Formal logic studies. Formal logic as a science of thinking

Formal logic is the science of the laws and forms of correct thinking. Human reasoning takes on a logical form and is constructed in accordance with logical laws. By the concept of logical form we understand a specific thought, which is the structure of this thought.

Developing the theory of logic, Aristotle set himself the task of finding out “on what the coercive power of speech rests, what means speech should have in order to convince people, force them to agree with something or recognize something as true.” New true thoughts can be obtained from other true thoughts in the case, the Greek philosopher argued, if they are connected according to the rules of logic. He called such a connection of true thoughts, which leads to a new, previously unknown true thought, inference.

Aristotle's merit lies in the fact that he was the first to deeply study deductive reasoning and created the doctrine of syllogism. He called a syllogism a statement in which “when something is asserted, something different from what is affirmed necessarily follows from it, and precisely because it is.” In a syllogism, from two certain judgments (premises) a third judgment (conclusion) is obtained. For example:

All metals are thermally conductive;

Iron is metal;

Therefore, iron is thermally conductive.

Aristotle revealed different kinds syllogical conclusions, laid the foundations for the doctrine of the figures of syllogism and formulated the rules of syllogism, which in modern writing read as follows:

“In the syllogism (in all three propositions) there should be only three terms (in the given example, the concepts of “metal”, “iron” and “thermal conductivity”);

“If one of the premises is negative, then the conclusion will also be negative and cannot be affirmative”;

“No conclusion can be obtained from two negative premises using a syllogism”;

“If one of the premises is private, then the conclusion, if it is possible at all, should only be private,” etc.

Basic concepts of formal logic:

Logical form is the structure of thought, or the process of thinking, obtained as a result of abstraction from the meaning / from most of it / non-logical terms.

Logical forms can be classified by type. Main types logical forms are concept, judgment and inference.

A concept is a thought in which objects are generalized and separated into a class based on a system of attributes common only to objects of this class.

Judgments include thoughts that state the presence or absence of properties in objects, relationships between objects, connections between objects.

Inference is the process of obtaining knowledge, expressed in a judgment, and their other knowledge, also expressed in judgments.

Aristotle developed a theory of judgments that make up a syllogism, a theory of concepts, discovered and first formulated the basic logical laws: the law of identity, the law of contradiction and the law of excluded middle, which he called “ the most important principles" All this, taken together, constituted the content of the science of thinking created by Aristotle.

It is important to note that he called logic the science of correct reasoning, the means of proving truth, and truth for him is nothing more than the correspondence of thought to reality. In obtaining the truth, a person connects his thoughts not arbitrarily, but ultimately in accordance with how real-life objects and phenomena reflected in these thoughts are connected. It followed from this that the laws, forms and rules of thinking, according to Aristotle, have an objective basis in material existence itself. Formal logic, created by Aristotle, has not lost its significance, because it contains a grain of absolute truth.

The most important features of any abstract thinking leading to truth are its consistency, logical harmony and validity. Thinking devoid of these qualities cannot lead to truth. In the process of correct thinking, some thoughts must necessarily follow from others and be logically consistent. If, for example, it is known general position, that “all Marxists are materialists” and that “this person is a Marxist,” then it necessarily follows that “this person is a materialist.”

These features of abstract thinking, studied by formal logic, acquire especially important because the logical structure of thinking, laws, forms and rules for constructing thoughts in reasoning are of a universal human nature. Whatever verbal form our thoughts take, whatever language they are expressed in, they must necessarily take on uniform universal forms. Without this, the exchange of thoughts and mutual understanding between people is impossible. various countries and peoples. For all peoples of all ages, all tribes and all levels mental development, wrote I.M. Sechenov, the verbal image of thought in its simplest form can be reduced to our three-term sentence. Thanks to this, we equally understand the thought of an ancient man, left in written monuments, the thought of a savage and the thought of a contemporary.

Of course, for different classes and social groups the content of thinking may vary, since it depends on the worldview, political beliefs, philosophical views, but the logical structure of thinking remains the same. In order to distort the truth, reactionary classes often violate the laws of logic, counterfeit lies as truth, replace logic with sophistry, which is only apparently logical, but in fact leads to deliberately false judgments. But this does not mean that they use some other logical structure of thinking. Sophists use the same universal human laws and forms of thinking studied by formal logic, but deliberately distort them, resorting to various intricacies to disguise violations of the logic of reasoning.

Laws of Formal Logic

In order for thoughts to be consistent, logically harmonious and justified, they must be clothed in certain forms, and logical operations with them must be performed in accordance with the laws of formal logic. Such laws that ensure the correctness of thinking are the laws of identity, contradiction, excluded middle and sufficient reason.

Law of Identity

This law is usually formulated as follows: “Every thought in the process of a given reasoning must retain the same content, no matter how many times it is repeated.” Thinking cannot lead to a positive result if, in the process of reasoning about any subject, we put first one or another content into the concept of this object. Consider, for example, this syllogism:

All metals are simple bodies;

Bronze - metal;

Bronze is a simple body.

This inference is correct in form, but its conclusion is false. In the course of the argument, the law of identity is violated: in the first premise, “metals” are considered as simple chemical elements, and in the second premise, “metal” is thought of as a complex compound (an alloy of tin and lead). The result was a logical error, which in formal logic is called quadrupling of terms (in this conclusion, in fact, there were not three terms and all three corresponding concepts, as is expected in such conclusions, but four), because the term “metal” in the first and second premises (judgments) is invested different content.

The law of identity precisely warns against such mistakes. It requires that in the process of the same reasoning about some object with a certain content of its properties, we think about this particular object with the same content of its properties (attributes).

In the process of thinking, we cannot operate with the vague, unstable content of concepts about objects. While an object is in a certain qualitative state, until in the process of development it has not changed its basic properties and characteristics, we must think about this object with its inherent basic properties. Otherwise, our very thinking will be vague, logically incorrect and therefore will not lead us to the truth. Such errors often occur in discussions when the disputing parties put different content into the concepts that appear in the course of the dispute. It seems to us that this is precisely the mistake made by some participants in the protracted discussion on the issue of the unity of dialectics, logic and the theory of knowledge.

Discrepancy in the interpretation of basic concepts, substitution of one concept content for another will not lead to the truth. The law of identity is precisely aimed at ensuring that our reasoning is not ambiguous and vague.

It may be said that this law is so simple and obvious that even people who have no idea of ​​logic automatically adhere to it. In general, that's true! And yet, there were even philosophers who did not understand the full importance of this law and sometimes rejected it. Among them we can note such an outstanding thinker as Hegel, who clearly underestimated and ignored the law of identity, believing that “this law of thinking is meaningless and leads nowhere further.” The law of identity, despite its elementary nature, is of great importance not only in everyday life, but also in the course of any scientific reasoning.

The law of identity cannot be understood dogmatically and presented as if it generally prohibits changing the content of concepts. Dialectics, including dialectical logic, considers identity as a moment of stability and relative peace in the process of change and development of reality. Therefore, the fundamental position of dialectical logic about the mobility, flexibility of concepts, which does not exclude, but presupposes the moment of their stability, is the fundamental condition of true knowledge.

And the law of identity of formal logic, reflecting the moment of peace and stability, does not prohibit changes in the content of concepts if it is already outdated, if the state of relative peace is disturbed as a result of a change in the essence of the objects covered by a given concept, or changes and development of our knowledge about them. The law of identity requires only one thing: in a given reasoning, in a given connection and under given conditions, it is necessary to invest one, completely definite content into the concepts appearing in the reasoning. Therefore, the law of identity, like other laws and provisions of formal logic, cannot be absolutized and considered that only they can lead us to the truth. Fulfilling its requirements in the thinking process is only one of the conditions for constructing a correct logical conclusion.

Law of contradiction

Usually contradictions in logic are such thoughts, one of which affirms what the other denies. This kind of thought has long been considered by the people as confused and inconsistent. In formal logic, such inconsistency of one thought with another is called a logical contradiction, which consists in the fact that in the process of thinking, different things are involuntarily or consciously identified or passed off as different identical things.

Formal logic has formulated a certain principle, a law that cannot be violated in any act of thought and which states that “two judgments, one of which affirms something about the subject of thought (for example, “all metals are heat conductors”), and the other denies the same thoughts about the same subject (for example, “some metals are non-heat-conducting”) cannot be true if the judgments are expressed at the same time in the same respect.” In logic, this law is called the law of contradiction, sometimes it is called the law of non-contradiction. In other words, the propositions “A is B” and “A is not B” cannot be both true. The ancient Greek philosopher and scientist Aristotle gave the following formulation of this law: “It is impossible to affirm and deny something together.”

The principle of non-contradiction requires that thinking be consistent. It requires that when we affirm something about something, we do not deny the same thing about the same thing in the same sense at the same time, i.e. prohibits the simultaneous acceptance of a certain statement and its negation. Contradictions in linguistic contexts are sometimes implicit. Thus, Socrates’ famous statement “I know that I know nothing” hides a contradiction. Indeed, if Socrates knows that he knows nothing, then he does not know this either.

Law of the excluded middle

In close connection with the law of contradiction is the third fundamental law of formal logic - the law of the excluded middle, according to which “two contradictory friends each other thoughts about the same object, taken at the same time and in the same relation (for example, “this wall is white” and “this wall is not white” or “all planets have an atmosphere” and “some planets do not have atmospheres") cannot be both false and true. If one of them is true, then the other is false. There is no third". In other words, “A is either B or not B.”

At first glance, the law of excluded middle to some extent repeats the law of contradiction.

Of course, both of these laws are closely related to each other. In both cases, we are talking about logical contradictions that arise only as a result of violation of the laws of thinking. However, each of them has its own specifics. The law of contradiction states that two mutually exclusive, opposing thoughts expressed on the same subject cannot be true at the same time. But the question remains open here as to whether they can both be false. The law of the excluded middle states that if of two contradictory judgments about the same subject, expressed at the same time and in the same relation, one is false, then the other is certainly true, and, conversely, if one is true, the other is false, and the third is not given. In other words. “A is either B or not B.”

All judgments that obey the law of excluded middle are also subject to the law of contradiction, but not vice versa. There are judgments that obey the law of contradiction, but do not obey the law of excluded middle. For example, the propositions “all planets have satellites” and “no planet has satellites” are subject to the law of contradiction, since they cannot be simultaneously true, but they are not subject to the law of excluded middle, since both judgments are false. The law of the excluded middle is of great importance in cognitive thinking. If the researcher knows that one of the contradictory judgments is true (which he discovered as a result of studying the subject of thought), then without any additional research he can firmly conclude (based on the law of the excluded middle) that the second judgment is false.

The law of the excluded middle was also previously and is sometimes subjected to unfounded criticism on the grounds that it is supposedly a way of eliminating any contradiction from thinking, both “logical” and real. But if the law of the excluded middle of formal logic really served as a way to expel all, including dialectical, contradictions from thinking, then it would not only not bring any benefit in the process of cognitive thinking, but would also cause enormous harm, because in the process of dialectical thinking, it is necessary not to exclude dialectical contradictions that objectively arise in the process of thinking, but to overcome them, resolve them and thereby achieve the truth.

Law of Sufficient Reason

This law says that any complete thought can be considered true only if sufficient reasons are known for which it is considered true.

The principle of sufficient reason requires that every statement be justified to some extent, i.e. the truth of the statements cannot be taken on faith.

Judgments from which a statement is derived when justifying it (if we consider the rules of logic as data) are called grounds, therefore the principle under consideration is called the principle of sufficient reason, which means: the grounds must be sufficient to derive the statement in question from them.

If the requirement of the principle of sufficient reason is not met, then the statements turn out to be unfounded and unfounded.

In formal logic we are not talking about objective, factual logic, but about logical validity and evidence, without which there cannot be a single reasonable exchange of thoughts. However, the figures of logic by which a logical proof is constructed are carried out according to rules developed on the basis of centuries-old study of reality itself in the course of people’s practical activities; they therefore have a completely objective basis, and are not arbitrary constructions, as the logical positivists claim.

If in material reality everything is causally determined, everything is “justified” by the real process of existence and development of phenomena, then our thoughts about these phenomena must be justified, demonstrative, convincing in accordance with the requirements of the law of sufficient reason.

It goes without saying that the law of sufficient reason expresses only the most general requirement to thinking. A specific substantiation of the truth of certain scientific propositions is the task of special natural and social sciences, which do this on the basis of a specific analysis of reality. The law of sufficient reason is directed against such thoughts in our reasoning that are not connected with each other in a necessary way, do not follow from one another, do not justify one another against illogical reasoning, when dubious provisions are taken as the basis for a conclusion or conclusion, which cannot serve as such, or when statements are taken on faith...

This law warns us against such mistakes, which were once brilliantly ridiculed by the great Russian writer N.V. Gogol in his comedy “The Inspector General”. This is how the characters of this comedy - Bobchinsky and Dobchinsky "justified" the truth of their conclusion that Khlestakov, who came to their city, is the auditor the mayor was waiting for.

“Governor. Who, what official?

Bobchinsky. The official about whom you deigned to receive a lecture is an auditor.

Mayor (in fear). What are you, God bless you! It's not him.

Dobchinsky. He! He doesn’t pay any money and doesn’t go. Who else could it be if not him? And the road ticket is registered in Saratov.

Bobchinsky. He, he, by God he... So observant. I looked at everything. He saw that Pyotr Ivanovich and I were eating salmon, more because Pyotr Ivanovich was talking about his stomach... yes, so he looked into our plates. I was filled with fear.

Mayor. Lord, have mercy on us sinners. Where does he live there?

The classics of Marxism-Leninism, waging a merciless struggle against opponents of the Marxist worldview, often exposed them precisely by revealing the logical and scientific inconsistency and groundlessness of their conclusions and reasoning.

formal logic as a specific method of research played a particularly important role in the period when science moved from the study of general patterns of material reality to a deeper study of the essence of individual phenomena, to the accumulation of factual scientific material, when it was necessary to decompose reality into its individual objects, phenomena, and the objects themselves, phenomena - into their constituent elements, highlight their main properties, features, aspects and study them separately, without their connection and development.

logic law abstract concrete

1. About formal logic

1. Formal approach to inference

Everyone has some ideas about how one can reason and how one cannot reason; We all, starting at a certain age, know something about the structure of correct reasoning - just as we all know something about the structure of the “things” around us. However, humanity was not satisfied with the knowledge about “things” that everyone has: it created natural sciences - physics, chemistry and others - which made it possible to learn incomparably more about these “things” and study them incomparably deeper.

Likewise, the structure of reasoning has become the subject of a special science called philosophical (formal) logic. For a long time, all logic was identified with formal logic; they were synonyms. Formal logic is a science that studies forms of thought - concepts, judgments, inferences, evidence - from the perspective of their logical structure, that is, abstracting from the specific content of thoughts and isolating only the general way of connecting the parts of this content. Basic The task of F.L. is to formulate laws and principles, compliance with which is a necessary condition for achieving true conclusions in the process of obtaining inferential knowledge.

The beginning of formal logic was laid by the works of Aristotle, who developed syllogistics. Further contributions to the development of F. l. contributed by the early Stoics, and in the Middle Ages by the Scholastics (Peter of Spain, Duns Scotus, Occam, Lull, etc.); in modern times - first of all, Leibniz.

2. Aristotle (384–322 BC) – founder of formal logic

Here logic is presented in the form that it acquired as a result of development along the Western path. This path originates from Aristotle (AristotelhV, 384–322 BC) who not only laid the foundations of logic, but also developed a number of its sections so deeply and with such completeness that then it practically did not appear for 2 thousand years in its development beyond the circle of ideas and concepts outlined by Aristotle. (One of the few exceptions were the works of philosophers of the Stoic school, especially Chrysippus (CrusippoV, 280–207 BC). Their logical ideas are in many ways similar to those that, many centuries later, formed the basis of the logic of propositions. However, these the ideas of the Stoics were not understood at that time (and caused bewilderment among historians of logic back in the middle of the 19th century.) By the way, the very term “logic” (in ancient Greek logikh, from logoV - word, speech, judgment, understanding) was introduced by the Stoics (The word logikh is a substantivized adjective; the noun tecnh – “art” is implied).

2. Concept

1. What is a concept?

Along with the study of reasoning, logic, according to a long tradition, includes the study of concepts. This tradition is completely justified, since it is concepts that represent the material with which we operate in all mental activity, including reasoning.

A concept is a thought that distinguishes a certain class of “objects” according to certain characteristics. For example: the concept “transparent” identifies a class of objects that do not interfere with seeing what is behind them; the concept of “watch” identifies a class of objects that are instruments for measuring time; the concept of “student” identifies a class of people studying in higher educational institutions; the concept of “triangle” identifies a class of geometric figures consisting of three points that do not lie on the same straight line and three segments connecting these points; the concept of “centaur” identifies a class of mythical creatures with a horse’s body and a human head; the concept of “running” distinguishes a class of methods of movement for humans and animals with a sharp push off the ground or quickly moving their paws; The concept of “surprise” identifies a class of feelings caused by something strange or unexpected.

From the above examples it is clear that it is no coincidence that we put the word “objects” in quotation marks. For us these were either real material objects, or fairy-tale creatures, or geometric figures that are ideal images of real objects, or feelings, or methods of movement. In general, “object” can mean here, in essence, everything that we can think of. (Tracing paper from the Latin objectum).

The use of the word “class” is no less conventional here. Usually this word denotes a collection whose elements are clearly separated from each other. But, for example, in the case of “surprise” there is no such aggregate: the feelings falling under this concept form a continuous spectrum that can hardly be naturally divided into individual elements. (If we try to get out of the difficulty by declaring that surprise is a certain unified feeling, so that the class distinguished by the corresponding concept consists of one “object,” then this will not save the situation: after all, someone who does not master this concept cannot imagine surprise as something unified.) The situation is approximately the same with the concept of “running.” And with the concept of “centaur” a difficulty of a different kind arises, even more serious: here, in reality, nothing at all corresponds to the “objects” that should be included in the “class”. And even with the concept of “student”, not everything is as simple as it might seem. After all, it undoubtedly applies not only to current students, but also to previous and future ones. Does it follow from this that the “class of students” includes not only first-year student Vanya Ivanov, but also his father, who graduated from the university twenty years ago? But what about his younger brother, who may or may not become a student over time? And with fictional students - characters from literary works, for example, Turgenev's Belyaev or Chekhov's Petya Trofimov? Answering these questions is not at all easy.

It is most natural, apparently, to consider that the class distinguished by the concept consists not of objects as such, but of ideas about them - meaning that each element of this class is an idea about one object considered “as a whole” (and not about some of its individual aspects or properties). Then among the elements of the class corresponding to the concept of “student” there will be an idea of ​​Van Ivanov, and an idea of ​​his father in his youth, and an idea of ​​his younger brother in the future, if he becomes a student, and ideas about Belyaev and Trofimov. Elements of the class corresponding to the concept of “centaur” will be, for example, ideas about the insidious Nessus and the wise Chiron. However, such a clarification will not eliminate all the difficulties (for example, the above-mentioned difficulty associated with the concepts of “surprise” and “run” will remain).

Thus, the above “definition” of the concept contains words whose meaning is rather vague and difficult to clarify. (This applies, of course, to both the word “feature” and the word “representation.”) It follows that this is not really a definition, but only an approximate explanation of the meaning of the term “concept.”

The set of characteristics by which a concept is distinguished is called its content (intension), and the class of “objects” that it distinguishes (or, more precisely, the set of ideas about “objects” it distinguishes) is called its volume (extensional).

Accordingly, the scope of the concept “watch” consists of ideas about all kinds of watches - ancient, modern and those that we only imagine, the scope of the concept “student” - from ideas about current, former, future and fictional students, the scope of the concept “centaur” - from ideas about several centaurs, to whom mythology gave names and individual characters, and non-individualized ideas about “centaurs in general.”

3. Equivalent concepts

2 concepts that differ in content can have the same volume. For example, “isosceles triangle” and “triangle with 2 equal angles” are different concepts, although their volumes are the same: they distinguish the same class, but according to different characteristics. (The opposite case - for 2 concepts to have the same content, but different volumes - is obviously impossible.) Concepts whose volumes coincide are called equal in volume or equivalent. These are, for example, the concepts of “a number divisible by 6” and “a number divisible by 2 and 3”, “the current capital of Russia” and “the city in which A.S. Pushkin was born”.

4. Generalization (generalization)

For example, by eliminating from the content of the concept “centaur” the signs “to have a human head” and “to have a horse’s body,” we obtain a more general concept “ mythical creature" By replacing the attribute “to serve for measuring time” in the content of the concept “clock” with the weaker attribute “to serve for measuring something,” we obtain a more general concept of “measuring device.” By replacing the attribute “to study at a higher educational institution” in the content of the concept “student” with the weaker attribute “to study at any educational institution,” we obtain a more general concept “student”. In the same way, the concepts “polygon” and “ geometric figure“are generalizations of the concept “triangle” (as well as the concepts “quadrangle”, “pentagon”, etc.); the concepts “predatory animal”, “mammal”, “vertebrate”, “animal” are generalizations of the concept “wolf”.

A mental operation with the help of which a generalization is formed from a concept, i.e. removing one or more features from the content of a concept or replacing them with weaker ones is also called generalization. We can say, for example, that the concept of “polygon” can be obtained by generalizing the concept of “triangle”.

5. Limitation

The mental operation opposite to generalization, i.e., adding one or more features to the content of a concept or replacing one or more features with stronger ones, is called concept limitation; its result is also called. For example, the concept of “centaur” is a limitation of the concept of “mythical creature”, the concept of “watch” is a limitation of the concept of “measuring instrument”, the concept of “triangle” is a limitation of the concepts of “polygon” and “geometric figure”, the concept of “square” is a limitation of the concepts “rectangle” and “rhombus” (as well as “quadrangle”, “polygon”, “geometric figure”).

When a concept is generalized, its scope expands, and when limited, it narrows. For example, the scope of the concept “mythical creature”, along with centaurs, includes sirens, harpies, Kerberos, etc.; The scope of the concept “polygon”, along with triangles, includes quadrangles, pentagons, etc.

A more general concept is often called generic in relation to a less general one, and a less general concept is often called specific in relation to a more general one.
6. Definition of the concept

A mental operation on a concept, consisting in the fact that it is expressed through some other concepts, is called definition, or determination. (Both of these terms were produced - the first by tracing, the second by direct borrowing - from Latin word definitio, coming from finis – border, limit. The word “definition” is used primarily in philosophical literature, as well as in some special cases (this is what they call, for example, the first sentence of an article in an encyclopedic dictionary); in other cases, it is preferable to use the word “definition.”) The same name is given to a sentence with the help of which one concept is expressed through others (“A prose writer is a writer who writes in prose,” “An insolvent debtor is a person who does not have the means to pay his debts ", "An isosceles triangle is a triangle that has two equal sides", etc.).

Most often, the definition of a concept consists in indicating some more general - generic - concept (“writer”, “triangle”, “person”, “device”) and additional features that need to be added to its content (“writing in prose”, “having two equal sides”, “studying at a higher educational institution”, “serving for measuring time”). If, in this case, the generic concept is closest to the one being defined (that is, there is no sufficiently natural intermediate concept between them), then they speak of definition through the closest genus and specific difference (definitio per genus proximum et differentiam specificam). These are, for example, the above definitions of the concepts “prose writer” and “isosceles triangle” (while the definitions of the concepts “student” and “clock” are not: for “student” the closest generic concept is not “person”, but “student” ", for "watch" - not "device", but "measuring device"). The definition of a concept through the closest genus and species difference does not have to be unique. For example, a square can be defined either as a rectangle, or a cat. all sides are equal, or like a rhombus, in a cat. all angles are right.

For “everyday” concepts - those with which we deal in everyday life - it is often very difficult to give a definition, and it is not always possible to formulate it with any precision. This is well known to the compilers of explanatory and encyclopedic dictionaries. – Definitions of scientific concepts play a much more important role. Scientific thinking deals with such objects, phenomena and patterns, cat. are discovered only through systematic, orderly and purposeful work of thought. At the same time, the results of scientific thinking must be verifiable and objective in nature, that is, not depend on the personality of the person who received them, on his beliefs, tastes, inclinations, likes and dislikes. (We are not talking here, of course, about those qualities of a person thanks to which he was able to receive scientific result: power of intellect, intuition, knowledge, perseverance, etc.). This can only be achieved provided that for each concept used there is a criterion that allows one to decide reliably whether this or that “subject” is included in its scope (otherwise it will become impossible to comply with the law of identity). And such a criterion - since “objects” in this case, as a rule, are inaccessible to direct contemplation - can only be based on the disclosure of the content of the concept, i.e. on its definition.

7. Tree of Porphyry (232–301)

Porphyry (a student of Plotinus) taught that any body, any thing exists, being involved in 5 characteristics that describe it. This:

3) species difference,

4) stable sign and

5) unstable (or random) sign (accident).

In accordance with this, Porfiry builds his famous classification, which went down in the history of logic under the name “Tree of Porphyry.” Thanks to this tree, one can ascend to more general entities - genera and, conversely, descend to more specific ones.

Let's say the most general essence is substance, genus. This genus can be divided into several species. Substance is either corporeal or incorporeal. Corporeal beings, in turn, are animate and inanimate. Let's consider animate beings: they can be sentient or non-sensing (say, animals and plants). Let's consider sentient beings: they are rational and unreasonable. Let's consider intelligent beings: among them there are people, and among people there are already individuals. Thus, descending the Porphyry tree, one can see an increase in the number of species differences. Some individual, for example, Socrates, has an essence, he has a body, he is a living being, animate, rational, etc. You can go further: say, by denying the presence of some essence in Socrates, you are ascending to a certain species. By removing some of Socrates' individual differences (for example, the bald spot on his head), we come to an understanding of man in general. By removing random features and leaving non-random ones, we come to the idea of ​​a person. By removing rational understanding, we ascend to the animate, etc. Each time the ascent up the tree of Porphyry occurs due to the fact that we remove some characteristics - accidents.

It is clear that the highest divine essence can only be described in apophatic language - because we have discarded all accidents. Only by throwing away all accidents do we come to an understanding of God, that is, that which cannot be defined in any way. The very word “define” means “to set a limit.”

The Tree of Porphyry was very popular in the Middle Ages.

8. Undefined concepts

No science can define all its concepts. After all, to define a concept means to express it through some other concepts; if we want to define these concepts, this will mean that we will have to express them through some third ones, etc. Such a process cannot continue indefinitely, and we will be forced to leave some concepts without definition. Therefore, the initial concepts of any science are indefinable. You just need to strive to ensure that such [primary] concepts are as few as possible and that they are simple enough so that their meaning can be well understood, based on examples and approximate explanations. – In general, the definition of a concept can be useful only when the concepts to which it is reduced are simpler and clearer than the concept itself. In prot. In this case, trying to give a definition is futile verbiage and can confuse matters.

Clarifying the content of a scientific concept can be far from an easy task. It happens that a concept that is familiar to everyone who went to school from childhood turns out to be very complex when analyzing its logical structure, and if it is possible to clarify it, this allows one to achieve greater clarity in the formulation of scientific problems and solve them more successfully. Sometimes different authors use the same term to designate different, albeit close, concepts, and this leads to disagreements and disputes in which it makes no sense to talk about the rightness of one side or the other due to the violation of the law of identity. In such cases, the only way to find out the essence of the matter is to clarify the concepts.

9. Single and general concepts

A concept is called single if its volume consists of one object. Examples of single concepts: “Moscow River”, “Eiffel Tower”, “Alexander the Great”, “Thirty Years’ War”, “number 5”. Concepts that are not isolated are usually called general. When classifying a concept as a single concept, caution must be exercised, remembering that the scope of the concept does not consist of objects as such, but of ideas about them. For example, the concept of “president of the USSR” should hardly be considered unique, although there was only one president in the USSR - M. S. Gorbachev: one can imagine, say, a novel by some writer about a certain fictional president of the USSR. At the same time, the concept of “M. S. Gorbachev, who served as President of the USSR in 1990–91.” – single.

10. Collective concepts

A concept is called collective if the objects included in its scope are collections of some “homogeneous” objects, considered “as a whole.” (Thus, the volume of a collective concept is a class, the elements of which are in turn classes.) Examples of collective concepts: “crowd”, “audience” (in the sense of “listeners of a lecture, report, etc.”), “flock”, "bush", "furniture", "peasantry". Collective concepts do not differ in any fundamental way from the rest. In particular, generalization and restriction operations can be performed on them; for example, the concept “flock of geese” is a limitation of the concept “flock”, “Russian peasantry of the 18th century” is a limitation of the concept “peasantry”, “vegetation” is a generalization of the concept “shrub”. Collective concepts can be single (for example, “1st “A” class of school No. 162 in Novosibirsk”).

11. Concrete and abstract concepts

In traditional logic, a distinction is made between concrete and abstract concepts. Specific concepts are those whose volumes consist of objects: “table”, “birch”, “city”, “student”, etc.

This also includes concepts such as “transparent”, “heavy”, since they correspond to classes consisting of specific transparent or heavy objects. Concepts whose volumes consist of imaginary objects that we imagine are somehow similar to real concrete objects - “centaur”, “unicorn”, “alien”, etc. - are also naturally considered concrete.

The remaining concepts are abstract. These include all scientific concepts (“triangle”, “energy”, “acid”, “mammal”, “feudalism”, etc.), as well as many “everyday” ones (“transparency”, “heaviness”, “running”) ", "surprise", "care", etc.) However, the boundary between concrete and abstract concepts is very arbitrary, and different authors draw it differently: some classify as concrete all concepts expressed by nouns that have a plural (or most of these concepts), others believe that all concepts are abstract.

3. Judgment (statement)

Reasoning is expressed in words. The study of sentences is, generally speaking, a matter of linguistics. Modern linguists also consider “semantic completeness” to be the main features of a sentence. Most often, the “complete thought” expressed in a sentence can represent a judgment (although there are questions, exclamations, orders, wishes, requests).

Any sufficiently rigorous proposition can be stated so that it consists only of sentences that are clearly stated statements about some facts, so that for each such statement one can ask whether it is true or false, and to this question there is an unambiguous answer “Yes” " or not". Only such proposals will interest us in the future; When we talk about judgments, we will always mean that they are just that.

For each proposition A of the type we are interested in, we will now write A = I if A is true (that is, the statement expressed by the sentence A is true) and A = A if A is false. In this case, sentence A can be written both verbally and in some symbolic form, for example:

The Volga flows into the Caspian Sea = And;

Dnieper flows into the Caspian Sea = L;

Whale – mammal = AND;

Whale – fish = L;

6 – even number = AND;

6 – odd number = L;

2 + 2 = 4 = AND;

2 + 2 = 5 = L.

We will call the letter I or L the truth value of the corresponding sentence.

4. Basic logical laws

The 4 laws listed below (they are often called the “basic laws of logic”), of course, do not exhaust all the conditions that any correct reasoning must satisfy; These are only the simplest and most obvious (but important!) patterns. Their observance is not sufficient for the correctness of reasoning, but it is necessary: ​​no reasoning in which at least one of these laws is violated can be considered correct. Let us now turn to their consideration. The inability or unwillingness to clarify the meaning of words is a constant source of errors in reasoning.

1. Law of identity

The law of identity is that when in one argument a thought about the same subject appears several times, we must each time have in mind the same subject, strictly making sure that it is not, voluntarily or unwittingly, replaced by another, in something similar to him.

Example. All people must be responsible for their actions. One year old child- Human. è A one-year-old child must be responsible for his actions.

2. Law of contradiction

The law of contradiction is that 2 opposing propositions cannot be true at the same time. (2 statements are called opposite, one of which is the negation of the other.) In other words: no statement can be both true and false.

It follows that no reasoning can be considered correct if it contains 2 opposite statements (an obvious violation of the law of contradiction) or statements that, although not themselves opposite, can be deduced from them 2 opposite statements (hidden violation). Discovering hidden judgment can be difficult.

Thus, a judgment about something is taken into account only when it does not contain mutually negating (i.e., opposite) parts. For example, we cannot consider the judgment “The Volga River both flows and does not flow into the Caspian Sea” as a full-fledged judgment, since it contains parts that deny each other. Similarly, the judgment “Seminarist Vikentyev was both present and not present at the philosophy lesson” is unacceptable.

This also includes statements that, although they do not contain directly opposite parts, allow opposite conclusions from their individual parts. Sometimes such a conclusion is not at all obvious (hidden violation).

Obvious violations of the law of non-contradiction are rare: few people will say, for example, “Ivan Ivanovich has already left and has not left yet,” because his interlocutors will think that he is either not speaking seriously or is not mentally well. But we have to deal with hidden violations very often. Such violations are common in judicial practice, investigators, lawyers and judges constantly have to deal with their exposure. But, unfortunately, they are also found in official documents, including legislative acts. Then the laws become unenforceable, and a wide path opens for lawlessness and arbitrariness. Therefore, without eliminating contradictions in legislation, a true rule of law state is impossible.

3. Law of the excluded middle

1. The law of the excluded middle is that of 2 opposing judgments, one must certainly be true and the other must be false. In other words: every statement is either true or false.

For example, of 2 judgments - “seminarist Vikentiev is present at the philosophy lesson” and “seminarist Vikentiev is not present at the philosophy lesson” - one must be true, while the other must be false.

Old logicians, formulating this law, often added to the words “either true or false”: “there is no third option” - in Latin tertium non datur. This is where the name “law of the excluded middle” comes from (sometimes it is also called the law of tertium non datur).

2. In the formulation of the law of excluded middle, it is impossible to replace the word “opposite” with the word “contradictory” (although such a formulation, unfortunately, can sometimes be found in the literature). For example, the statements “A.S. Pushkin was born in Kyiv” and “A.S. Pushkin was born in Kazan” contradict each other, but both of them are false.

3. A consequence of the law of excluded middle is the fact that if we have proven the falsity of a statement, then the truth of the opposite judgment automatically follows from this. This property of the law of excluded middle is used in mathematics to obtain “proof by contradiction”.

4. In essence, we cannot even imagine anything “third”, different from truth and from lies and standing on the same level with them. Therefore, it is difficult to imagine a violation of this law. But in modern constructive mathematics the law of excluded middle is not fulfilled.

5. Task. In the fairy tale, the king ordered the “wise maiden” to come to him “neither with a gift nor without a gift,” hoping that she could not bypass the law of the excluded middle. The girl nevertheless coped with the task: she appeared with a live quail in her hands, gave it to the king, and “the quail fluttered and flew away!” How did the girl get out of the situation (Answer: she violated the law of identity.)

4. The Law of Sufficient Reason

It was formulated quite late - by Leibniz (1646–1716). This law states: one cannot be sure of the truth of a judgment if there is no sufficient reason for this.

Sufficient reason should not be confused with reason. For example, for the statement that the air temperature dropped by 10 degrees overnight, the thermometer readings can be a sufficient basis, although they, of course, cannot be the cause of the cold snap.

Concluding the consideration of the basic logical laws, you should pay attention to the fact that the 2nd and 3rd laws are formulated much more clearly than the 1st and 4th. The reason is not difficult to understand: in the laws of contradiction and the excluded middle, only the concept of truth appears, which is intuitively quite clear, and in the other two laws we are dealing with the incomparably less clear concepts of “one and the same object” and “sufficient reason”.

Logic as a science originated in Ancient Greece and for many centuries was considered a criterion of education. IN early XIX V. G.V.F. Hegel pointed out its limitations and insufficiency, from the point of view of reflecting the process of the movement of thought. He noted that such logic does not reflect the movement of the content of thought, but the form of the thought process. To compensate for this shortcoming, Hegel created a new dialectical logic, and called the one that existed before it formal. The subject of the study of dialectical logic is the laws of the development of human thinking and the methodological principles based on them (objectivity, comprehensive consideration of the subject, the principle of historicism, the bifurcation of the whole into opposite sides, the ascent from the abstract to the concrete, etc.).

Dialectical logic is one of the ways to understand the dialectics of reality.

Formal logic using mathematical methods studying reality, at the beginning of the 20th century. received the name “logistics”, meaning the art of calculation. Now this term has almost fallen out of use, giving way to the terms “mathematical logic” or “symbolic logic”. Formal logic studies form as something separate, separate from content. The subject of the study of formal logic is the form of thinking. Let's consider the external and internal forms of thinking as any phenomenon.

The external form of a phenomenon is the way a given phenomenon manifests itself outside, its surface (for example, for thinking, speech becomes such a form).

The internal form of a phenomenon is the structural construction of the elements that make up the phenomenon. The internal form of thinking can be called the process of combination and interaction of formations, which are called thoughts.

Thought structure is the different ways in which thoughts are grouped during the thinking process.

In contrast to thinking itself and, moreover, its structure, we see their external speech form. It is impossible to make thinking a stable subject of research unless it takes the form of speech (oral or written). Obviously, speech is empirical material that serves as a source for formal logic. But speech and language as the external structure of thinking are of interest to logic as a means for its expression.

Formal logic is the science of common structures correct thinking in its linguistic form, revealing the underlying patterns.

Logical forms are called various connections of thoughts, considered as structural formations of thinking. Logical forms consist of thoughts, including, for example, other logical forms and various ways of connecting them, or so-called connectives. Three types of logical forms, such as concept, judgment, inference, consist of thoughts and means of their connection, connectives. General logic is the study of three logical forms: concept, judgment, and inference.

The history of logic can be divided into two main stages: the first lasted more than two thousand years, during which logic developed very slowly; the second began in the second half of the 19th century, when a scientific revolution took place in logic, radically changing its face. This was due, first of all, to the penetration of mathematical methods into it. Aristotelian or traditional logic has been replaced by modern logic, also called mathematical or symbolic. This new logic is not, of course, a logical study of purely mathematical proofs. It represents a modern theory of correct reasoning, “logic by subject and mathematics by method,” as the famous Russian logician P.S. characterized it. Poretsky. The 1st stage is associated with the works of the scientist and philosopher Aristotle (384-322 BC). He tried to find the answer to the question “how we reason,” and studied “rules of thinking.” Aristotle was the first to give a systematic presentation of logic. He analyzed human thinking, its forms - concept, judgment, inference, and examined thinking from the side of structure, structure, that is, from the formal side. This is how formal logic arose. Aristotle explored various shapes reasoning and their combinations, introduced the concept of syllogism, i.e. reasoning in which a third is derived from given two judgments.

For example:

• 1. “All mammals have a skeleton. All whales are mammals. Therefore, all whales have a skeleton.”
• 2. “All squares are rhombuses, all rhombuses are parallelograms. Therefore, all squares are parallelograms.”

IN general view this syllogism has the form:

All A's are B's, all B's are C's. Therefore, all A's are C's.

Here is an example of an irregular syllogism:

“All squares are diamonds. Some diamonds have an acute angle. Therefore, some squares have an acute angle.”

This means that a syllogism has the form “all a are in, some are c.” This means that some a are c” can lead to false conclusions.

Aristotle identified all the correct forms of syllogisms that can be made from reasoning like:

• - "All. And the point. IN"
• - “Some, but the essence. IN"
• - "All. Not the point. IN"
• - "Some. Not the point. IN"

Logic based on the theory of syllogisms is called classical. It has been proven that total number The number of syllogisms that can be composed from reasoning of this type is 256. Of these, only 24 are correct. To check the correctness of syllogisms, you can use the method of geometric illustration of logical reasoning, which was proposed by the great mathematician of the 18th century. Petersburg academician L. Euler (1707 - 1783) and was widely used by the English mathematician J. Venn (1834 - 1923).

At the end of the 16th century. in algebra, the verbal form of writing algebraic expressions began to slow down the development of science and, in order to facilitate the implementation of algebraic transformations, letter symbols were created that made it possible to carry out these transformations according to strictly defined rules. Likewise, to facilitate the verification and transformation of complex chains of reasoning, a special letter calculus was created. It is called algebra of logic or mathematical logic.

Stage 2 - the emergence of mathematical or symbolic logic. Its foundations were laid by the German scientist and philosopher Gottfried Wilhelm Leibniz (1646-1716). He tried to build the first logical calculus, believed that it was possible to replace simple reasoning with actions with signs, and gave rules. But Leibniz only expressed the idea, and it was finally developed by the Englishman George Boole (1815-1864). Boole is considered the founder of mathematical logic as an independent discipline. In his works, logic acquired its own alphabet, its own spelling and grammar. No wonder initial section mathematical logic is called the algebra of logic, or Boolean algebra. A great contribution to the development of mathematical logic was made by the Russian mathematician P.S. Poretsky (1846-1907).

P.S. Ehrenfest (1880-1933) proved that the operations of the algebra of logic can be illustrated by physical and technical phenomena, and, therefore, applied. The development of mathematical logic was especially intensified in the middle of our century in connection with its use in computer technology and programming. The scope of specific interests of logic has changed significantly throughout its history, but the main goal has always remained the same: the study of how others can be deduced from some statements. It is assumed that the conclusion depends only on the way the statements included in it are connected and their structure, and not on their specific content. By studying “what follows from what,” logic reveals the most general or, as they say, formal conditions of correct thinking. Here are some examples of logical, or formal, requirements for thinking:

• - no matter what we are talking about, you cannot affirm and deny something at the same time;
• - you cannot accept some statements without accepting at the same time everything that follows from them;
• - the impossible is not possible, the proven is doubtful, the obligatory is prohibited, etc.

These and similar requirements do not depend, of course, on the specific content of our thoughts, on what exactly is affirmed or denied, what is considered possible and what is impossible. Another basis for the division of logic is the difference in the principles applied in it, on which research is based. As a result of this division we have classical logic and non-classical logics.

V.S. Meskov highlights the principles of classical logic:

• 1) the field of study consists of ordinary reasoning;
• 2) the assumption that any problem is solvable;
• 3) abstraction from the content of statements and from the connections in meaning between them;
• 4) abstraction of the double meaning of statements.

In addition to formal logic, there is dialectical logic, the subject of special study of which is the forms and patterns of development of knowledge. The means of dialectical logic are used in cases where one cannot be distracted from the development of knowledge. Dialectical logic explores such forms of development of knowledge as problem, hypothesis, and so on, such methods of cognition as ascent from the abstract to the concrete, analysis and synthesis. In the process of cognition, the methods of formal logic are complemented by the methods of dialectical logic and vice versa. Plato and Aristotle made a certain contribution to the development of dialectical logic; certain ideas were expressed by medieval and modern philosophers. Classical forms were given to it by Kant, Fichte, Schelling, and Hegel. Hegel's dialectical logic is a systematic teaching, although it was developed from the standpoint of objective idealism. Dialectical logic on a materialistic basis was developed by K. Marx, F. Engels, V. I. Lenin.

Dialectical logic studies the laws of the development of human thinking. These include objectivity and comprehensiveness of consideration of the subject, the principle of historicism, the bifurcation of the whole into opposite sides, and so on. Dialectical logic serves as a method of understanding the dialectics of the objective world.

Formal logic and dialectical logic study the same object - human thinking, but each of them has its own subject of study. Dialectical logic does not and cannot replace formal logic. These are two sciences of thinking; they develop in close interaction, which is clearly manifested in the practice of scientific and theoretical thinking, which uses in the process of cognition both the formal logical apparatus and the means developed by dialectical logic. Logic deals not only with the connections of statements in correct conclusions, but also with many other problems: the meaning and meaning of language expressions, various relationships between terms, operations of definition and logical division of concepts, probabilistic and statistical reasoning, paradoxes and logical errors, and so on. But the main topics of logical research are the analysis of the correctness of reasoning, the formulation of laws and principles, the observance of which is a necessary condition for obtaining true conclusions in the process of inference. In correct reasoning, the conclusion follows from the premises with logical necessity; the general scheme of such reasoning expresses a logical law. To reason logically correctly means to reason in accordance with the laws of logic. The concept of logical form and logical law.

Formal logic is the science of the laws and forms of correct thinking. V. S. Meskov writes: “...The subject of the science of logic is reasoning, and it itself is the science of reasoning. The task of logic as a science is to establish the laws and rules to which reasoning is subject." Reasoning is put into a logical form and constructed in accordance with logical laws. "...Logical forms and laws are not an empty shell, but a reflection of the objective world" (2). Let us find out in more detail what is meant by logical form and logical law.

The logical form of a specific thought is the structure of this thought, i.e. way of connecting its components. The logical form reflects the objective world, but this is not a reflection of the entire content of the world that exists outside of us, but of its general structural connections, which are necessarily embodied in the structure of our thoughts. Concepts, judgments, conclusions have their own specific forms (structures). The structure of thought, i.e. its logical form can be expressed using symbols. Let us identify the structure (logical form) of the following three propositions: “All crucian carp are fish,” “All people are mortal,” “All butterflies are insects.” Their content is different, but the form is the same: “All S are P.”; it includes S (subject), i.e., the concept of the subject of the judgment, P (predicate), i.e., the concept of the attribute of the object, a connective (“is”, “essence”), a quantifier word (“all”). Sometimes the link may be missing or replaced at the dash. The following two conditional propositions have the same form:

• 1) “If iron is heated, it expands”;
• 2) “If a student studies logic, he improves the clarity of his thinking.” The form of these judgments is: “If S is P, then S is P1.”

Logical laws. Compliance with the laws of logic - necessary condition achieving truth through the process of reasoning. The main formal logical laws are usually considered:

• 1) the law of identity;
• 2) the law of no contradiction,
• 3) the law of the excluded middle;
• 4) the law of sufficient reason.

These laws (principles) express certainty, consistency, and evidence-based thinking.

Logical principles operate independently of the will of people; they are not created by their will and desire, but are a reflection of the connections and relationships of things in the material world. The universal human nature of the principles of formal logic lies in the fact that in all historical eras all people thought according to the same logical principles. In addition to formal logical principles, correct thinking is also subject to the basic laws of dialectics: the law of unity and struggle of opposites, the law of mutual transition of quantitative and qualitative changes, the law of negation. The truth of thought and the formal correctness of reasoning. The concept of truth (falsehood) refers only to the specific content of a particular judgment. If a judgment truly reflects what takes place in reality, then it is true, otherwise it is false. For example, the proposition: “All wolves are predatory animals” is true, but the proposition “All mushrooms are poisonous” is false. The concept of formal correctness of reasoning refers only to logical actions and operations of thinking. If among the premises of a conclusion there is a false premise, then, subject to the rules of logic, in conclusion we can obtain both truth and falsehood. To show this, let's take two conclusions:

1. All metals are solids;

Mercury is not a solid;

Mercury is not a metal.

2. Everything celestial bodies- planets;

Jupiter is a celestial body;

Jupiter is a planet.

In the first conclusion, the conclusion turned out to be false precisely because a false judgment was taken as the first premise. In the second conclusion, despite the first false premise, the conclusion is a true judgment. For a conclusion to be true, both premises must be true propositions and the rules of logic must be followed. If the rules of logic are not followed (if the premises are true), we can also get both a true and a false conclusion. To show this, let’s take the following conclusions:

3. All tigers are striped;

This animal is striped.

This animal is a tiger.

4. All eared seals are pinnipeds;

All eared seals are aquatic mammals.

All aquatic mammals are pinnipeds.

In the third inference, both premises are true judgments, but the resulting conclusion can be either false or true because one of the rules of inference was violated. In the fourth inference, both premises are true judgments, but the conclusion is false, because the rule for constructing inferences is violated (according to the rule, instead of the word “all” there should be the word “some”). So, from the point of view of content, thinking can give a true or false reflection of the world, and from the point of view of form, it can be logically correct or incorrect. Truth is the correspondence of thought to reality, and correctness of thinking is compliance with the laws and rules of logic. The following concepts cannot be identified (mixed): “truth” (“truth”) and “correctness,” as well as the concepts “falsity” (“falsehood”) and “incorrectness.” Modern logic is an intensively developing science, which includes formal logic and dialectical logic. On their basis, the logic of scientific knowledge is formed, using the methods of both sciences to analyze scientific knowledge. Theoretical and practical significance logic. You can reason logically, draw your own conclusions correctly, refute your opponent’s arguments without knowing the rules of logic, just as people often speak correctly without knowing the rules of language grammar. But knowledge of logic improves the culture of thinking, promotes clarity, consistency and evidence of reasoning, enhances the effectiveness and persuasiveness of speech. Knowledge of the basics of logic is especially important in the process of mastering new knowledge, in training, in preparation for a lesson, when writing an essay, speech, report; knowledge of logic helps to notice logical errors in the oral speech and written works of other people, to find shorter and more correct ways to refute these erroneous thoughts, and to avoid making mistakes in one’s thinking. In the conditions of the scientific and technological revolution and the increasing flow of scientific information, the task of rationally constructing the learning process in high school, university, college, etc.

To define the logical form of thought and indicate ways to identify the logical forms of various thoughts, we will highlight among the expressions of natural language the terms called logical. These include conjunctions “and”, “or”, “if..., then...”, negation “it is not true that” (“not”), words characterizing the number of objects about which something is affirmed or denied: “ all” (“none”), “some”, the connective “essence” (“is”), etc. The process of identifying the logical form of a thought consists in abstracting from the meaning of non-logical terms included in the phrase expressing this thought. This can be done in various ways. For example, omit non-logical terms in a phrase and replace them with dots, dashes and other lines. As a result of replacing non-logical terms with an ellipsis and a dashed line from the sentence “All lawyers are lawyers,” we get the expression “Everything ... is - - -”.

Another way of abstracting from the meaning of non-logical terms is to replace these terms with special symbols (variables). In this case, instead of different occurrences of the same non-logical term, the same variable is put, and instead of different terms - different variables. Moreover, instead of the terms various types symbols of various types are placed.

Let us identify the logical forms of the following reasoning:

(1) All first-year students of the Moscow State University College of Law. M.V. Lomonosov study logic.

Some first-year students at the Moscow State University College of Law. M.V. Lomonosov will specialize in civil law.

Consequently, some students who will major in civil law study logic.

(2) The investigator is a lawyer. Therefore, an educated investigator is an educated lawyer.

Replacing non-logical terms with symbols, we get:

(1) All M are P. Some M are S. Therefore, some S are P.

(2) S is P. Therefore, sq is pq.

These expressions represent the logical forms of the original thoughts.

Thus, logical form of thought - this is its structure, revealed as a result of abstraction from the meanings and meanings of non-logical terms.

The logical form is meaningful and informative. Thus, the expression obtained as a result of abstraction from the meanings and meanings of non-logical terms of the first argument carries the following information: “If all objects of class M are included in class P and some objects of class M are included in class S, then some objects of class S are included in class P "

Thoughts can be divided into classes depending on the types of their logical forms. The main of these classes will consist of thoughts called concepts, judgments and inferences.

Concept - This is a thought in which objects are generalized and highlighted on the basis of a system of attributes common only to these highlighted objects. An example of a concept: an action or inaction qualified by law as a criminal offense (the concept of a crime).

Judgments are thoughts that assert the presence or absence of any state of affairs. Examples: “Man received from God two blessed abilities - to speak the truth and to do good”; “ The best way to study something is to discover it for yourself.”

Conclusion - This is the process of obtaining knowledge, expressed in a judgment, from other knowledge, also expressed in judgments. Examples of inferences include the above reasoning (1), (2).

There are connections between thoughts that depend only on their logical forms. Such connections take place between concepts, and between judgments, and between inferences. Thus, between the thoughts of the logical forms “some S are P” and “some P are S” there is the following connection: if one of these thoughts is true, then the second is true, regardless of what the non-logical content of these thoughts is.

Connections between thoughts according to forms, in which the truth of some of these thoughts determines the truth of others, are called formal logical laws, or logical laws.

The connection between thoughts in reasoning (1) is a logical law. In order to establish whether the connection between some initial statements and the statement obtained as a result of reasoning is a logical law, it is necessary to substitute arbitrary terms of the same types into these statements instead of non-logical terms and, at the same time, each time find out whether the resulting statement turns out to be true if the original ones are true. If such a dependence of the truth of statements is always revealed, then the connection between them is a logical law. If a counterexample is found, then there is no natural connection, and the reasoning is not correct. So, the above reasoning “The investigator is a lawyer. Therefore, an educated investigator is an educated lawyer” is incorrect. A counterexample to this is the clearly incorrect reasoning:

A fly is an animal. Therefore, a large fly is a large animal.

In modern logic, simpler and more productive methods have been developed for identifying the natural connections between thoughts. These methods are outlined in the chapter "Inference".

Having the concepts of logical form and logical law, we can define formal logic.

Formal logic - This is the science of forms of thinking, of formal logical laws and other connections and relationships between thoughts according to their logical forms.

By exploring the necessary connections between thoughts according to logical forms - logical laws, logic formulates statements about the truth of all statements of a certain logical form. These statements are also called laws, but in contrast to logical laws (connections that exist regardless of whether we know about them or not) - laws(Sciences) logic. For example, having established that whenever thoughts of the form “All M are P” and “All M are S” are true, the thought of the form “Some S are P” is true, we can formulate a law of logic: “For any S, P and M it is true, that if all M are P and all M are S, then some S are P.” The laws of logic, once formulated, act as norms in accordance with which reasoning must be carried out. In logic, requirements of another kind are also developed, which are recommended to be fulfilled in the process of cognition. Formal logic, therefore, is a normative science about the forms, laws and techniques of intellectual cognitive activity.

Thinking carried out in accordance with the requirements of logic is called correct. Formal logic, being the science of correct thinking, also explores and systematizes typical errors made in the process of thinking, i.e. typical illogicalisms.

Long time attempts are being made to develop dialectical logic. The means of this logic should be used in cases where one cannot be distracted from the development of knowledge. Within the framework of dialectical logic, a number of methodological principles (concreteness, objectivity of consideration, etc.) and methods of cognition (ascent from the abstract to the concrete, etc.) have been developed.

It is assumed that in the process of cognition the methods of formal logic should be complemented by the methods of dialectical logic and vice versa.

Exercise

Using the method described above, establish whether there are formal logical laws of connection in form between the initial judgments and the resulting ones in the following reasoning (i.e., whether these reasoning is correct):

1. All criminals are subject to criminal punishment. Some Moscow residents are subject to criminal penalties. Consequently, some Moscow residents are criminals.

2. All students in our group are lawyers. All students in our group are members of the logic circle. Consequently, all members of the circle of logic are lawyers.

3. Some participants in this crime were identified by the victim. None of the Petrov family members have been identified by the victim. None of the persons who participated in the commission of this crime have been brought to criminal responsibility for its commission. Consequently, not a single member of the Petrov family has been brought to criminal responsibility for committing this crime.

4. “If Socrates died, then he died either when he lived or when he died. If he lived at some point, then he did not die, since the same person would have lived and been dead; but not when he died, for he would have been twice dead. Therefore, Socrates did not die.” (Empiricist Sextus. Op. In 2 vols. M., 1976. T. 2. P. 289).

5. All metals are heat-conducting substances. All metals are electrically conductive substances. Therefore, all electrically conductive substances are thermally conductive.

FROM THE HISTORY OF LOGIC

Formal logic is one of the most ancient sciences. It began to be developed in Ancient Greece in the 6th-5th centuries. BC. A little later, fragments of logical science arose independently in ancient India, where the first logicians were Dattariya Punarvasa Atreya, the female ascetic Sulabhu and Ashtvakra. Greek logic later spread to Western and Eastern Europe and the Middle East, and Indian logic - to China, Japan, Tibet, Mongolia, Ceylon and Indonesia.

Initially, logic was developed in connection with the needs of judicial practice and oratory. The connection of logic with these areas of human activity can be traced in Ancient India, Ancient Greece and Rome. So, in public life In ancient India, during the period when interest in logic emerged, discussions were a constant occurrence. The famous Russian orientalist Academician V. Vasiliev writes about this: “If someone appears and begins to preach completely unknown ideas, they will not be shunned and persecuted without any trial: on the contrary, they will willingly recognize them if the preacher of these ideas satisfies all objections and will refute old theories. An arena for competition was erected, judges were chosen, and kings, nobles and people were constantly present during the dispute; determined in advance, regardless of the royal reward, what the result of the dispute should be. If only two persons argued, then sometimes the defeated one had to take his own life - throw himself into a river or from a cliff, or become a slave of the winner; convert to his faith. If this was a person who was respected, for example, who had achieved a rank like the sovereign's teacher and, therefore, possessed a huge fortune, then his property was often given to a poor man in rags, who managed to challenge it. It is clear that these benefits were a great lure to direct the ambition of the Indians in this direction. But most often we see (especially later) that the dispute was not limited to individuals, entire monasteries took part in it, which, due to failure, could suddenly disappear after a long existence. As can be seen, the right of eloquence and logical proof was so undeniable in India that no one dared to evade a challenge to an argument.”

Judicial and political discussions were also common in Ancient Greece. Often, a judicial decision depended on the logical evidence of the speech of the accused or prosecutor. People who prepared speeches for participants in trials were highly respected. Outstanding speakers on political issues were elected to honorary government positions and sent as ambassadors to other countries.

Sometimes, when determining the winner of the discussion, the opinions of those present (or the judges) were divided. Some considered one of the speakers the winner, others - the other. This put on the agenda the task of developing logical norms of reasoning that would make it possible to avoid such disagreements and come to a common opinion.

Another incentive for the creation of the science of logic was the demands of mathematics, where rigorous proofs were required.

In Ancient Greece, logic was developed by Parmenides (VI-V centuries BC), Zeno of Elea (c. 500/490 - c. 430 BC), Democritus (c. 460 - c. 370 BC), Socrates (470/469 - 399 BC), Plato (428/27 - ca. 348 BC). However, the founder of the science of logic is rightfully considered the greatest thinker of antiquity, a student of Plato - Aristotle(384-322 BC). Aristotle was the first to thoroughly systematize logical forms and rules of thinking. He wrote a number of works on logic “Categories”, “On Interpretation”, “First Analytics”, “Second Analytics”, “Topics”, “On Sophistic Refutations”), which were later united under the general title “Organon” (instrument of knowledge) .

Because logic was developed by ancient authors as a guide for discussion, it was often called dialetics (from the Greek word “dialego” - “I argue”). Discussions were often held with the aim of gaining polemic skills. In these cases, specially invented situations were discussed. For example, a merchant enters into an agreement with fishermen, according to which he pays in advance for their future catch, but what the fishermen catch in the net is not a fish, but a barrel of gold. The question of who owns the gold is the merchant or the fishermen is being discussed.

After Aristotle in Ancient Greece, logic was developed by the Stoics (IV-II centuries BC). Significant contributions to Latin logical terminology were made by the ancient Roman judicial and political orator M. T. Cicero (106-44 BC) and the ancient Roman theorist of oratory and orator M. F. Quintilian (c. 35 - c. 96). . AD).

Logic was developed by Arabic-speaking scientists Al-Farabi (c. 870-950) and others, as well as European logicians of the Middle Ages. Medieval logic is called scholastic. Its heyday dates back to the 14th century. and are associated with the names of William of Occam (c. 1294-1349/50), Walter Burley (1273/75-1337/57), Albert of Saxony (c. 1316-1390).

Logic developed during the Renaissance and Modern times. In 1620, the “New Organon”, written by the famous philosopher Francis Bacon (1561-1626), was published in London, which contained the foundations of inductive methods, later improved by John Stuart Mill (1806-1873) and called methods for establishing causal relationships between phenomena ( Bacon-Mill methods).

In 1662, the famous textbook “Logic of Port-Royal” was published in Paris. In 1991 it was translated into Russian. Its authors P. Nicole and A. Arno created a logical doctrine based on methodological principles famous philosopher R. Descartes (1596-1650).

Logic, based on the teachings of Aristotle, largely supplemented and developed, existed until the beginning of the 20th century. At the beginning of the 20th century. A kind of scientific revolution took place in logic, associated with the widespread use of the methods of so-called symbolic, or mathematical, logic. The ideas of the latter were expressed by a German scientist G.W. Leibniz(1646-1716): “The only way to improve our conclusions is to make them, like mathematicians, visual, so that we can find our mistakes with our eyes, and if a dispute arises among people, we must say: “Let’s count!”, then without any special formalities, it will be possible to see who is right.”

Leibniz's idea about the possibility and productivity of reducing reasoning to calculations did not find development and application for many years. Symbolic logic began to be created only in the middle of the 19th century. Its development is associated with the activities J. Boulya, A.M. De-Morgan, C. Pierce, G. Frege and other famous scientists. Russian scientists made a significant contribution to the creation of symbolic logic P. S. Poretsky, E. L. Bunitsky and etc.

Thus, by the beginning of the current century, symbolic logic took shape as a relatively independent discipline within the framework of logical science. The first major work on symbolic logic was the work B.Russell And A.Whitehead“Principia mathematica” (3 volumes), published in 1910-1913. The application of the methods of symbolic logic to the solution of problems posed by traditional logic, as well as problems that could not even be posed by it, caused at the beginning of the 20th century. revolution in logic. It is the use of symbolic logic methods that distinguishes modern logic from traditional. At the same time, in modern logic all the achievements and all the problems of traditional logic are preserved.

Dialectical logic also has ancient origins. The ideas of dialectics of thinking go back to the ancient Eastern and ancient philosophy. The main categories of dialectical logic were already used in the early Greek classics (VI-V centuries BC), however, they were not united into a system, and dialectical logic was far from being isolated as an independent science. Plato and Aristotle made a certain contribution to the development of dialectical logic; certain ideas of this logic were expressed by medieval philosophers. Classical forms of dialectical logic were given by German philosophers of the New Age: Kant, Fichte, Schelling and, especially, Hegel. Hegel's dialectical logic is a systematic teaching created from the position of objective idealism.

Dialectical logic on a materialistic basis was developed by K. Marx, F. Engels and V.I. Lenin. It received further development in the works of modern philosophers.

Control questions

1. What are the main features of abstract thinking? 2. What is the form of thought and how does it appear? 3. The concept and methods of identifying a natural connection between thoughts. 4. What does formal logic study? 5. What is the difference between traditional and modern logic?

CHAPTER II

LOGIC AND LANGUAGE OF LAW

SPECIFICITY OF THE LANGUAGE OF LAW

The special area of ​​relations regulated by law (legal relations) determines the specificity of the language of law. This specificity lies in the use of terms that must be understood uniformly different people V various cases and situations. Such terms are called legal terms. For example, in everyday life we can use the expressions “Today it rained”, “Tonight there was a lot of noise on the street”, “Petrov is a native Muscovite”, “Ivanov is a participant in the Great Patriotic War”. The words and phrases included in these expressions “night” (“night time”), “native Muscovite”, “participant of the Second World War” are understood differently by different people. Thus, the time 22 hours 50 minutes will be attributed by some to night time, and by others to evening time, some consider a native Muscovite to be a person born in Moscow, others - a person whose parents were also born in Moscow, others - someone who has been living for many years lives in Moscow, some consider participants of the Second World War only those who directly participated in the hostilities, while others also consider those who were at the front, but did not directly participate in the hostilities (for example, surgeons who worked in field hospitals). Such vagueness of expressions in everyday language turns out to be unacceptable when resolving legal issues.

Let's say that there is a law prohibiting night flights of aircraft over large populated areas. The plane flies over the city at 22:50. Is the law broken or not? Another situation. Several years ago, a resolution was adopted to place native Muscovites living in communal apartments on a waiting list to receive separate apartments. Who is eligible to be placed on the waiting list? Third case. The Duma is deciding the issue of benefits for WWII participants. A special budget item is allocated for this purpose. How to calculate expenses for these purposes without specifying who should be considered a participant in the Second World War?

To avoid uncertainties, instead of the ordinary language expressions highlighted above, legal terms are introduced through the following definitions: “Night time is the time from 10 pm to 6 am”, “A native Muscovite is a person who has lived in Moscow for 40 years”, “ A BOB member is someone who served in the active military.”

This method of administration legal terms(by highlighting one of the senses in which the expression is used in natural language) is not the only one. Another way is to give the expression some additional meaning, compared to the generally accepted one. Example: “A crime is committed for the first time if it was actually committed for the first time, or the statute of limitations for prosecution for a previous crime has expired, or the criminal record has been withdrawn or expunged.”

There are other ways to introduce legal terms: introducing expressions that do not exist in ordinary language as legal terms; clarification of expressions through examples, descriptions, characteristics, etc. The methods and rules for introducing legal terms are described in Chapter VII.

In addition to legal terms, the language of law also uses expressions that are not specified in it. These are expressions that have been given precise meaning in other sciences, as well as those that are not ambiguous in ordinary language. Thus, defining a native Muscovite as a person who has lived in Moscow for 40 years, we clearly understand the expressions “live in Moscow”, “40 years”, “person”. These expressions do not need clarification.

Formal logic is a broad area of ​​logical research that studies idealized reasoning and their systems through logical calculus based on method formalization(cm. ). The formalization method implies that logical reasoning is studied in abstraction from their specific content; at the same time, the logical reasoning itself is formulated in some precise (formalized) language using a special apparatus of symbols (see). Such precise languages ​​have two components: syntax(mass media semantics(cm. ). Syntax is a set of rules for constructing language objects (usually called formulas). Semantics is a set of conventions that describe our understanding of formulas (or some of them) and allow us to consider some formulas true and others not. Formalized language allows you to avoid the ambiguous and logical ambiguity of the natural language used to describe reasoning traditional logic(see), developed within the framework of philosophy (see). Formalization methods gave logic such advantages as high precision of formulations and the ability to study objects that were more complex, from the point of view of logical form. The definition of “formal logic” was introduced by I. Kant with the intention of emphasizing its leading feature in the approach to the objects under study and thereby distinguishing it from other possible logics.

The ability of human thinking for constructive linguistic activity gives rise to the ability to operate with the following logical forms: concepts, judgments, conclusions, which represent the space of logical research. As the most complex type logical forms are sometimes distinguished and theories(cm. ). Often this sequence is perceived as a kind of structural hierarchy. The concept is declared to be the simplest form of thinking, judgment is presented as a system of concepts, inference as a system of judgments, and theory as a system of inferences. This hierarchy is not clear enough, and its justification is sometimes easily criticized, but it is often used as a convenient scheme for presenting the subject area of ​​formal logic, which, in fact, is supported by the centuries-old tradition of teaching this discipline. These logical forms and the laws and principles underlying operations with them, that is, the so-called logical apparatus, constitute the main area of ​​research in formal logic, and the development of effective logical apparatuses themselves is its main goal.

Due to the difference in logical forms, two main directions of formal logic are distinguished:

1. Conceptual analysis, that is, the study of procedures for defining linguistic terms (concepts) and formulating the principles of relations between them. This direction includes a wide range of theories, from the classification of genus-species relationships to the construction of conceptual “fields”.
2. The theory of inference, that is, the analysis of reasoning, the formalization of laws and principles of connection between statements (judgments) in conclusions. Here, methods are formulated for correctly obtaining a judgment, called a conclusion, from some initial judgments, called premises, through reasoning. Within the framework of the theory of inference, logic is distinguished, which considers deductive reasoning (see), that is, certain methods of evidence, and logic, which deals with plausible reasoning: induction, analogy and others.

In addition, formal logic also touches on such issues as the formalization of meaningful theories, the problem of meaning and meaning, logical errors and paradoxes, and many others. The independent identification of these issues is quite arbitrary; they are all immersed in the problems of the main directions and are closely intertwined with each other.

Logic originated in Ancient Greece within the framework of philosophy (see). The history of its development goes back about two and a half millennia and is divided into two main periods:

1. Traditional formal logic (IV century BC) new era- mid-19th century). In the development of traditional logic, in turn, three periods are distinguished:
   1. Ancient logic (5th century BC - mid-5th century).
   2. Scholastic (Medieval) logic (mid-V century - XV century).
   3. Logic of the New Age (XV–XVIII centuries).
2. Modern (symbolic or mathematical) logic (since the middle of the 19th century).

Ancient and scholastic logic are now united by the common name “traditional logic”. It, in addition to the historical and philosophical, still has an important propaedeutic significance and, being a kind of core of human intellectual culture, is recognized integral element broad humanitarian education.

A new stage in the development of logic (from the second half of the 19th century) was associated with its formalization and subsequent mathematization. In this regard, the new logic was called mathematical(or symbolic) logic (see, ). Modern logical systems, for the most part, rely entirely on formal mathematical methods and are logically interpreted calculus. Main branches of mathematical logic - classical propositional logic(mass media predicate logic(cm. ). Research has become widespread modal logic(cm. ). Systems of logic that deny certain fundamental laws of logic have formed a spectrum non-classical logics(cm. ). Significant number various systems formal logic is due to the wide scope of their application. Theoretical mathematics, perhaps, has lost its absolutely leading place in this sense, since no less interesting applications are carried out in the fields of theoretical physics (quantum logic), applied mathematics (computational mathematics and theory of algorithms), computer science (computer technology, networks, programming and research in the field of artificial intelligence), humanitarian knowledge (linguistics, law, ethics) and others.

An important section of modern formal logic is metalogic(see), which examines various problems related to logical theories. The main questions here are about the properties that logical theories have: consistency, completeness, the presence of resolving procedures, the independence of the original deductive principles, as well as various relations between theories, and so on. In this sense, metalogic is a kind of self-reflection of logic regarding its constructions. All metatheoretical research is carried out in a special metalanguage, which uses natural language, enriched with special terminology and metatheoretical deductive means.