Lecture
French philosopher of the 17th century R. Descartes argued that the ability to use language normally is the only reliable indication that a certain being has a human mind. This ability cannot be detected either in the automaton or in the animal. The animal, however, is also, according to Descartes, a kind of automaton endowed with reflexes. In all respects, except for language, the automaton can detect signs of intelligence, sometimes surpassing the corresponding signs of a person. According to the language, neither an animal nor a car, deprived of reason, will be capable, even if they are endowed with physiological organs necessary for the production of speech.
This hypothesis about the fundamental inability of animals to speak, like man, caused endless attacks on Descartes. However, its idea is fundamentally correct: only beings endowed with reason can speak speech, and it is the only way for the mind to manifest itself without.
Language is a necessary condition for the existence of abstract thinking. It is not by chance that such thinking, which is a distinctive feature of a person, is usually called “thinking in concepts”.
Language arises simultaneously with consciousness and thinking. Being a sensible perception shell of thought, language provides a person’s thoughts with a real, objective existence in the form of air vibrations (sounds) or traces of paint on paper (letters). Outside such a shell, thought is inaccessible to others.
Like thinking, language is dialogical: it exists for an individual only insofar as it exists for others.
Logical analysis of thinking is always a study of the language in which it flows and without which it is not possible. In this respect, logic — the science of thinking — is equally the science of language.
Thinking and using language are two sides of both the cognitive process and the communication process. Language participates not only in the expression of thought, but also in its very formation. You can not oppose the "pure", non-linguistic thinking and its subsequent expression in language.
However, language and thinking are not identical. Each of the sides of the unity made by them is relatively independent and has specific laws.
Language is a sign system that serves for the purposes of communication and cognition.
The system is expressed in the presence of vocabulary, syntax, semantics and pragmatics in each language .
The syntactic rules of a language establish ways of forming complex expressions from simple ones and ways of transforming expressions of a language.
Semantic rules define ways of giving meaning, or meaning, to language expressions. This is achieved by indicating the circumstances in which proposals of a certain type should be accepted.
The rules of meaning are usually divided into three groups: axiomatic, excretory, and empirical. Axiomatic rules require the acceptance of certain types of proposals in all circumstances. For example, the rules of the Russian language instruct all speakers in this language to always accept sentences: “Every bachelor is single”, “A centimeter is equal to one hundredth of a meter”, “Red is not black”, etc. Lead rules require the acceptance of consequences arising from certain premises if the packages themselves are accepted. For example, this is the rule according to which, having accepted the proposals: “If Ivan Ilyich is a man, then he is mortal” and “Ivan Ilyich a man”, one should also accept the proposal “Ivan Ilyich is mortal”. The situation of accepting sentences, indicated by the empirical rules of meaning, implies going beyond the limits of language and extra-linguistic observation. Such rules include, for example, the rules requiring the adoption of the sentence “It hurts” in the case of sensation of pain, the sentence “This subject is red” - when a red object is perceived, etc.
Languages that include empirical rules of meaning are commonly called "empirical." The languages of all sciences, with the exception of logic and mathematics, are empirical.
Pragmatic rules speak of the relationship between language and the person using the language.
All languages can be divided into natural, artificial and partially artificial. Natural languages, also called everyday, spoken, ordinary, etc., are formed spontaneously and gradually. The history of each such language is inseparable from the history of the people owning it. Artificial languages are consciously created by people for any special purposes: languages of mathematics, logic, algorithmic languages, ciphers, etc.
The languages of the natural sciences and humanities are partly artificial. Let's say a logic textbook is always written in a natural language: Russian, English, German, etc. At the same time, in addition to the words of this language, the textbook necessarily includes the logical terminology proper, which is primarily international. The special terms of partially artificial languages and the clearly established connections of these terms give such scientific languages the clarity and precision they need.
One of the features of artificial languages consists in the strict definiteness of their vocabulary, syntax and semantics, which in many cases turns out to be an undoubted advantage of such languages in comparison with natural languages. Artificial languages are genetically and functionally secondary to a natural language: the first arise on the basis of the second and can function only in connection with it.
In logic for a long time it was implicitly assumed that the main or even the only function of a language, expressing its very essence, is a description of reality. Descriptive expressions stood out as a privileged canonical form, to which should be reduced all the observed diversity of statements, or "use of language."
The idea of exceptional descriptions in comparison with other types of language use only in the late 50s. last century began gradually to disappear.
There are countless types of language use, wrote the Austro-English philosopher and logician L. Wittgenstein, infinitely diverse ways of using what we call "signs", "words", "sentences". And this diversity is not something fixed, given once and for all. On the contrary, new types of language use are emerging, or, as one might say, new “language games”, while other language games become obsolete and forgotten.
A variety of language games are easy to grasp based on examples provided by Wittgenstein. Language can be used to: order and use orders; describe the appearance of the object or its size; to make an object in accordance with its description (picture); report on the course of events; make assumptions about the course of events; put forward and prove a hypothesis; present the results of the experiment in the form of tables and diagrams; compose a story and read it; pretend; sing round dance songs; guess riddles; joke, tell jokes; solve arithmetic problems; translate something from one language to another; ask, thank, curse, greet, pray.
Language permeates our whole life, and it must be as rich as herself. With the help of language we can describe a variety of situations, evaluate them.
Is it possible to list all the tasks that a person solves by means of language? Which of the uses, or functions, of the language are basic, and which are secondary, reducible to basic? Oddly enough, these questions arose only at the beginning of the last century.
Among the uses of the language, a special place is occupied by the description - the statement, the main function of which is to report on the real state of things and which is true or false.
The actual description is true. A description that does not correspond to the real state of affairs is false. For example, the description “Snow is white” is true, and the description “Oxygen is metal” is false. It is sometimes assumed that the description may be vague, lying between truth and falsehood. Many descriptions of the future can be attributed to the indefinite (“In a year this day will be overcast,” etc.). Sometimes the descriptions use the words "true", "true", "in fact", etc.
The description, despite its importance, is not the only problem solved with the help of language. It is not even his main task. The language has many tasks beyond description.
In the 20s. of the last century, C. Ogden and A. Richard wrote a book in which they drew attention to expressive and convincingly showed that the emotive (expressing) use of language is not reducible to its denoting, descriptive meaning. Phrases “I regret that I woke you up”, “I congratulate you on the holiday”, etc. not only describe the state of feelings of the speaker, but also express certain mental states associated with a particular situation.
For example, I have the right to congratulate you on your victory in competitions, if you really won and if I am really glad for your victory. In this case, the greeting will be sincere, and it can be considered true, i.e. relevant external circumstances and my feelings. If I congratulate you on the fact that you look good, although in fact you look unimportant, my congratulations are insincere. It does not correspond to reality, and if I know about it, it does not correspond to my feelings. Such a congratulation can be assessed as false. A congratulation about the fact that you discovered quantum mechanics would also be false: everyone, including you, is well aware that this is not the case, and the congratulation would be a mockery.
Of particular importance for the development of the theory of language use were the ideas of the English philosopher J. Austin. In particular, he drew attention to the unusual fact that language can be directly used to change the world.
It is this problem that is solved by expressions called Austin declarations. Examples of such expressions are: “I appoint you as chairman”, “I am retiring”, “I declare: our contract has been terminated”, “I wrap you” (“I declare you husband and wife”), etc. When, for example, I successfully carry out the act of appointing someone as chairman, he becomes the chairman, and before that act he was not. If the act of production is successfully fulfilled to the generals, the world immediately becomes one more general. When a football referee says: “You are leaving the field,” the player is out of the game, and its course, obviously, changes.
The declarations do not explicitly describe some existing situation. They directly change the world and do it by the very fact of their utterance. Obviously, declarations are not true or false. They can, however, be justified or unreasonable (I can appoint someone to chair, if I have the right to do this, if there is a sense in such an appointment, etc.).
Another use of language is normative. With the help of language, norms are formulated through which the speaker wants to ensure that the listener performs certain actions. Normative utterances are also called “deontic” (from Greek. Сleop - duty, obligation) or “prescriptive” (from lat. - prescribe) and are usually contrasted with descriptive statements, also called “descriptive” (from lat. - describe).
A norm (normative, or deontic, utterance) is a statement that binds, permits, or prohibits something to do under the threat of punishment.
Standards are extremely diverse and include commands, orders, requirements, regulations, laws, rules, etc. Examples of norms include: “Stop talking!”, “Try to bring maximum benefit to as many people as possible”, “You should be persistent” and so on. The rules, unlike descriptions, are not true or false, although they may be reasonable or unfounded.
Language can also be used for promises, i.e. to impose an obligation on the speaker to perform an action in the future or to adhere to a certain line of conduct. Promises are, for example, the expressions: “I promise to behave approximately”, “I swear to tell the truth and only the truth”, “I will always be polite”, etc. Promises can be interpreted as norms addressed to one who speaks to himself and in some way predetermines his behavior in the future. Like all norms, promises are not true or false. They can be thoughtful or hasty, expedient or inexpedient, etc.
Language can also be used for ratings. The latter express a positive, negative or neutral attitude of the subject to the object in question, or, if two objects are matched, to express one’s preference to the other.
Assessment (evaluative utterance) - a statement establishing the absolute or comparative value of a certain object.
Evaluations are, for example, the expressions: “It's good that the lights went out”, “It's bad when someone is late”, “It’s better to come before you are late”, etc. Estimates are as fundamental and not reducible as descriptions. However, unlike descriptions, they are not true or false.
There is, therefore, a large number of different language uses: a message about the state of affairs (description), an attempt to force something to do (norm), an expression of feelings (expressiveness), a change in the world by a word (declaration), an obligation to do something (promise ), the expression of a positive or negative attitude to something (assessment), etc.
Wittgenstein believed, and it can be remembered again, that the number of different uses of a language (different “language games,” as he said) is unlimited.
Multiple uses of the language can be given in a certain system, which is described below.
In the second half of the XX century. within the framework of linguistics, the so-called “theory of speech acts” was developed, which is a simplified classification of language uses (J. Austin, J. Searle, P. Stroson, etc.). This theory has played a major role in the study of the functions of language. However, now it does not seem to be particularly successful. It misses a number of fundamental uses of the language (assessments, expressions of the language, inspiring any feelings, etc.), does not trace the connections between the different uses of the language, does not reveal the possibility of reducing some of them to others, etc.
From the point of view of logic, the theory of argumentation and philosophy, it is primarily important to distinguish between the two main uses of language: description and evaluation. In the case of the first, the starting point of the juxtaposition of the utterance and reality is the real situation and the utterance acts as its description, characterized in the terms “true” and “false”. In the second function, the source is a statement that acts as a standard, perspective, plan. Compliance with this statement is characterized by the terms “good”, “indifferent” and “bad” (in the case of comparative assessments - “better”, “equivalent”, “worse”).
Description and evaluation are two poles, between which there is a mass of transitions. Both in everyday language and in spider language there are many varieties of both descriptions and assessments. Pure descriptions and pure assessments are quite rare, most language expressions are of a dual, or “mixed,” descriptive-evaluative nature.
All this should be taken into account when studying the set of "language games" or language uses. It is likely that many of these "games" is unlimited. It is necessary to take into account, however, that a more subtle analysis of the use of language moves within the framework of the original and fundamental opposition of descriptions and assessments and is merely its specification. It may be useful in many areas, in particular in linguistics, but it is most likely deprived of interest in logic, in the theory of argumentation, etc.
Further important is the distinction between expressive, similar descriptions, and similar to the estimates.
The directive is a statement used to arouse feelings, will, impulse to action.
The directives are, for example, the expressions: “Pull yourself together”, “You will overcome difficulties”, “Believe that you are right and act!”, Etc.
The so-called numinous function - enchanting the listener with words (sorcerer spells, words of love, adulation, threats, etc.) can be considered a particular case of the orectical use of language.
To systematize the use of language, we use two oppositions. We oppose thought to feeling (will, striving, etc.), and expressing certain states of the soul to the suggestion of such states. This will give a simple coordinate system within which you can locate all the basic and derivative uses of the language.
Descriptions are expressions of thoughts, expressive expressions of feelings. Descriptions and expressions refer to what can be called passive use of language and characterized in terms of truth and deception. Estimates and directives refer to the active use of the language and have no truth value.
The norms are a special case of assessments: some action is necessary if and only if this action is positively valuable and it is good that abstention from this action entails punishment.
Promises - a particular, or degenerate, case of norms. Declarations are a special case of the magic function of a language when it is used to change the world of human relationships. As such declarations are a kind of prescriptions, or norms, concerning the behavior of people. Promises are a special case of a hypothetical function, covering not only promises in the direct sense of the word, but also the adoption of conventions, the axioms of newly introduced theory, etc.
There are thus four main uses of the language: description, expressive, assessment and directives, as well as a number of intermediate uses of it, to a greater or lesser extent, to the main ones: normative, magical, hypothetical, etc.
The importance of classifying language uses for logic is undeniable. Many concepts of logic (for example, the concepts of proof, the law of logic, etc.) are defined in terms of truth. But there is a large class of such uses of language, which clearly stand outside the "kingdom of truth." This means that it is necessary for logic to take a broader look at the objects under study and propose new, broader definitions of some of its basic concepts. On the other hand, the classification allows to clarify the connection between individual sections, or branches, of logic. If, for example, norms are only a special case of assessments, then the logic of norms should be a special case of evaluation logic. Anyone who tries, say, to build a “logic of declarations” or a “logic of promises”, should be remembered that declarations and promises are a special case of norms whose logic has been around for a long time.
From ordinary grammar is well known division into parts of speech. Among these parts of speech are the noun, adjective, verb, etc. The division of language expressions into logical categories resembles this grammatical subdivision and, in principle, derives from it. On this basis, the theory of logical categories is sometimes called "logical grammar."
The result of the decomposition of the sentence into simple, further indecomposable parts will be two types of expression: meaningful and logical.
Content parts are language expressions that have content, even if they are taken by themselves.
Logical parts, or symbols, are expressions of a language that do not have independent content, but in combination with one or several meaningful expressions, form complex expressions with independent content.
In short, the content parts of a sentence are meaningful expressions; logical symbols are non-content expressions that serve to form some meaningful expressions from others.
Logical symbols are also called logical constants.
The difference between the substantive and logical parts of a sentence can be likened to the difference between numbers and arithmetic operations on them. Numbers have some content, even when viewed by themselves. Operations, such as addition and subtraction, do not have independent content, but they allow you to get other numbers from some numbers. Say, from the numbers 7 and 3, using addition, we get a new number 10, and by subtracting the second number from the first - a new number 4.
The content parts of language expressions include names (concepts) and statements. Names denote some objects, statements describe or evaluate some situations, or state of affairs. The names are, for example, “Alexander the Great”, “commander”, “table”, “painting”, etc. The statements include: "Alexander of Macedon won a victory over King Darius", "It became cold, and the wind rose," etc.
Logical symbols are subdivided into types depending on what they are applied to (to concepts or to statements) and what arises as a result of their application (concept or statement).
Of the many types of logical symbols, select the following:
• logical connectives, which allow one to form new sayings from the existing statements: “... and ...”, “... or ...”, “if ..., then ...”, “it is not true that .. ." etc.;
• logical connectives that allow one of the two concepts to get the statement: "... is ...", "everything ... is ...", "some ... is ...", "everything ... is not ... "," some ... not to eat ... ".
Using the logical connectives from the statements “Letter sent” and “Letter burned”, you can get new statements: “Letter sent and burned” (obviously contradictory statement), “Letter sent, or it burned”, “Letter is neither sent nor burned "," It is not true that the letter has been sent ", etc.
With the help of bundles "... there is ...", "everything ... there is ..." and the like from the concepts "metal" and "conductor of electricity" one can get the statements: "Metal is a conductor of electricity"; "Every metal is a conductor of electricity"; "Some metals are conductors of electricity," etc.
The substantive parts of the sentence determine the content of our thoughts, the logical ones - their logical form, i.e. method of communication of their constituent parts. If the idea is to liken it to a house built of bricks and cement mortar, then meaningful expressions will be bricks, and logical symbols will be such a mortar. By itself, the cement mortar does not have a spatial form, but it allows you to get from the elements with form, new elements that have a spatial form. Our thinking is usually focused only on the content. Logical symbols do not have their own content and belong to a logical form. They start to somehow interest us only in those rare cases when we doubt the correctness of the reasoning and intend to check them.
To identify a logical form, it is necessary to move away from the content, replace the content parts with some spaces or letters. Only the connection of these parts will remain. It is expressed by the words "and", "or", "if, then", "is", etc. Do we often think about them? Hardly.Do we know the rules that govern their use? Pretty vague. The study of logic implies a change in the orientation of our mind: from analyzing the content, it must switch to the logical form of the argument. It seems difficult, but only at first.
To identify the logical form of reasoning, should be distracted from its content. To this end, it is customary in logic to replace the substantive elements of reasoning (concepts and statements) with variables, i.e. characters that have no content and indicate only the type or category of the replaced expression.
As variables for concepts, letters 5, P, <2 11, etc. are usually used . Variables for statements are usually the letters A, B, C , etc. The letters 5 and P themselves do not carry specific content. They only indicate that the expression "5 is P" or "Some 5 are not P" instead of these letters should be substituted for some specific concepts to make a meaningful statement. The letters A and B are just as empty. They only indicate that instead of them in the expression of the type "A and B", "if L, then B" , etc. You should substitute specific statements to get a new meaningful statement.
Bundles that allow you to get new sayings from names and sayings are called propositional (from Lat. - saying, judgment). In the future, of all possible logical operations, special attention will be paid to the propositional bundles, since the logical theory describing them — the logic of statements — forms the foundation of logic.
Aristotle introduced the variables into logic. In modern logic, variables are used very widely. In addition, instead of the logical symbols of the ordinary language, special characters are introduced, which are given strict meaning. As a result, a new language appears, containing only variables and special signs and not including a single word of the natural language. This artificial language is suitable, however, only for one purpose - for the strict formulation of logical laws.
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Logics
Terms: Logics