) and surface (directly perceived) grammatical structures, as well as transformations that describe the transition from deep structures to surface ones. Several surface structures can correspond to one deep structure (for example, a passive structure The decree is signed by the president derived from the same Deep Structure as the active construct The President signs the decree) and vice versa (thus, the ambiguity mother loves daughter described as the result of a coincidence of surface structures that go back to two different deep ones, in one of which the mother is the one who loves the daughter, and in the other, the one who is loved by the daughter).

Chomsky's standard theory is considered to be the "Aspects" model set forth in Chomsky's book "Aspects of the Theory of Syntax". In this model, for the first time, rules of semantic interpretation were introduced into formal theory, attributing meaning to deep structures. In Aspects, linguistic competence is opposed to the use of language (performance), the so-called Katz-Postal hypothesis about the preservation of meaning during transformation is adopted, in connection with which the concept of optional transformation is excluded, and an apparatus of syntactic features describing lexical compatibility is introduced.

In the 1970s, Chomsky worked on the theory of control and binding (GB-theory - from the words government and binding) is more general than the previous one. In it, the scientist abandoned the specific rules that describe the syntactic structures of specific languages. All transformations have been replaced with one universal move transformation. Within the framework of the GB theory, there are also private modules, each of which is responsible for its own part of the grammar.

Already recently, in 1995, Chomsky put forward a minimalist program, where human language is described like machine language. This is just a program - not a model or a theory. In it, Chomsky identifies two main subsystems of the human language apparatus: the lexicon and the computing system, as well as two interfaces - phonetic and logical.

Chomsky's formal grammars have become classic for describing not only natural but also artificial languages ​​- in particular, programming languages. The development of structural linguistics in the second half of the 20th century can rightly be considered a "Chomskian revolution".

Moscow Phonological School, whose representatives were A.A. Reformatsky, V.N. Sidorov, P.S. Kuznetsov, A.M. Sukhotin, R.I. Avanesov, used a similar theory to study phonetics. Gradually, "exact" methods are beginning to be applied with regards not only to phonetics, but also to syntax. Both linguists and mathematicians, both here and abroad, are beginning to study the structure of the language. In the 1950s and 60s, a new stage in the interaction between mathematics and linguistics began in the USSR, associated with the development of machine translation systems.

The impetus for the beginning of these works in our country was the first developments in the field of machine translation in the United States (although the first mechanized translation device by P.P. Smirnov-Troyansky was invented in the USSR back in 1933, it, being primitive, did not become widespread). In 1947, A. Butt and D. Britten came up with a code for word-by-word translation using a computer; a year later, R. Richens proposed a rule for splitting words into stems and endings in machine translation. Those years were quite different from today. These were very large and expensive machines that took up entire rooms and required a large staff of engineers, operators and programmers to maintain them. Basically, these computers were used to carry out mathematical calculations for the needs of military institutions - the new in mathematics, physics and technology served, first of all, military affairs. In the early stages, the development of the MP was actively supported by the military, with all this (in the conditions of the Cold War), the Russian-English direction developed in the USA, and the Anglo-Russian direction in the USSR.

In January 1954, the "Georgetown Experiment" took place at the Massachusetts Technical University - the first public demonstration of translation from Russian into English on the IBM-701 machine. Abstract of the message about the successful passage of the experiment, made by D.Yu. Panov, appeared in the RJ "Mathematics", 1954, No. 10: "Translation from one language to another using a machine: a report on the first successful test."

D. Yu. Panov (at that time director of the Institute of Scientific Information - INI, later VINITI) attracted I. K. Belskaya, who later headed the machine translation group at the Institute of Precise Mathematics and Computer Engineering of the USSR Academy of Sciences, to work on machine translation. By the end of 1955, the first experience of translating from English into Russian with the help of the BESM machine dates back. Programs for BESM were compiled by N.P. Trifonov and L.N. Korolev, whose Ph.D. thesis was devoted to methods for constructing dictionaries for machine translation.

In parallel, work on machine translation was carried out at the Department of Applied Mathematics of the Mathematical Institute of the USSR Academy of Sciences (now the M.V. Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences). At the initiative of the mathematician A.A. Lyapunov. He involved O.S. Kulagin and her students T.D. Wentzel and N.N. Ricco. The ideas of Lyapunov and Kulagina about the possibility of using technology to translate from one language into another were published in the journal Nature, 1955, No. 8. From the end of 1955, T.N. Moloshnaya, who then began independent work on the English-Russian translation algorithm.

R. Frumkina, who at that time was engaged in the translation algorithm from Spanish, recalls that at this stage of the work it was difficult to take any consistent steps. Much more often I had to follow the heuristic experience - my own or colleagues.

At the same time, the first generation of machine translation systems was very imperfect. All of them were based on sequential translation algorithms "word by word", "phrase by phrase" - semantic connections between words and sentences were not taken into account in any way. For example, the sentences are: John was looking for his toy box.Finally he found it. The box was in the pen.John was very happy. (John was looking for his toy box. Finally he found it. The box was in the playpen. John was very happy.).” "Pen" in this context is not a "pen" (writing tool), but a "playpen" ( play-pen). Knowledge of synonyms, antonyms and figurative meanings is difficult to enter into a computer. A promising direction was the development of computer systems focused on the use of a human translator.

Over time, direct translation systems were replaced by T-systems (from the English word "transfer" - transformation), in which translation was carried out at the level of syntactic structures. The algorithms of T-systems used a mechanism that made it possible to build a syntactic structure according to the grammar rules of the language of the input sentence (similar to how a foreign language is taught in high school), and then synthesize the output sentence by transforming the syntactic structure and substituting the necessary words from the dictionary.

Lyapunov talked about translation by extracting the meaning of the translated text and presenting it in another language. The approach to building machine translation systems based on obtaining the semantic representation of the input sentence by semantic analysis and synthesis of the input sentence according to the obtained semantic representation is still considered the most perfect. Such systems are called I-systems (from the word "interlingua"). At the same time, the task of creating them, set back in the late 50s and early 60s, has not been fully resolved so far, despite the efforts of the International Federation of IFIP - the world community of scientists in the field of information processing.

Scientists thought about how to formalize and build algorithms for working with texts, what dictionaries should be entered into the machine, what linguistic patterns should be used in machine translation. Traditional linguistics did not have such ideas - not only in terms of semantics, but also in terms of syntax. At that time, there were no lists of syntactic constructions for any language, the conditions for their compatibility and interchangeability were not studied, the rules for constructing large units of syntactic structure from smaller constituent elements were not developed.

The need to create the theoretical foundations of machine translation led to the formation and development of mathematical linguistics. The leading role in this matter in the USSR was played by the mathematicians A.A. Lyapunov, O.S. Kulagina, V.A. Uspensky, linguists V.Yu. Rosenzweig, P.S. Kuznetsov, R.M. Frumkina, A.A. Reformatsky, I.A. Melchuk, V.V. Ivanov. Kulagina's dissertation was devoted to the study of the formal theory of grammars (simultaneously with N. Khomsky in the USA), Kuznetsov put forward the task of axiomatization of linguistics, which goes back to the works of F.F. Fortunatov.

On May 6, 1960, the Decree of the Presidium of the USSR Academy of Sciences "On the development of structural and mathematical methods for the study of language" was adopted, and the corresponding divisions were created at the Institute of Linguistics and the Institute of the Russian Language. Since 1960, the country's leading humanitarian universities - the Faculty of Philology of Moscow State University, Leninrad, Novosibirsk Universities, Moscow State Institute of Foreign Languages ​​- began training personnel in the field of automatic text processing.

At the same time, works on machine translation of this period, called "classical", are of more theoretical than practical interest. Cost-effective machine translation systems began to be created only in the eighties of the last century. I will talk about this later in Section 2.1, Machine Translation.

The 1960s - 70s include deep theoretical developments using the methods of set theory and mathematical logic, such as field theory and fuzzy set theory.

The author of field theory in linguistics was the Soviet poet, translator and linguist V.G. Admoni. He initially developed his theory on the basis of the German language. For Admoni, the concept of "field" denotes an arbitrary non-empty set of linguistic elements (for example, "lexical field", "semantic field").

The structure of the field is heterogeneous: it consists of a core, the elements of which have a complete set of features that define a set, and a periphery, the elements of which can have both the features of a given set (not all) and neighboring ones. I will give an example illustrating this statement: for example, in English, the field of compound words (“day-dream” - “dream” is difficult to separate from the field of phrases (“tear gas” - “tear gas”).

The theory of fuzzy sets already mentioned above is closely related to field theory. In the USSR, linguists V.G. Admoni, I.P. Ivanova, G.G. Pochentsov, however, its ancestor was the American mathematician L. Zadeh, who in 1965 published the article “Fuzzy Logic”. Giving a mathematical justification for the theory of fuzzy sets, Zade considered them on the basis of linguistic material.

In this theory, we are talking not so much about the belonging of elements to a given set (Aa), but about the degree of this membership (Aa), since peripheral elements can belong to several fields to one degree or another. Zade (Lofti-zade) was a native of Azerbaijan, until the age of 12 he had the practice of communicating in four languages ​​- Azerbaijani, Russian, English and Persian - and used three different alphabets: Cyrillic, Latin, Arabic. When a scientist is asked what is common between fuzzy set theory and linguistics, he does not deny this connection, but clarifies: “I am not sure that the study of these languages ​​\u200b\u200bhas had a big impact on my thinking. If this was the case, then only subconsciously. In his youth, Zadeh studied at a Presbyterian school in Tehran, and after World War II he emigrated to the United States. “The question is not whether I am an American, Russian, Azerbaijani or someone else,” he said in one of the conversations, “I am shaped by all these cultures and peoples and feel quite comfortable among each of them.” In these words there is something akin to what characterizes the theory of fuzzy sets - a departure from unambiguous definitions and sharp categories.

In our country, in the 70s, the works of Western linguists of the twentieth century were translated and studied. I.A. Melchuk translated the works of N. Chomsky into Russian. ON THE. Slyusareva in her book "The Theory of F. de Saussure in the Light of Modern Linguistics" connects the postulates of Saussure's teaching with the actual problems of linguistics of the 70s. There is a tendency towards further mathematization of linguistics. The leading domestic universities are training personnel in the specialty "Mathematical (theoretical, applied) linguistics". At the same time in the West there is a sharp leap in the development of computer technology, which requires more and more new linguistic foundations.

In the 1980s, Professor of the Institute of Oriental Studies of the Academy of Sciences Yu.K. Lekomtsev, while analyzing the language of linguistics through the analysis of schemes, tables and other types of notation used in linguistic descriptions, considers mathematical systems suitable for these purposes (mainly systems of matrix algebra).

Thus, throughout the twentieth century, there was a convergence of the exact and humanities. The interaction of mathematics with linguistics increasingly found practical applications. More on this in the next chapter.

Chapter 2. Selected examples of the use of mathematics in linguistics

2.1 Machine translation

The idea of ​​translating from one language into another with the help of a universal mechanism arose several centuries before the first developments in this area began - back in 1649, Rene Descartes proposed the idea of ​​a language in which the equivalent ideas of different languages ​​would be expressed by one symbol. The first attempts to implement this idea in the 1930s-40s, the beginning of theoretical developments in the middle of the century, the improvement of translation systems with the help of technology in the 1970s-80s, the rapid development of translation technology in the last decade - these are the stages in the development of machine translation as an industry. It is from the works on machine translation that computer linguistics as a science has grown.

With the development of computer technology in the late 70s and early 80s, researchers set themselves more realistic and cost-effective goals - the machine became not a competitor (as was previously assumed), but an assistant to a human translator. Machine translation ceases to serve exclusively military tasks (all Soviet and American inventions and research, focused primarily on Russian and English, contributed to the Cold War in one way or another). In 1978, natural language words were transmitted over the Arpa interconnected network, and six years later, the first microcomputer translation programs appeared in the United States.

In the 70s, the Commission of the European Communities buys the English-French version of the Systran computer translator, ordering also the French-English and Italian-English versions, and the Russian-to-English translation system used by the US Armed Forces. This is how the foundations of the EUROTRA project were laid.

About the revival of machine translation in the 70-80s. The following facts testify: the Commission of the European Communities (CEC) buys the English-French version of Systran, as well as the translation system from Russian into English (the latter developed after the ALPAC report and continued to be used by the US Air Force and NASA); in addition, the CEC orders the development of the French-English and Italian-English versions. Simultaneously, there is a rapid expansion of machine translation activities in Japan; in the USA, the Pan American Health Organization (PAHO) orders the development of a Spanish-English direction (SPANAM system); The US Air Force is funding the development of a machine translation system at the Linguistic Research Center at the University of Texas at Austin; The TAUM group in Canada is making notable progress in developing their METEO (meteorological translation) system. A number of projects started in the 70s and 80s. subsequently developed into full-fledged commercial systems.

During the period 1978-93, 20 million dollars were spent on research in the field of machine translation in the USA, 70 million in Europe, and 200 million in Japan.

One of the new developments is the TM (translation memory) technology, which works on the principle of accumulation: during the translation process, the original segment (sentence) and its translation are saved, resulting in the formation of a linguistic database; if an identical or similar segment is found in the newly translated text, it is displayed along with the translation and an indication of the percentage match. The translator then makes a decision (to edit, reject or accept the translation), the result of which is stored by the system, so there is no need to translate the same sentence twice. A well-known commercial system based on TM technology is currently developed by the TRADOS system (founded in 1984).

Currently, several dozen companies are developing commercial machine translation systems, including: Systran, IBM, L&H (Lernout & Hauspie), Transparent Language, Cross Language, Trident Software, Atril, Trados, Caterpillar Co., LingoWare; Ata Software; Linguistica b.v. and others. Now you can use the services of automatic translators directly on the Web: alphaWorks; PROMT's Online Translator; LogoMedia.net; AltaVista's Babel Fish Translation Service; InfiniT.com; Translating the Internet.

Commercially effective translation systems appeared in the second half of the 80s in our country as well. The very concept of machine translation has expanded (it began to include “the creation of a number of automatic and automated systems and devices that automatically or semi-automatically perform the entire translation cycle or individual tasks in a dialogue with a person”), and government appropriations for the development of this industry have increased.

Russian, English, German, French and Japanese became the main languages ​​of domestic translation systems. The All-Union Translation Center (VTsP) developed a system for translating from English and German into Russian on a computer ES-1035-ANRAP. It consisted of three dictionaries - input English and German and output Russian - under a single software. There were several interchangeable specialized dictionaries - for computer technology, programming, radio electronics, mechanical engineering, agriculture, metallurgy. The system could work in two modes - automatic and interactive, when the screen displayed the source text and translation per phrase, which a person could edit. The speed of translating text into ANRAP (from the beginning of typing to the end of printing) was approximately 100 pages per hour.

In 1989, a family of commercial translators of the SPRINT type was created, working with Russian, English, German and Japanese. Their main advantage was their compatibility with the IBM PC - thus, domestic machine translation systems reached the international level of quality. At the same time, a system of machine translation from French into Russian FRAP is being developed, which includes 4 stages of text analysis: graphematic, morphological, syntactic and semantic. In LGPI them. Herzen, work was underway on a four-language (English, French, Spanish, Russian) SILOD-MP system (English-Russian and Franco-Russian dictionaries were used in industrial mode.

For specialized translation of texts on electrical engineering, the ETAP-2 system existed. The analysis of the input text in it was carried out at two levels - morphological and syntactic. The ETAP-2 dictionary contained about 4 thousand entries; the stage of text transformation - about 1000 rules (96 general, 342 private, the rest are dictionary). All this ensured a satisfactory quality of translation (say, the title of the patent "Optical phase grid arrangement and coupling device having such an arrangement" was translated as "An optical phase grid device and a connecting device with such a device" - despite the tautology, the meaning is preserved).

At the Minsk Pedagogical Institute of Foreign Languages, on the basis of the English-Russian dictionary of word forms and phrases, a system for machine translation of titles was invented, at the Institute of Oriental Studies of the Academy of Sciences - a system for translating from Japanese into Russian. The first automatic vocabulary and terminology service (SLOTHERM) for computing and programming, created at the Moscow Research Institute of Automation Systems, contained approximately 20,000 terms in an explanatory dictionary and special dictionaries for linguistic research.

Machine translation systems gradually began to be used not only for their intended purpose, but also as an important component of automatic learning systems (for teaching translation, checking spelling and grammatical knowledge).

The 90s brought with it the rapid development of the PC market (from desktop to pocket) and information technology, the widespread use of the Internet (which is becoming more international and multilingual). All this made the further development of automated translation systems in demand. Since the early 1990s Domestic developers are also entering the PC systems market.

In July 1990, the first commercial machine translation system in Russia called PROMT (PROgrammer's Machine Translation) was presented at the PC Forum in Moscow. In 1991, ZAO [!!! In accordance with Federal Law-99 of 05.05. 2014, this form was replaced by a non-public joint-stock company] "Proekt MT", and already in 1992, the PROMT company won the NASA competition for the supply of MP systems (PROMT was the only non-American company in this competition). a whole family of systems under the new name STYLUS for translating from English, German, French, Italian and Spanish into Russian and from Russian into English, and in 1993, based on STYLUS, the world's first machine translation system for Windows was created. STYLUS 2.0 for Windows 3.X/95/NT was released, and in 1995-1996 the third generation of machine translation systems, fully 32-bit STYLUS 3.0 for Windows 95/NT, was introduced, at the same time, the development of a completely new, the world's first Russian-German and Russian-French machine translation systems.

In 1997, an agreement was signed with the French company Softissimo on the creation of translation systems from French into German and English and vice versa, and in December of this year, the world's first German-French translation system was released. In the same year, the PROMT company released a system implemented using the Giant technology, which supports several language directions in one shell, as well as a special translator for working on the Internet WebTranSite.

In 1998, a whole constellation of programs was released under the new name PROMT 98. A year later, PROMT released two new products: a unique software package for working on the Internet - PROMT Internet, and a translator for corporate mail systems - PROMT Mail Translator. In November 1999, PROMT was recognized as the best machine translation system tested by the French magazine PC Expert, outperforming its competitors by 30 percent. Special server solutions have also been developed for corporate clients - the corporate translation server PROMT Translation Server (PTS) and the Internet solution PROMT Internet Translation Server (PITS). In 2000, PROMT updated its entire line of software products by releasing a new generation of MT systems: PROMT Translation Office 2000, PROMT Internet 2000 and Magic Gooddy 2000.

Online translation with the support of the PROMT system is used on a number of domestic and foreign sites: PROMT's Online Translator, InfiniT.com, Translate.Ru, Lycos, etc., as well as in institutions of various profiles for translating business documents, articles and letters (there are translation systems built directly into Outlook Express and other email clients).

Nowadays, new machine translation technologies are emerging based on the use of artificial intelligence systems and statistical methods. About the latter - in the next section.

2.2 Extraical methods in language learning

Considerable attention in modern linguistics is given to the study of linguistic phenomena using the methods of quantitative mathematics. Quantitative data often help to more deeply comprehend the phenomena under study, their place and role in the system of related phenomena. The answer to the question "how much" helps to answer the questions "what", "how", "why" - such is the heuristic potential of a quantitative characteristic.

Statistical methods play a significant role in the development of machine translation systems (see section 2.1). In the statistical approach, the translation problem is considered in terms of a noisy channel. Imagine that we need to translate a sentence from English into Russian. The noisy channel principle offers us the following explanation of the relationship between an English and a Russian sentence: an English sentence is nothing but a Russian sentence distorted by some kind of noise. In order to recover the original Russian sentence, we need to know what people usually say in Russian and how Russian phrases are distorted into English. The translation is carried out by searching for such a Russian sentence that maximizes the products of the unconditional probability of the Russian sentence and the probability of the English sentence (original) given the given Russian sentence. According to Bayes' theorem, this Russian sentence is the most likely translation of English:

where e is the translation sentence and f is the original sentence

So we need a source model and a channel model, or a language model and a translation model. The language model must assign a probability score to any sentence in the target language (in our case, Russian), and the translation model to the original sentence. (see table 1)

In general, a machine translation system operates in two modes:

1. System training: a training corpus of parallel texts is taken, and using linear programming, such values ​​of translation correspondence tables are searched for that maximize the probability of (for example) the Russian part of the corpus with the available English according to the selected translation model. A model of the Russian language is built on the Russian part of the same corpus.

2. Exploitation: based on the obtained data for an unfamiliar English sentence, a Russian is searched that maximizes the product of the probabilities assigned by the language model and the translation model. The program used for such a search is called a decoder.

The simplest statistical translation model is the literal translation model. In this model, it is assumed that to translate a sentence from one language to another, it is enough to translate all the words (create a “bag of words”), and the model will provide their placement in the correct order. To reduce P(a, f | e) to P(a | e , f), i.e. probabilities of a given alignment given a pair of sentences, each probability P(a, f | e) is normalized by the sum of the probabilities of all alignments of a given pair of sentences:

The implementation of the Viterbi algorithm used to train Model #1 is as follows:

1. The entire table of translation correspondence probabilities is filled with the same values.

2. For all possible variants of pairwise connections of words, the probability P(a, f | e) is calculated:

3. The values ​​of P(a, f | e) are normalized to obtain the values ​​of P(a | e, f).

4. The frequency of each translation pair is calculated, weighted by the probability of each alignment option.

5. The resulting weighted frequencies are normalized and form a new table of translation correspondence probabilities

6. The algorithm is repeated from step 2.

Consider, as an example, the training of a similar model on a corpus of two pairs of sentences (Fig. 2):

White House

After a large number of iterations, we will get a table (Table 2), which shows that the translation is carried out with high accuracy.

Also, statistical methods are widely used in the study of vocabulary, morphology, syntax, and style. Scientists from Perm State University conducted a study based on the assertion that stereotypical phrases are an important "building material" of the text. These phrases consist of "nuclear" repeated words and dependent words-specifiers and have a pronounced stylistic coloring.

In the scientific style, "nuclear" words can be called: research, study, task, problem, question, phenomenon, fact, observation, analysis etc. In journalism, other words will be “nuclear”, which have an increased value specifically for the text of the newspaper: time, person, power, business, action, law, life, history, place etc. (total 29)

Of particular interest to linguists is also the professional differentiation of the national language, the originality of the use of vocabulary and grammar, depending on the type of occupation. It is known that drivers in professional speech use the form w about fer, the medics say k about club instead of cocktail Yu sh - such examples can be given. The task of statistics is to track the variability of pronunciation and the change in the language norm.

Professional differences lead to differences not only grammatical, but also lexical. Yakut State University named after M.K. Ammosov, 50 questionnaires were analyzed with the most common reactions to certain words among physicians and builders (Table 3).

		Builders
human	patient (10), personality (5)	man (5)
good	help (8), help (7)	evil (16)
life	death (10)	lovely (5)
death	corpse (8)	life (6)
the fire	heat (8), burn (6)	fire (7)
finger	hand (14), panaritium (5)	large (7), index (6)
eyes	vision (6), pupil, ophthalmologist (5 each)	brown (10), large (6)
head	mind (14), brains (5)	big (9), smart (8), smart (6)
lose	consciousness, life (4 each)	money (5), find (4)

It can be noted that physicians more often than builders give associations related to their professional activities, since the stimulus words given in the questionnaire have more to do with their profession than with the profession of a builder.

Statistical regularities in a language are used to create frequency dictionaries - dictionaries that give numerical characteristics of the frequency of words (word forms, phrases) of any language - the language of the writer, any work, etc. Usually, the frequency of occurrence of a word is used as a characteristic of the frequency of occurrence of a word in the text of a certain volume

The model of speech perception is impossible without a dictionary as its essential component. In the perception of speech, the basic operational unit is the word. From this it follows, in particular, that each word of the perceived text must be identified with the corresponding unit of the listener's (or reader's) internal vocabulary. It is natural to assume that from the very beginning the search is limited to some subdomains of the dictionary. According to most modern theories of speech perception, the actual phonetic analysis of the sounding text in a typical case provides only some partial information about the possible phonological appearance of the word, and this kind of information corresponds to not one, but a certain MANY words of the dictionary; Therefore, two problems arise:

(a) select the appropriate set according to certain parameters;

(b) within the bounds of the outlined set (if it is allocated adequately) to "eliminate" all words, except for the only one that best corresponds to the given word of the recognized text. One of the "dropout" strategies is to exclude low-frequency words. It follows that the vocabulary for speech perception is a frequency dictionary. It is the creation of a computer version of the frequency dictionary of the Russian language that is the initial task of the presented project.

Based on the material of the Russian language, there are 5 frequency dictionaries (not counting branch dictionaries). Let us note only some general shortcomings of the existing dictionaries.

All known frequency dictionaries of the Russian language are based on processing arrays of written (printed) texts. Partly for this reason, when the identity of a word is largely based on formal, graphic coincidence, semantics is not sufficiently taken into account. As a result, the frequency characteristics are also shifted, distorted; for example, if the compiler of the frequency dictionary includes words from the combination "each other" in the general statistics of the use of the word "friend", then this is hardly justified: given the semantics, we must admit that these are already different words, or rather, that an independent dictionary unit is just the combination as a whole.

Also, in all existing dictionaries, words are placed only in their basic forms: nouns in the singular form, nominative case, verbs in the infinitive form, etc. Some of the dictionaries provide information about the frequency of word forms, but usually they do not do it consistently enough, not in an exhaustive way. The frequencies of different word forms of the same word obviously do not match. The developer of a speech perception model must take into account that in a real perceptual process, it is precisely a specific word form that is “immersed” in the text that is subject to recognition: based on the analysis of the initial section of the exponent of the word form, a set of words with an identical beginning is formed, and the initial section of the word form is not necessarily identical to the initial section of the dictionary form . It is the word form that has a specific rhythmic structure, which is also an extremely important parameter for the perceptual selection of words. Finally, in the final representation of the recognized utterance, again, the words are represented by the corresponding word forms.

There are many works that demonstrate the importance of frequency in the process of speech perception. But we are not aware of works where the frequency of word forms would be used - on the contrary, all authors practically ignore the frequency of individual word forms, referring exclusively to lexemes. If the results obtained by them are not considered artifacts, one has to assume that the native speaker somehow has access to information about the ratio of the frequencies of word forms and dictionary forms, i.e., in fact, lexemes. Moreover, such a transition from a word form to a lexeme, of course, cannot be explained by natural knowledge of the corresponding paradigm, since frequency information must be used before the final identification of the word, otherwise it simply loses its meaning.

According to the primary statistical characteristics, it is possible to determine with a given relative error that part of the dictionary, which includes words with a high frequency of occurrence, regardless of the type of text. It is also possible, by introducing stepwise ordering into the dictionary, to obtain a series of dictionaries covering the first 100, 1000, 5000, etc. of frequent words. The statistical characteristics of the dictionary are of interest in connection with the semantic analysis of vocabulary. The study of subject-ideological groups and semantic fields shows that lexical associations are supported by semantic links that are concentrated around lexemes with the most common meaning. The description of meanings within the lexico-semantic field can be carried out by identifying words with the most abstract lexemes in meaning. Apparently, "empty" (from the point of view of nominative potencies) dictionary units constitute a statistically homogeneous layer.

Vocabularies for individual genres are no less valuable. Studying the measure of their similarity and the nature of statistical distributions will provide interesting information about the qualitative stratification of vocabulary depending on the sphere of speech use.

Compilation of large frequency dictionaries requires the use of computer technology. INTRODUCING partial mechanization and automation into the process of working on a dictionary is of interest as an experiment in the machine processing of dictionaries for different texts. Such a dictionary requires a more rigorous system for processing and accumulating vocabulary material. In miniature, this is an information retrieval system that is able to provide information about various aspects of the text and vocabulary. Some basic requests to this system are planned from the very beginning: the total number of inventory words, the statistical characteristics of a single word and entire dictionaries, the ordering of frequent and rare zones of the dictionary, etc. The machine card file allows you to automatically build reverse dictionaries for individual genres and sources. Many other useful statistical information about the language will be extracted from the accumulated array of information. The computer frequency dictionary creates an experimental basis for the transition to a more extensive automation of vocabulary work.

The statistical data of frequency dictionaries can also be widely used in solving other linguistic problems - for example, in analyzing and determining the active means of word formation of the modern Russian language, solving issues of improving graphics and spelling, which are related to taking into account statistical information about the vocabulary (with all this, it is important to take into account probabilistic characteristics of grapheme combinations, types of letter combinations realized in words), practical transcription and transliteration. The statistical parameters of the dictionary will also be useful in solving problems of automating typing, recognition and automatic reading of literal text.

Modern explanatory dictionaries and grammars of the Russian language are mainly built on the basis of literary and artistic texts. There are frequency dictionaries of the language of A.S. Pushkin, A.S. Griboedova, F.M. Dostoevsky, V.V. Vysotsky and many other authors. At the Department of History and Theory of Literature of the Smolensk State. Pedagogical University has been working for a number of years to compile frequency dictionaries of poetic and prose texts. For this study, frequency dictionaries of all the lyrics of Pushkin and two more poets of the golden age - "Woe from Wit" by Griboyedov and all of Lermontov's poetry were selected; Pasternak and five other poets of the Silver Age - Balmont 1894-1903, "Poems about the Beautiful Lady" by Blok, "Stone" by Mandelstam, "Pillar of Fire" by Gumilyov, "Anno Domini MCMXXI" by Akhmatova and "Sisters of My Life" by Pasternak and four more poets of the Iron Age - "Poems by Yuri Zhivago", "When it clears up", the entire corpus of lyrics by M. Petrovs, "The road is far away", "Windshield", "Farewell to the snow" and "Horseshoes" by Mezhirov, "Antimirov" by Voznesensky and "Snezhnitsa » Rylenkova.

It should be noted that these dictionaries are different in nature: some represent the vocabulary of one dramatic work, others - books of lyrics, or several books, or the entire corpus of the poet's poems. The results of the analysis presented in this paper should be taken with caution, they cannot be taken as an absolute. At the same time, with the help of special measures, the difference in the ontological nature of texts can be reduced to a certain extent.

In recent years, the opposition between colloquial and book speech has become more and more clearly realized. This issue is especially sharply discussed among methodologists who demand a turn in teaching towards the spoken language. At the same time, the specificity of colloquial speech still remains unexplained.

Dictionaries were processed by creating a user application in the environment of the EXCEL97 office program. The application includes four worksheets of the EXCEL book - "Title Sheet", "Dictionaries" sheet with initial data, "Proximity" and "Distances" with results, as well as a set of macros.

The initial information is entered on the "Dictionaries" sheet. In EXCEL cells, dictionaries of the studied texts are written, the last column S is formed from the results obtained and is equal to the number of words found in other dictionaries. The tables "Proximity" and "Distances" contain calculated measures of proximity M, correlation R and distance D.

Application macros are event-based programming procedures written in Visual Basic for Application (VBA). Procedures are based on VBA library objects and their processing methods. So, for operations with worksheets of the application, the key object Worksheet (worksheet) and the corresponding method of activating the sheet Activate (activate) are used. Setting the range of the analyzed source data on the Dictionary sheet is performed by the Select method of the Range object (range), and the transfer of words as values ​​to variables is performed as the Value property (value) of the same Range object.

Despite the fact that rank correlation analysis makes us cautious about the dependence of topics between different texts, most of the most frequent words in each text have matches in one or more other texts. Column S shows the number of such words among the 15 most frequent words for each author. Words in bold type appear only in one poet's words in our table. Blok, Akhmatova and Petrovs have no highlighted words at all, they have S = 15. These three poets have the same 15 most frequent words, they differ only in the place in the list. But even Pushkin, whose vocabulary is the most original, has S = 8, and there are 7 highlighted words.

The results show that there is a certain layer of vocabulary that concentrates the main themes of poetry. As a rule, these words are short: out of the total number (225) of single-syllable word usages 88, two-syllable 127, three-syllable 10. Often these words represent the main mythologemes and can fall into pairs: night - day, earth - sky (sun), God - man (people), life - death, body - soul, Rome - world(at Mandelstam); can be combined into mythologems of a higher level: sky, star, sun, earth; in a person, as a rule, the body, heart, blood, arm, leg, cheek, eyes stand out. Of the human states, preference is given to sleep and love. The house and cities belong to the human world - Moscow, Rome, Paris. Creativity is represented by lexemes word and song.

Griboedov and Lermontov have almost no words denoting nature among the most frequent words. They have three times as many words denoting a person, parts of his body, elements of his spiritual world. Pushkin and poets of the twentieth century. designations of man and nature are approximately equal. In this important aspect of the subject, we can say that the twentieth century. followed Pushkin.

Minimal Theme a business among the most frequent words, it is found only in Griboyedov and Pushkin. Lermontov and poets of the twentieth century. it gives way to a minimal theme word. The word does not exclude deeds (the biblical interpretation of the topic: in the New Testament, all the teachings of Jesus Christ are regarded as the word of God or the word of Jesus, and the apostles sometimes call themselves ministers of the Word). The sacred meaning of the lexeme word is convincingly manifested, for example, in Pasternak's verse "And the image of the world, revealed in the Word." The sacred meaning of the lexeme word in conjunction with and contrast with human affairs, it is convincingly manifested in the poem of the same name by Gumilyov.

Tokens that are found only in one text characterize the originality of a given book or a collection of books. For example, the word "mind" is the most frequent in Griboedov's comedy "Woe from Wit" - but it does not occur among the frequency words of other texts. The theme of the mind is by far the most significant in comedy. This lexeme accompanies the image of Chatsky, and the name of Chatsky is the most frequent in comedy. Thus, the work organically combines the most frequent common noun with the most frequent proper name.

The highest correlation coefficient connects the themes of the tragic books "The Pillar of Fire" by Gumilyov and "Anno Domini MCMXXI" by Akhmatova. Among the 15 most frequent nouns, there are 10 common ones, including blood, heart, soul, love, word, sky. Recall that Akhmatova's book included a miniature "You will not be alive ...", written between the arrest of Gumilyov and his execution.

The themes of the candle and the crowd in the studied material are found only in the "Poems of Yuri Zhivago". The theme of the candle in the verses from the novel has many contextual meanings: it is associated with the image of Jesus Christ, with the themes of faith, immortality, creativity, love date. The candle is the most important source of light in the central scenes of the novel. The theme of the crowd develops in connection with the main idea of ​​the novel, in which the private life of a person with its unshakable values ​​is opposed to the immorality of the new state, built on the principles of pleasing the crowd.

The work also involves the third stage, also reflected in the program, - this is the calculation of the difference in the ordinal numbers of words common to two dictionaries and the average distance between the same words of two dictionaries. This stage allows moving from the general trends in the interaction of dictionaries identified with the help of statistics to a level approaching the text. For example, the books of Gumilyov and Akhmatova correlate statistically significantly. We look at which words turned out to be common for their dictionaries, and, first of all, we choose those whose serial numbers differ minimally or equal to zero. It is these words that have the same rank number and, consequently, it is these minimal themes in the minds of the two poets that are equally important. Next, you should move to the level of texts and contexts.

Quantitative methods also help to study the characteristics of peoples - native speakers. Say, there are 6 cases in Russian, there are no cases in English, and in some languages ​​of the peoples of Dagestan, the number of cases reaches 40. L. Perlovsky in his article “Consciousness, Language and Culture” correlates these characteristics with the tendency of peoples to individualism or collectivism, with perception of things and phenomena separately or in connection with others. After all, it was in the English-speaking world (there are no cases - the thing is perceived “by itself”) that such concepts as individual freedom, liberalism and democracy appeared (I note that I use these concepts only in connection with the language, without any evaluative characteristics). Despite the fact that such guesses still remain only at the level of bold scientific hypotheses, they help to look at already familiar phenomena in a new way.

As we can see, quantitative characteristics can be applied in completely different areas of linguistics, which increasingly blurs the boundaries between "exact" and "humanitarian" methods. Linguistics is increasingly resorting to the help of not only mathematics, but also computer technology to solve its problems.

2.3 Learning Ilanguage by methods of formal logic

With non-quantitative methods of mathematics, in particular, with logic, modern theoretical linguistics interacts no less fruitfully than with quantitative ones. The rapid development of computer technologies and the growth of their role in the modern world required a revision of the approach to the interaction of language and logic in general.

The methods of logic are widely used in the development of formalized languages, in particular, programming languages, the elements of which are some symbols (akin to mathematical), chosen (or constructed from previously selected symbols) and interpreted in a certain way, related to any "traditional" use, understanding and understanding. functions of the same symbols in other contexts. A programmer constantly deals with logic in his work. The meaning of programming is just to teach the computer to reason (in the broadest sense of the word). At the same time, the methods of "reasoning" turn out to be very different. Every programmer spends a certain amount of time looking for bugs in their own and other people's programs. That is, to search for errors in reasoning, in logic. And this also leaves its mark. It is much easier to detect logical errors in ordinary speech. The relative simplicity of the languages ​​studied by logicians allows them to elucidate the structures of these languages ​​more clearly than is achievable by linguists who analyze exclusively complex natural languages. In view of the fact that the languages ​​studied by logicians use relations copied from natural languages, logicians are able to make significant contributions to the general theory of language. The situation here is similar to that which takes place in physics: the physicist also formulates theorems for ideally simplified cases that do not occur in nature at all - he formulates laws for ideal gases, ideal liquids, talks about motion in the absence of friction, etc. For these idealized cases, simple laws can be established that would greatly contribute to the understanding of what really happens and what would probably remain unknown to physics if it tried to consider reality directly, in all its complexity.

In the study of natural languages, logical methods are used so that language learners can not stupidly “memorize” as many words as possible, but better understand its structure. L. Shcherba also used in his lectures an example of a sentence built according to the laws of the Russian language: “The glitched kuzdra shteko boked the bokra and curls the bokra,” and then asked the students what this meant. Despite the fact that the meaning of the words in the sentence remained unclear (they simply do not exist in Russian), it was possible to clearly answer: “kuzdra” is the subject, a feminine noun, in the singular, nominative case, “bokr” is animated, and etc. The translation of the phrase turns out to be something like this: “Something feminine in one go did something over some kind of male creature, and then began to do something long, gradual with its cub.” A similar example of a text (artistic) from non-existent words, built entirely according to the laws of the language, is Lewis Carroll's Jabberwock (in Alice in Wonderland, Carroll, through the mouth of his character Humpty Dumpty, explains the meaning of the words he invented: "cooked" - eight o'clock in the evening, when it's time to cook dinner, "chlivky" - flimsy and dexterous, "shorek" - a cross between a ferret, a badger and a corkscrew, "dive" - ​​jump, dive, spin, "nava" - grass under the sundial (extends a little to the right , a little to the left and a little back), “grunt” - grunt and laugh, “zelyuk” - a green turkey, “myumzik” - a bird; her feathers are disheveled and stick out in all directions, like a broom, “mova” - far from home) .

One of the main concepts of modern logic and theoretical linguistics, used in the study of languages ​​of various logico-mathematical calculus, natural languages, to describe the relationship between languages ​​of different "levels" and to characterize the relationship between the languages ​​under consideration and the subject areas described with their help, is the concept of metalanguage. A metalanguage is a language used to express judgments about another language, the language-object. With the help of a metalanguage, they study the structure of character combinations (expressions) of the language-object, prove theorems about its expressive properties, about its relation to other languages, etc. The language being studied is also called the subject language in relation to this metalanguage. Both the subject language and the metalanguage can be ordinary (natural) languages. The metalanguage may differ from the object language (for example, in an English textbook for Russians, Russian is the metalanguage, and English is the object language), but it may also coincide with it or differ only partially, for example, in special terminology (Russian linguistic terminology is an element of the metalanguage to describe the Russian language, the so-called semantic factors are part of the metalanguage for describing the semantics of natural languages).

The concept of "metalinguage" has become very fruitful in connection with the study of formalized languages ​​that are built within the framework of mathematical logic. Unlike formalized subject languages, in this case the metalanguage, by means of which the metatheory is formulated (studying the properties of the subject theory formulated in the subject language), is, as a rule, an ordinary natural language, in some special way a limited fragment of a natural language that does not contain any kind of ambiguity. , metaphors, "metaphysical" concepts, etc. elements of ordinary language that prevent its use as a tool for accurate scientific research. At the same time, the metalanguage itself can be formalized and (regardless of this) become the subject of research carried out by means of the metametalanguage, and such a series can be “thought” as growing indefinitely.

Logic teaches us a fruitful distinction between the language-object and the metalanguage. The language-object is the very subject of logical research, and the metalanguage is that inevitably artificial language in which such research is conducted. Logical thinking just consists in formulating the relations and structure of a real language (object language) in the language of symbols (metalanguage).

The metalanguage must in any case be “not poorer” than its objective language (that is, for each expression of the latter in the metalanguage there must be its name, “translation”) - otherwise, if these requirements are not met (which certainly takes place in natural languages, if special agreements do not provide otherwise), semantic paradoxes (antinomies) arise.

As more and more new programming languages ​​were created, in connection with the problem of programming translators, there was an urgent need to create metalanguages. At present, the Backus-Naur form metalanguage (abbreviated as BNF) is the most commonly used for describing the syntax of programming languages. It is a compact form in the form of some formulas similar to mathematical ones. For each concept of the language there is a unique metaformula (normal formula). It consists of left and right parts. The left side specifies the concept being defined, and the right side specifies the set of admissible language constructs that are combined into this concept. The formula uses special metacharacters in the form of angle brackets, which contain the defined concept (in the left side of the formula) or a previously defined concept (in its right side), and the separation of the left and right parts is indicated by the "::=" metacharacter, the meaning of which is equivalent to the words "by definition there is". Metalinguistic formulas are embedded in translators in some form; with their help, the constructs used by the programmer are checked for formal compliance with any of the constructs that are syntactically valid in this language. There are also separate metalanguages ​​of various sciences - thus, knowledge exists in the form of various metalanguages.

Logical methods also served as the basis for the creation of artificial intelligence systems based on the concept of connectionism. Connectionism is a special trend in philosophical science, the subject of which is questions of knowledge. Within the framework of this trend, attempts are being made to explain the intellectual abilities of a person using artificial neural networks. Composed of a large number of structural units similar to neurons, with a weight assigned to each element that determines the strength of the connection with other elements, neural networks are simplified models of the human brain. Experiments with neural networks of this kind have demonstrated their ability to learn to perform tasks such as pattern recognition, reading, and identifying simple grammatical structures.

Philosophers began to take an interest in connectionism, as the connectionist approach promised to provide an alternative to the classical theory of the mind and the idea widely held within this theory that the workings of the mind are similar to the processing of symbolic language by a digital computer. This concept is very controversial, but in recent years it has found more and more supporters.

The logical study of language continues Saussure's concept of language as a system. The fact that it is constantly continuing confirms once again the boldness of scientific conjectures of the beginning of the last century. I will devote the last section of my work to the prospects for the development of mathematical methods in linguistics today.

2.4 Prospects for the application of mathematical methods in linguistics

In the era of computer technology, the methods of mathematical linguistics have received a new development perspective. The search for solutions to the problems of linguistic analysis is now increasingly being implemented at the level of information systems. At the same time, automation of the process of processing linguistic material, providing the researcher with significant opportunities and advantages, inevitably puts forward new requirements and tasks for him.

The combination of "exact" and "humanitarian" knowledge has become fertile ground for new discoveries in the field of linguistics, computer science and philosophy.

Machine translation from one language to another remains a rapidly growing branch of information technology. Despite the fact that computer-assisted translation can never be compared in quality to human translation (especially for literary texts), the machine has become an indispensable assistant to a person in translating large volumes of text. It is believed that in the near future more advanced translation systems will be created, based primarily on the semantic analysis of the text.

An equally promising direction is the interaction of linguistics and logic, which serves as a philosophical foundation for understanding information technology and the so-called "virtual reality". In the near future, work will continue on the creation of artificial intelligence systems - although, again, it will never be equal to the human in its capabilities. Such competition is meaningless: in our time, the machine should become (and becomes) not a rival, but an assistant to man, not something from the realm of fantasy, but part of the real world.

The study of the language by statistical methods continues, which makes it possible to more accurately determine its qualitative properties. It is important that the most daring hypotheses about language find their mathematical, and therefore logical, proof.

The most significant thing is that various branches of the application of mathematics in linguistics, previously quite isolated, in recent years have been correlated with each other, connecting into a coherent system, by analogy with the language system discovered a century ago by Ferdinand de Saussure and Yvan Baudouin de Courtenay. This is the continuity of scientific knowledge.

Linguistics in the modern world has become the foundation for the development of information technology. As long as computer science remains a rapidly developing branch of human activity, the union of mathematics and linguistics will continue to play its role in the development of science.

Conclusion

Over the 20th century, computer technologies have come a long way - from military to peaceful use, from a narrow range of goals to penetration into all branches of human life. Mathematics as a science found ever new practical significance with the development of computer technology. This process continues today.

The previously unthinkable "tandem" of "physicists" and "lyricists" has become a reality. For the full interaction of mathematics and computer science with the humanities, qualified specialists were required from both sides. While computer scientists are increasingly in need of systematic humanitarian knowledge (linguistic, cultural, philosophical) in order to comprehend changes in the reality around them, in the interaction of man and technology, to develop more and more new linguistic and mental concepts, to write programs, then any "Humanities" in our time for their professional growth must master at least the basics of working with a computer.

Mathematics, being closely interconnected with informatics, continues to develop and interact with natural sciences and the humanities. In the new century, the trend towards the mathematization of science is not weakening, but, on the contrary, is increasing. On the basis of quantitative data, the laws of the development of the language, its historical and philosophical characteristics are comprehended.

Mathematical formalism is most suitable for describing patterns in linguistics (as, indeed, in other sciences - both the humanities and the natural). The situation sometimes develops in science in such a way that without the use of an appropriate mathematical language, it is impossible to understand the nature of physical, chemical, etc. process is not possible. Creating a planetary model of the atom, the famous English physicist of the XX century. E. Rutherford experienced mathematical difficulties. At first, his theory was not accepted: it did not sound convincing, and the reason for this was Rutherford's ignorance of the theory of probability, on the basis of the mechanism of which it was only possible to understand the model representation of atomic interactions. Realizing this, already by that time an outstanding scientist, the owner of the Nobel Prize, enrolled in the seminar of the mathematician Professor Lamb and for two years, together with the students, attended a course and worked out a workshop on the theory of probability. Based on it, Rutherford was able to describe the behavior of the electron, giving his structural model convincing accuracy and gaining recognition. The same is with linguistics.

This begs the question, what is so mathematical in objective phenomena, thanks to which they can be described in the language of mathematics, in the language of quantitative characteristics? These are homogeneous units of matter distributed in space and time. Those sciences that have gone farther than others towards the isolation of homogeneity, and turn out to be better suited for the use of mathematics in them.

The Internet, which rapidly developed in the 1990s, brought together representatives of various countries, peoples and cultures. Despite the fact that English continues to be the main language of international communication, the Internet has become multilingual in our time. This led to the development of commercially successful machine translation systems that are widely used in various fields of human activity.

Computer networks have become an object of philosophical reflection - more and more new linguistic, logical, worldview concepts have been created that help to understand "virtual reality". In many works of art, scenarios were created - more often pessimistic ones - about the dominance of machines over a person, and virtual reality - over the outside world. Far from always such forecasts turned out to be meaningless. Information technology is not only a promising industry for investing human knowledge, it is also a way to control information, and, consequently, over human thought.

This phenomenon has both a negative and a positive side. Negative - because control over information is contrary to the inalienable human right to free access to it. Positive - because the lack of this control can lead to catastrophic consequences for humanity. Suffice it to recall one of the wisest films of the last decade - "When the World Ends" by Wim Wenders, whose characters are completely immersed in the "virtual reality" of their own dreams recorded on a computer. At the same time, not a single scientist and not a single artist can give an unambiguous answer to the question: what awaits science and technology in the future.

Focusing on the "future", sometimes seeming fantastic, was a distinctive feature of science in the mid-twentieth century, when inventors sought to create perfect models of technology that could work without human intervention. Time has shown the utopian nature of such research. At the same time, it would be superfluous to condemn scientists for this - without their enthusiasm in the 1950s - 60s, information technology would not have made such a powerful leap in the 90s, and we would not have what we have now.

The last decades of the twentieth century changed the priorities of science - research, inventive pathos gave way to commercial interest. Again, this is neither good nor bad. This is a reality in which science is increasingly integrated into everyday life.

The 21st century has continued this trend, and in our time behind inventions are not only fame and recognition, but, first of all, money. This is also why it is important to ensure that the latest achievements of science and technology do not fall into the hands of terrorist groups or dictatorial regimes. The task is difficult to the point of impossibility; to realize it as much as possible is the task of the entire world community.

Information is a weapon, and weapons are no less dangerous than nuclear or chemical weapons - only it does not act physically, but rather psychologically. Humanity needs to think about what is more important for it in this case - freedom or control.

The latest philosophical concepts related to the development of information technologies and an attempt to comprehend them have shown the limitations of both natural-science materialism, which dominated during the 19th and early 20th centuries, and extreme idealism, which denies the significance of the material world. It is important for modern thought, especially the thought of the West, to overcome this dualism in thinking, when the surrounding world is clearly divided into material and ideal. The path to this is a dialogue of cultures, a comparison of different points of view on the surrounding phenomena.

Paradoxically, information technology can play an important role in this process. Computer networks, and especially the Internet, are not only a resource for entertainment and vigorous commercial activity, they are also a means of meaningful, controversial communication between representatives of various civilizations in the modern world, as well as for a dialogue between the past and the present. We can say that the Internet pushes the spatial and temporal boundaries.

And in the dialogue of cultures through information technology, the role of language as the oldest universal means of communication is still important. That is why linguistics, in interaction with mathematics, philosophy and computer science, has experienced its second birth and continues to develop today. The trend of the present will continue in the future - "until the end of the world", as 15 years ago, the same V. Wenders predicted. True, it is not known when this end will occur - but does it matter now, because the future will sooner or later become the present anyway.

Attachment 1

Ferdinand de Saussure

The Swiss linguist Ferdinand de Saussure (1857-1913) is widely considered to be the founder of modern linguistics in its attempts to describe the structure of language rather than the history of particular languages ​​and language forms. In fact, the method of Structuralism in linguistics and literary studies and a significant branch of Semiotics find their major starting point in his work at the turn of the twentieth century. It has even been argued that the complex of strategies and conceptions that has come to be called "poststructuralism" - the work of Jacques Derrida, Michel Foucault, Jacques Lacan, Julia Kristeva, Roland Barthes, and others - is suggested by Saussure"s work in linguistics and anagrammatic readings of late Latin poetry. literary modernism to psychoanalysis and philosophy in the early twentieth century. As Algirdas Julien Greimas and Joseph Courtes argue in Semiotics and Language: An Analytic Dictionary, under the heading "Interpretation," a new mode of interpretation arose in the early twentieth century which they identify with Saussurean linguistics, Husserlian Phenomenology, and Freudian psychoanalysis. In this mode, "interpretation is no longer a matter of attributing a given content to a form which would otherwise lack one; rather, it is a paraphrase which formulates in another fashion the equivalent content of a signifying element within a given semiotic system" ( 159). in this understanding of "interpretation," form and content are not distinct; rather, every "form" is, alternatively, a semantic "content" as well, a "signifying form," so that interpretation offers an analogical paraphrase of something that already signifies within some other system of signification.

Such a reinterpretation of form and understanding - which Claude Levi-Strauss describes in one of his most programmatic articulations of the concept of structuralism, in "Structure and Form: Reflections on a Work by Vladimir Propp" - is implicit in Saussure"s posthumous Course in General Linguistics (1916, trans., 1959, 1983).In his lifetime, Saussure published relatively little, and his major work, the Course, was the transcription by his students of several courses in general linguistics he offered in 1907-11. In the Course Saussure called for the "scientific" study of language as opposed to the work in historical linguistics that had been done in the nineteenth century. That work is one of the great achievements of Western intellect: taking particular words as the building blocks of language, historical (or "diachronic") linguistics traced the origin and development of Western languages ​​from a putative common language source, first an "Indo-European" language and then an earlier "p roto-Indo-European" language.

It is precisely this study of the unique occurrences of words, with the concomitant assumption that the basic "unit" of language is, in fact, the positive existence of these "word-elements," that Saussure questioned. His work was an attempt to reduce the mass of facts about language, studied so minutely by historical linguistics, to a manageable number of propositions. The "comparative school" of nineteenth-century Philology, Saussure says in the Course, "did not succeed in setting up the true science of linguistics" because "it failed to seek out the nature of its object of study" ( 3). That "nature," he argues, is to be found not simply in the "elemental" words that a language comprises - the seeming "positive" facts (or "substances") of language - but in the formal relationships that give rise to those "substances."

Saussure"s systematic reexamination of language is based upon three assumptions. The first is that the scientific study of language needs to develop and study the system rather than the history of linguistic phenomena. For this reason, he distinguishes between the particular occurrences of language - its particular "speech-events," which he designates as parole - and the proper object of linguistics, the system (or "code") governing those events, which he designates as langue. Such a systematic study, moreover, calls for a " synchronic" conception of the relationship among the elements of language at a particular instant rather than the "diachronic" study of the development of language through history.

This assumption gave rise to what Roman Jakobson in 1929 came to designate as "structuralism," in which "any set of phenomena examined by contemporary science is treated not as a mechanical agglomeration but as a structural whole the mechanical conception of processes yields to the question of their function" ("Romantic" 711). In this passage Jakobson is articulating Saussure"s intention to define linguistics as a scientific system as opposed to a simple, "mechanical" accounting of historical accidents. Along with this, moreover, Jakobson is also describing the second foundational assumption in Saussurean - we can now call it "structural" - linguistics: that the basic elements of language can only be studied in relation to their functions rather than in relation to their causes. European "words"), those events and entities have to be situated within a systemic framework in which they are related to other so-called events and entities. This is a radical reorientation in conceiving of experience and phenomena, one whose importance the philosopher Ernst Cassirer has compared to "the new science of Galileo which in the seventeenth century changed our whole concept of the physical world" (cited in Culler, Pursuit 2 four). This change, as Greimas and Courtes note, reconceives "interpretation" and thus reconceives explanation and understanding themselves. Instead of explanation "s being in terms of a phenomenon"s causes, so that, as an "effect," it is in some ways subordinate to its causes, explanation here consists in subordinating a phenomenon to its future-oriented "function" or "purpose." Explanation is no longer independent of human intentions or purposes (even though those intentions can be impersonal, communal, or, in Freudian terms, "unconscious").

In his linguistics Saussure accomplishes this transformation specifically in the redefinition of the linguistic "word," which he describes as the linguistic "sign" and defines in functionalist terms. The sign, he argues, is the union of "a concept and a sound image," which he called "signified and signifier " (66-67; Roy Harris"s 1983 translation offers the terms "signification" and "signal" ). The nature of their "combination" is "functional" in that neither the signified nor the signifier is the "cause" of the other; rather, "each its values ​​from the other" (8). element of language, the sign, relationally and makes the basic assumption of historical linguistics, namely, the identity of the elemental units of language and signification (i.e., "words"), subject to rigorous analysis. the word "tree" as the "same" word is not because the word is defined by inherent qualities - it is not a "mechanical agglomeration" of such qualities - but because it is defined as an element in a system, the "structural whole" ," of language.

Such a relational (or "diacritical") definition of an entity governs the conception of all the elements of language in structural linguistics. This is clearest in the most impressive achievement of Saussurean linguistics, the development of the concepts of the "phonemes" and "distinctive features" of language. Phonemes are the smallest articulated and signifying units of a language. They are not the sounds that occur in language but the "sound images" Saussure mentions, which are apprehended by speakers - phenomenally apprehended - as conveying meaning. (Thus, Elmar Holenstein describes Jakobson's linguistics, which follows Saussure in important ways, as "phenomenological structuralism.") It is for this reason that the leading spokesperson for Prague School Structuralism, Jan Mukarovsky, noted in 1937 that "structure . . . is a phenomenological and not an empirical reality; it is not the work itself, but a set of functional relationships which are located in the consciousness of a collective (generation, milieu, etc.)" (cited in Galan 35). Similarly, Levi-Strauss, the leading spokesperson for French structuralism , noted in 1960 that "structure has no distinct content; it is content itself, and the logical organization in which it is arrested is conceived as a property of the real" (167; see also Jakobson, Fundamentals 27-28).

Phonemes, then, the smallest perceptible elements of language, are not positive objects but a "phenomenological reality." In English, for instance, the phoneme /t/ can be pronounced in many different ways, but in all cases an English speaker will recognize it as functioning as a /t/. An aspirated t (i.e., a t pronounced with an h-like breath after it), a high-pitched or low-pitched t sound, an extended t sound, and so on, will all function in the same manner in distinguishing the meaning of "to" and "do" in English. Moreover, the differences between languages ​​are such that phonological variations in one language can constitute distinct phonemes in another; thus, English distinguishes between /l/ and /r/, whereas other languages ​​are so structured that these articulations are considered variations of the same phoneme (like the aspirated and unaspirated t in English). In every natural language, the vast number of possible words is a combination of a small number of phonemes. English, for instance, possesses less than 40 phonemes that combine to form over a million different words.

The phonemes of language are themselves systematically organized structures of features. In the 1920s and 1930s, following Saussure "s lead, Jakobson and N. S. Trubetzkoy isolated the "distinctive features" of phonemes. These features are based upon the physiological structure of the speech organs - tongue, teeth, vocal chords, and so on - that Saussure mentions in the Course and that Harris describes as "physiological phonetics" ( 39; Baskin"s earlier translation uses the term "phonology" [(1959) 38]) - and they combine in "bundles" of binary oppositions to form phonemes. For instance, in English the difference between /t/ and /d/ is the presence or absence of "voice" (the engagement of the vocal chords), and on the level of voicing these phonemes reciprocally define one another. In this way, phonology is a specific example of a general rule of language described by Saussure: In language there are only differences. even more important: a difference generally implies positive terms between which the difference is set up; but in language there are only differences without positive terms. Whether we take the signified or the signifier, the language has neither ideas nor sounds that existed before the linguistic system. ( 120)

In this framework, linguistic identities are determined not by inherent qualities but by systemic ("structural") relationships.

I have said that phonology "followed the lead" of Saussure, because even though his analysis of the physiology of language production "would nowadays," as Harris says, "be called "physical," as opposed to either "psychological" or "functional "" (Reading 49), consequently in the Course he articulated the direction and outlines of a functional analysis of language. Similarly, his only extended published work, Memoire sur le systeme primitif des voyelles dans les langues indo-europeennes (Memoir on the primitive system of vowels in Indo-European languages), which appeared in 1878, was fully situated within the project of nineteenth- century historical linguistics. Nevertheless, within this work, as Jonathan Culler has argued, Saussure demonstrated "the fecundity of thinking of language as a system of purely relational items, even when working at the task of historical reconstruction" (Saussure 66). By analyzing the systematic structural relationships among phonemes to account for patterns of vowel alternation in existing Indo-European languages, Saussure suggested that in addition to several different phonemes /a/, there must have been another phoneme that could be described formally. "What makes Saussure"s work so very impressive," Culler concludes, "is the fact that nearly fifty years later, when cuneiform Hittite was discovered and deciphered, it was found to contain a phoneme, written h, which behaved as Saussure had predicted . He had discovered, by a purely formal analysis, what are now known as the laryngeals of Indo-European" (66).

This conception of the relational or diacritical determination of the elements of signification, which is both implicit and explicit in the Course, suggests a third assumption governing structural linguistics, what Saussure calls "the arbitrary nature of the sign." By this he means that the relationship between the signifier and signified in language is never necessary (or "motivated"): one could just as easily find the sound signifier arbre as the signifier tree to unite with the concept "tree". But more than this, it means that the signified is arbitrary as well: one could as easily define the concept "tree" by its woody quality (which would exclude palm trees) as by its size (which excludes the "low woody plants" we call bushes). This should make clear that the numbering of assumptions I have been presenting does not represent an order of priority: each assumption - the systemic nature of signification (best apprehended by studying language "synchronously"), the relational or "diacritical" nature of the elements of signification, the arbitrary nature of signs - derives its value from the others.

That is, Saussurean linguistics the phenomena it studies in overarching relationships of combination and contrast in language. In this conception, language is both the process of articulating meaning (signification) and its product (communication), and these two functions of language are neither identical nor fully congruent (see Schleifer, "Deconstruction"). Here, we can see the alternation between form and content that Greimas and Courtes describe in modernist interpretation: language presents contrasts that formally define its units, and these units combine on succeeding levels to create the signifying content. Since the elements of language are arbitrary, moreover, neither contrast nor combination can be said to be basic. Thus, in language distinctive features combine to form contrasting phonemes on another level of apprehension, phonemes combine to form contrasting morphemes, morphemes combine to form words, words combine to form sentences, and so on. In each instance, the whole phoneme, or word, or sentence, and so on, is greater than the sum of its parts (just as water, H2O, in Saussure"s example [(1959) 103] is more than the mechanical agglomeration of hydrogen and oxygen).

The three assumptions of the Course in General Linguistics led Saussure to call for a new science of the twentieth century that would go beyond linguistic science to study "the life of signs within society." Saussure named this science "semiology (from Greek semeion "sign")" (16). The "science" of semiotics, as it came to be practiced in Eastern Europe in the 1920s and 1930s and Paris in the 1950s and 1960s, widened the study of language and linguistic structures to literary artifacts constituted (or articulated) by those structures. Throughout the late part of his career, moreover, even while he was offering the courses in general linguistics, Saussure pursued his own "semiotic" analysis of late Latin poetry in an attempt to discover deliberately concealed anagrams of proper names. The method of study was in many ways the opposite of the functional rationalism of his linguistic analyses: it attempted, as Saussure mentions in one of the 99 notebooks in which he pursued this study, to examine systematically the problem of "chance," which " becomes the inevitable foundation of everything" (cited in Starobinski 101). Such a study, as Saussure himself says, focuses on "the material fact" of chance and meaning (cited 101), so that the "theme-word" whose anagram Saussure is seeking, as Jean Starobinski argues, "is, for the poet , an instrument, and not a vital germ of the poem. The poem is required to re-employ the phonic materials of the theme-word" (45). In this analysis, Starobinski says, "Saussure did not lose himself in a search for hidden meanings." Instead, his work seems to demonstrate a desire to evade all the problems arising from consciousness: "Since poetry is not only realized in words but is something born from words, it escapes the arbitrary control of consciousness to depend solely on a kind of linguistic legality "(121).

That is, Saussure"s attempt to discover proper names in late Latin poetry - what Tzvetan Todorov calls the reduction of a "word . . . to its signifier" (266) - emphasizes one of the elements that governed his linguistic analysis, the arbitrary nature of the sign. (It also emphasizes the formal nature of Saussurean linguistics - "Language," he asserts, "is a form and not a substance" - which eliminate effectivelys semantics as a major object of analysis.) As Todorov concludes, Saussure"s work appears remarkably homogeneous today in its refusal to accept symbolic phenomena . . . . In his research on anagrams, he pays attention only to the phenomena of repetition, not to those of evocation. . . . In his studies of the Nibelungen, he recognizes symbols only in order to attribute them to mistaken readings: since they are not intentional, symbols do not exist. Finally in his courses on general linguistics, he contemplates the existence of semiology, and thus of signs other than linguistic ones; but this affirmation is at once limited by the fact that semiology is devoted to a single type of sign: those which are arbitrary. (269-70)

If this is true, it is because Saussure could not conceive of "intention" without a subject; he could not quite escape the opposition between form and content his work did so much to call into question. Instead, he resorted to "linguistic legality." Situated between, on the one hand, nineteenth-century conceptions of history, subjectivity, and the mode of causal interpretation governed by these conceptions and, on the other hand, twentieth-century "structuralist" conceptions of what Levi-Strauss called "Kantianism without a transcendental subject" (cited in Connerton 23) - concepts that erase the opposition between form and content (or subject and object) and the hierarchy of foreground and background in full-blown structuralism, psychoanalysis, and even quantum mechanics - the work of Ferdinand de Saussure in linguistics and semiotics circumscribes a signal moment in the study of meaning and culture.

Ronald Schleifer

Annex 2

Ferdinand de Saussure (translation)

The Swiss linguist Ferdinand de Saussure (1857-1913) is considered the founder of modern linguistics - thanks to his attempts to describe the structure of the language, rather than the history of individual languages ​​and word forms. By and large, the foundations of structural methods in linguistics and literary criticism and, to a large extent, semiotics were laid in his works at the very beginning of the twentieth century. It is proved that the methods and concepts of the so-called "post-structuralism", developed in the works of Jacques Derrida, Michel Foucault, Jacques Lacan, Julia Kristeva, Roland Barthes and others, go back to the linguistic works of Saussure and anagrammatic readings of late Roman poetry. It should be noted that Saussure's work on linguistics and linguistic interpretation helps to connect a wide range of intellectual disciplines - from physics to literary innovations, psychoanalysis and philosophy of the early twentieth century. A. J. Greimas and J. Kurte write in Semiotics and Language: “An analytical dictionary with the title “Interpretation” as a new kind of interpretation appeared at the beginning of the 20th century along with the linguistics of Saussure, the phenomenology of Husserl and the psychoanalysis of Freud. In such a case, "interpretation is not the attribution of a given content to a form that would otherwise lack one; rather, it is a paraphrase which formulates in another way the same content of a significant element within a given semiotic system" (159). In this understanding of "interpretation", form and content are inseparable; on the contrary, each form is filled with semantic meaning (“meaningful form”), so the interpretation offers a new, similar retelling of something meaningful in another sign system.

A similar understanding of form and content, presented by Claude Lévi-Strauss in one of the programmatic works of structuralism, ("Structure and Form: Reflections on the Works of Vladimir Propp"), can be seen in Saussure's posthumous book, A Course in General Linguistics (1916, trans., 1959, 1983). During his lifetime, Saussure published little, "Course" - his main work - was collected from the notes of students who attended his lectures on general linguistics in 1907-11. In the Course, Saussure called for a "scientific" study of language, contrasting it with nineteenth-century comparative-historical linguistics. This work can be considered one of the greatest achievements of Western thought: taking individual words as the structural elements of language as a basis, historical (or “diachronic”) linguistics proved the origin and development of Western European languages ​​​​from a common, Indo-European language - and an earlier Proto-Indo-European.

It is precisely this study of the unique occurrences of words, with the concomitant assumption that the basic "unit" of language is, in fact, the positive existence of these "word elements" that Saussure questioned. His work was an attempt to reduce the many facts about language casually studied by comparative linguistics to a small number of theorems. The comparative philological school of the 19th century, writes Saussure, "did not succeed in creating a real school of linguistics" because "it did not understand the essence of the object of study" (3). This "essence", he argues, lies not only in individual words - the "positive substances" of language - but also in the formal connections that help these substances to exist.

Saussure's "test" of language is based on three assumptions. First, the scientific understanding of language is based not on a historical, but on a structural phenomenon. Therefore, he distinguished between individual phenomena of the language - "events of speech", which he defines as "parole" - and the proper, in his opinion, object of study of linguistics, the system (code, structure) that controls these events ("langue"). Such a systematic study, moreover, requires a "synchronous" conception of the relationship between the elements of language at a given moment, rather than a "diachronic" study of the development of language through its history.

This hypothesis was the forerunner of what Roman Jakobson in 1929 would call "structuralism" - a theory where "any set of phenomena investigated by modern science is considered not as a mechanical accumulation, but as a structural whole in which the constructive component is correlated with the function" ("Romantic "711). In this passage, Jakobson formulated Saussure's idea of ​​defining language as a structure, as opposed to the "mechanical" enumeration of historical events. In addition, Jakobson develops another Saussurean assumption, which became the forerunner of structural linguistics: the basic elements of language should be studied in connection not so much with their causes, but with their functions. Separate phenomena and events (say, the history of the origin of individual Indo-European words) should be studied not by themselves, but in a system in which they are correlated with similar components. This was a radical turn in the comparison of phenomena with the surrounding reality, the significance of which was compared by the philosopher Ernst Cassirer with "the science of Galileo, which turned the ideas about the material world in the seventeenth century." Such a turn, as Greimas and Kurthe note, changes the idea of ​​"interpretation", consequently, the explanations themselves. Phenomena began to be interpreted not in relation to the causes of their occurrence, but in relation to the effect that they can have in the present and future. Interpretation ceased to be independent of a person’s intentions (despite the fact that intentions can be impersonal, “unconscious” in the Freudian sense of the word).

In his linguistics, Saussure especially shows this turn in the change in the concept of the word in linguistics, which he defines as a sign and describes in terms of its functions. A sign for him is a combination of sound and meaning, "signified and designation" (66-67; in the English translation of 1983 by Roy Harris - "signification" and "signal"). The nature of this compound is "functional" (neither one nor the other element can exist without each other); moreover, "one borrows qualities from the other" (8). Thus, Saussure defines the main structural element of language - the sign - and makes the basis of historical linguistics the identity of signs to words, which requires a particularly rigorous analysis. Therefore, we can understand different meanings of, say, the same word "tree" - not because the word is only a set of certain qualities, but because it is defined as an element in the sign system, in the "structural whole", in the language.

Such a relative ("diacritical") concept of unity underlies the concept of all elements of language in structural linguistics. This is especially clear in the most original discovery of Saussurean linguistics, in the development of the concept of "phonemes" and "distinctive features" of language. Phonemes are the smallest of the spoken and meaningful language units. They are not only sounds that occur in the language, but "sound images", notes Saussure, which are perceived by native speakers as having meaning. (It should be noted that Elmar Holenstein calls Jakobson's linguistics, which continues the ideas and concepts of Saussure in its main provisions, "phenomenological structuralism"). That is why the leading speaker of the Prague School of Structuralism, Jan Mukarowski, observed in 1937 that “structure. . . not an empirical, but a phenomenological concept; it is not the result itself, but a set of significant relations of the collective consciousness (generation, others, etc.)”. A similar thought was expressed in 1960 by Lévi-Strauss, the leader of French structuralism: “The structure has no definite content; it is meaningful in itself, and the logical construction in which it is enclosed is the imprint of reality.

In turn, phonemes, as the smallest linguistic elements acceptable for perception, represent a separate integral "phenomenological reality". For example, in English, the sound "t" can be pronounced differently, but in all cases, a person who speaks English will perceive it as "t". Aspirated, raised or lowered, a long "t" sound, etc. will equally distinguish the meaning of the words "to" and "do". Moreover, the differences between languages ​​are such that varieties of one sound in one language can correspond to different phonemes in another; for example, "l" and "r" in English are different, while in other languages ​​they are varieties of the same phoneme (like the English "t", pronounced with and without aspiration). The vast vocabulary of any natural language is a set of combinations of a much smaller number of phonemes. In English, for example, only 40 phonemes are used to pronounce and write about a million words.

The sounds of a language are a systematically organized set of features. In the 1920s -1930s, following Saussure, Jacobson and N.S. Trubetskoy singled out the "distinctive features" of phonemes. These features are based on the structure of the organs of speech - tongue, teeth, vocal cords - Saussure notices this in the "Course of General Linguistics", and Harris calls it "physiological phonetics" (in Baskin's earlier translation, the term "phonology" is used) - they are connected in "knots » durg against a friend to make sounds. For example, in English, the difference between "t" and "d" is the presence or absence of "voice" (the tension of the vocal cords), and the level of voice that distinguishes one phoneme from another. Thus, phonology can be considered an example of the general language rule described by Saussure: "There are only differences in language." Even more important is not this: the difference usually implies the exact conditions between which it is located; but in language there are only differences without precise conditions. Whether we are considering "designation" or "signified" - in the language there are neither concepts nor sounds that would have existed before the development of the language system.

In such a structure, linguistic analogies are defined not with the help of their inherent qualities, but with the help of system (“structural”) relations.

I have already mentioned that phonology in its development relied on the ideas of Saussure. Although his analysis of linguistic physiology in modern times, Harris says, "would be called 'physical', as opposed to 'psychological' or 'functional', in The Course he clearly articulated the direction and basic principles of the functional analysis of language. His only work published during his lifetime, Memoire sur le systeme primitif des voyelles dans les langues indo-europeennes (Notes on the original vowel system in the Indo-European languages), published in 1878, was completely in line with comparative historical linguistics of the 19th century. Nevertheless, in this work, says Jonathan Culler, Saussure showed "the fruitfulness of the idea of ​​language as a system of interconnected phenomena, even with its historical reconstruction." Analyzing the relationship between phonemes, explaining the alternation of vowels in the modern languages ​​of the Indo-European group, Saussure suggested that in addition to several different sounds "a", there must be other phonemes that are described formally. “What makes Saussure’s work particularly impressive,” Kaller concludes, “is that almost 50 years later, when Hittite cuneiform was discovered and deciphered, a phoneme was found, in writing denoted by “h”, which behaved as Saussure predicted. Through formal analysis, he discovered what is now known as the guttural sound in the Indo-European languages.

In the concept of a relative (diacritical) definition of signs, both explicit and implied in the Course, there is a third key assumption of structural linguistics, called by Saussure the "arbitrary nature of the sign." By this is meant that the relation between sound and meaning in language is not motivated by anything: one can just as easily connect the word "arbre" and the word "tree" with the concept of "tree". Moreover, this means that the sound is also arbitrary: one can define the concept of "tree" by the presence of bark (except for palm trees) and by size (except for "low woody plants" - shrubs). From this it should be clear that all the assumptions I present are not divided into more and less important ones: each of them - the systemic nature of signs (most understandable in the "synchronous" study of the language), their relative (diacritical) essence, the arbitrary nature of signs - comes from from the rest.

Thus, in Saussurean linguistics, the studied phenomenon is understood as a set of comparisons and oppositions of language. Language is both an expression of the meaning of words (designation) and their result (communication) - and these two functions never coincide (see Shleifer's "Deconstruction of Language"). We can see the alternation of form and content that Greimas and Kurte describe in the latest version of interpretation: linguistic contrasts define its structural units, and these units interact on successive levels to create a certain meaningful content. Since the elements of language are random, neither contrast nor combination can be the basis. This means that in a language, distinctive features form a phonetic contrast at a different level of understanding, phonemes are combined into contrasting morphemes, morphemes - into words, words - into sentences, etc. In any case, an entire phoneme, word, sentence, etc. is more than the sum of its parts (just as water, in Saussure's example, is more than a combination of hydrogen and oxygen).

The three assumptions of the "Course of General Linguistics" led Saussure to the idea of ​​a new science of the twentieth century, separate from linguistics, studying the "life of signs in society." Saussure called this science semiology (from the Greek "semeion" - a sign). The "science" of semiotics, which developed in Eastern Europe in the 1920s and 1930s and in Paris in the 1950s and 1960s, extended the study of language and linguistic structures into literary finds composed (or formulated) in terms of these structures. In addition, in the twilight of his career, in parallel to his course in general linguistics, Saussure engaged in a "semiotic" analysis of late Roman poetry, trying to discover deliberately composed anagrams of proper names. This method was in many ways the opposite of rationalism in its linguistic analysis: it was an attempt, as Saussure writes in one of the 99 notebooks, to study in the system the problem of "probability", which "becomes the basis of everything." Such an investigation, Saussure himself claims, helps to focus on the "real side" of probability; The “key word” for which Saussure is looking for an anagram is, according to Jean Starobinsky, “a tool for the poet, and not the source of life for the poem. The poem serves to reverse the sounds of the key word. According to Starobinsky, in this analysis, "Saussure does not delve into the search for hidden meanings." On the contrary, in his works, a desire to avoid questions related to consciousness is noticeable: “since poetry is expressed not only in words, but also in what these words give rise to, it goes beyond the control of consciousness and depends only on the laws of language.”

Saussure's attempt to study proper names in late Roman poetry (Tsvetan Todorov called this an abbreviation of "a word ... only before it is written") emphasizes one of the components of his linguistic analysis - the arbitrary nature of signs, as well as the formal essence of Saussurean linguistics ("Language," claims he, “the essence is a form, not a phenomenon”), which excludes the possibility of analyzing the meaning. Todorov concludes that today Saussure's writings seem remarkably consistent in their reluctance to study symbols [phenomena that have a well-defined meaning]. . . . Exploring anagrams, Saussure pays attention only to repetition, but not to previous options. . . . Studying the Nibelungenlied, he defines the symbols only to assign them to erroneous readings: if they are unintentional, the symbols do not exist. After all, in his writings on general linguistics, he makes the assumption of the existence of a semiology that describes not only linguistic signs; but this assumption is limited by the fact that semilogy can only describe random, arbitrary signs.

If this is really so, it is only because he could not imagine "intention" without an object; he could not completely bridge the gap between form and content - in his writings this turned into a question. Instead, he turned to "linguistic legitimacy". Standing between, on the one hand, nineteenth-century concepts based on history and subjective conjectures, and methods of accidental interpretation based on these concepts, and, on the other hand, structuralist concepts, which Lévi-Strauss called "Kantianism without a transcendent actor" - erasing the opposition between form and content (subject and object), meaning and origin in structuralism, psychoanalysis and even quantum mechanics, the works of Ferlinand de Saussure on linguistics and semiotics mark a turning point in the study of meanings in language and culture.

Ronald Shleifer

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Introduction? Lecture Translation Theory